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PL/NL Texas Hold'em >> Small Stakes

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goofyballer
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Suited Connectors, Implied Odds, and You (Theory/Math)
#6996709 - 08/21/06 12:13 AM

A recent thread about using the 5/10 rule to call preflop raises with PPs and suited connectors got me thinking about the kind of implied odds required to call preflop raises with SCs; people tend to arbitrarily use things like the 5/10 rule, even though I've never seen any mathematical description of the kind of odds you need to call these raises. I'm going to attempt to solve that problem (but I still need some help!).

I'll list the conclusions first, and leave the tl;dr math for the bottom for those of you that want to peruse it. I also encourage math-head-types to check my math to make sure I didn't mess anything up.

There are two kinds of hands you can flop with SCs: Good made hands (most of which can be made by calling with ATC, which of course we don't do) and draws. First, made hands, stolen off some page I googled:

Odds of flopping...
Flush: 0.84%
Two pair: 2%
Trips: 1.35%
Full house: 0.09%
Straight: 1.31%
-------
Total: 5.6% (1 in 18 times, 17:1)

However, most of the time you will be flopping draws instead of big hands with SCs, and that's where things get complicated. Let's separate this into two categories: combo draws and regular draws.

COMBO DRAWS

Odds of flopping...
20 outer (OESD + FD + pair): 0.077%
17 outer (Gutshot + FD + pair): 0.153%
15 outer (OESD + flush draw): 1.424%
14 outer (Pair + flush draw): 1.450%
13 outer (Pair + straight draw): 1.147%
12 outer (Gutshot + flush draw): 2.664%
------------------------
Total: 6.9% (1 in 14 times, 13:1)

These draws are all hands that can be played profitably after the flop; either you are a favorite against an overpair, or getting AI on the flop is +EV when you take some fold equity (and thus taking down dead money) into account.

Combining these big draws with good made hands, you'll have a relatively "big hand" on the flop 12.5% of the time, or 1 in 8 (very close to how often you will flop a set with an overpair). However, since a set is a near-invincible hand and you still have to improve with these draws, you can't say that you also need about 7:1 odds to call with a suited connector. Your average equity on the flop with these made hands and combo draws against an overpair is 66% (the made hands go from 75%-99%; the combo draws range from 45%-65%); compare this with sets, where your equity is generally 90+%.

REGULAR DRAWS

Odds of flopping...
9 outer (flush draw): 5.2%
8 outer (straight draw): 8.0%
-----------------
Total: 13.2% (1 in 7.5 times, 6.5:1)

These are your standard draws; when you flop a hand with which you can continue, it will most frequently be one of these. These draws improve to a flush or straight on the river about 1 time in 3.

Summary

- you have a 5.6% (1 in 18, 17:1 chance) of flopping a good made hand
- you have a ~7% (1 in 14, 13:1) chance of flopping a strong (12+ outs) combo draw
- you have a ~13% chance (1 in 7.5, 6.5:1) chance of flopping a standard OESD or FD

Adding these all together, you will flop a hand you can continue with on the flop 25% of the time (1 in 4). However, only half of the time will these hands be immediately profitable (i.e. +EV to shove it in); the other half, you'll have your standard old OESD or FD which requires playing some poker.

So, a question from me to all you math-heads: How do you combine these preflop odds with the odds of hitting your hand postflop to figure out the implied odds required to call with SCs preflop?

If you don't like numbers, skip the rest of the post; what follows is how I calculated everything.

tl;dr math

I calculated the odds of flopping a straight myself; with 65s, for example, there are four flops that give you a straight (789, 478, 347, 234). The odds of hitting each of those flops are 12/50 * 8/49 * 4/48; multiply that by 4 flops, and you get 1.31%.

Combo draws

All examples assume you have 6c5c.

OESD + flush draw + pair (20 outs ZOMG):
You need a flop of 87(6/5), 7(6/5)4, (6/5)43, with two clubs each.
8c 7c 6/5x: 2/50 * 1/49 * 5/48 * 3 = .0255%
Multiply by 3 to get odds for all three flops = 0.07653%. Not very high.

Gutshot + flush draw + pair (17 outs):
You need a flop of 98(6/5), 97(6/5), 8(6/5)4, 7(6/5)3, (6/5)42, (6/5)32 with two clubs.
9c 8c 6/5x: 2/50 * 1/49 * 5/48 * 3 = .00255%
Multiply by 6 to get odds for all six flops = 0.153%.

OESD + flush draw (15 outs):
You need a flop of 87x, 74x, or 43x with two clubs; in addition, you can catch ultra-deceptive flops of 973 with two clubs or 842 with two clubs.

Odds of flopping 87x with two clubs, where x does not complete a flush or straight and does not pair your hand:
87x: 7c 8c x = 2/50 * 1/49 * 27/48 * 3 = 0.138%
7c 8x xc = 1/50 * 3/49 * 10/48 * 6 = 0.153%
7x 8c xc = 3/50 * 1/49 * 10/48 * 6 = 0.153%
Total = 0.444%
Total for all 3 flops = 1.332%

973: 9c 7c 3x = 2/50 * 1/49 * 3/48 * 3 = 0.0153%
*3 for 9c 7x 3c/9x 7c 3c = 0.0459%
*2 for 842 = 0.0918%

Total odds of flopping 15-outer: 1.424%

Pair + flush draw (14 outs):
Two clubs and one of your hole cards:
6/50 * 11/49 * 10/48 * 3 = 1.68%

Since we already counted pair + FD + OESD and pair + FD + gutshot, subtract 0.07653 and 0.153 to get 1.45%

Pair + straight draw (13 outs):
using 65s, possible flops are 87(6/5), 7(6/5)4, (6/5)43
8/50 * 4/49 * 5/48 * 3 = 0.408%
Multiply by 3 for all three flops = 1.224%

Since we already counted pair + FD + OESD, subtract 0.07653 to get 1.147%

Gutshot + flush draw (12 outs):
You need a flop of 98x, 97x, 84x, 73x, 42x, 32x (where each flop has two clubs).

Same calculation as OESD + flush draw; 0.444% per flop * 6 flops = 2.664%

So, total odds of flopping a combo draw = 0.07653% (20 outs) + 0.153% (17 outs) + 1.424% (15 outs) + 1.45% (14 outs) + 1.147% (13 outs) + 2.664% (12 outs) = 6.915% = 1 in 14 times (13:1)

Regular draws

OESD (8 outs):
There are five flops you can catch an OESD with: using 65s as an example, there's 87x, 74x, 43x, 973, and 842.

Odds of flopping 87x (where x does not pair your hand and does not complete a straight):
8/50 * 4/49 * 34/48 * 3 = 02.94%
Subtract 0.442% for the times it makes an OESFD (which we already counted) = 2.498%
Multiply by 3 for the odds of 87x/74x/43x: 7.494%

Odds of flopping 973: 12/50 * 8/49 * 4/48 = 0.33%
Multiply by 2 for the odds of 973/842: 0.65%
Subtract 0.0918 since we already counted double gutshot + FD: = 0.558%

Total odds of flopping non-combo OESD = 8.05%

Flush draw (9 outs):
Two clubs + a blank that does not complete a flush or pair your hand:
11/50 * 10/49 * 33/48 * 3 = 9.26%

Subtract 1.424 and 2.661 since we already counted the times where the flush draw gives you an OESD, and you get 5.175% non-combo flush draws.

So, your total chances of flopping a standard 8 or 9 out draw are 8.05% (OESD) + 5.175% (flush) = 13.225% (1 in 7.5, 6.5:1).

I calculated the average equity of made hands/combo draws against overpairs by taking the weighted average of each:

0.077 / 12.5 * 65.556 (0.077 / 12.5 = %age of time you flop oesfd+pair, 65.556% = equity of 6s5s on 9s8s6x board against AcAd)
+ .153 / 12.5 * 57.677
+ 1.424 / 12.5 * 56.26
+ 1.45 / 12.5 * 50.71
+ 1.147 / 12.5 * 45.86
+ 2.664 / 12.5 * 47.78
+ 0.84 / 12.5 * 97.17
+ 2 / 12.5 * 74.55
+ 1.35 / 12.5 * 87.78
+ 0.09 / 12.5 * 91.414
+ 0.01 / 12.5 * 99.899
+ 1.31 / 12.5 * 96.717

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Keys Myaths
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#6996796 - 08/21/06 12:20 AM

Quote:

Adding these all together, you will flop a hand you can continue with on the flop 25% of the time (1 in 4). However, only half of the time will these hands be immediately profitable (i.e. +EV to shove it in); the other half, you'll have your standard old OESD or FD which requires playing some poker.

So, basically, it's a 12% chance (~7.5:1) to flop something you'll want to shove.

So, it's near the 6.5:1 that a pocket pair gives you, plus the little something extra for flopping the other kinds of draws.

I'd say the same rule would be in effect here.

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wslee00
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#6996817 - 08/21/06 12:21 AM

Wow - crazy math. I hope you apply this analysis instead of just leaving it at this.

I just want to add that continuing on the flop depends on your opponent. Depending on their pfr frequency, I play my hand differently on the flop. You can't forget one-pair hands which you can float/raise if the board is safe.

Your analysis is assuming villain always has a hand. You must take into account the times when you can profitably call flop w/ just one pair w/ respect to his range, and also the frequency of him folding to a raise on the flop when you only have a straight/flush draw.

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Dory
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: wslee00]
#6996913 - 08/21/06 12:28 AM

Very nice.

I have always been much more reluctant to call preflop raises with SCs compared with small pairs.

This post really helps me get my head around what kind of odds I need to be calling.

Thanks heaps!!

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goofyballer
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: wslee00]
#6997088 - 08/21/06 12:43 AM

Quote:

Wow - crazy math. I hope you apply this analysis instead of just leaving it at this.

Me too, I just need someone like Pokey to help me figure out how to do that

Quote:

So, basically, it's a 12% chance (~7.5:1) to flop something you'll want to shove.

So, it's near the 6.5:1 that a pocket pair gives you, plus the little something extra for flopping the other kinds of draws.

I was trying to make the point that thinking this way is dangerous; if you get it in on the flop with a set you'll lose 1 out of 10 times, but if you get it all in on the flop with the made hands/combo draws you flop with SCs, you'll lose your stack 1 out of 3 times. For this reason, even though the odds of flopping a made hand/combo draw is about the same as flopping a set, you need better implied odds to call with SCs to account for the times you lose.

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PBJaxx
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: wslee00]
#6997091 - 08/21/06 12:43 AM

Wow, great post. I appreciate all the leg work you put in, but I hope we can get some help with application from some of the great minds around here. I am going to put some serious thought into this and post again later. I look forward to reading other responses.

-Jaxx

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PBJaxx
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#6997119 - 08/21/06 12:45 AM

Quote:

So, basically, it's a 12% chance (~7.5:1) to flop something you'll want to shove.

So, it's near the 6.5:1 that a pocket pair gives you, plus the little something extra for flopping the other kinds of draws.

I was trying to make the point that thinking this way is dangerous; if you get it in on the flop with a set you'll lose 1 out of 10 times, but if you get it all in on the flop with the made hands/combo draws you flop with SCs, you'll lose your stack 1 out of 3 times. For this reason, even though the odds of flopping a made hand/combo draw is about the same as flopping a set, you need better implied odds to call with SCs to account for the times you lose.

Word.

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goofyballer
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#7005223 - 08/21/06 05:48 PM

bump for weekday

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kitaristi0
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#7006324 - 08/21/06 07:17 PM

Rebump. Try x-posting this in Probability too. Maybe they can help.

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Jamougha
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: kitaristi0]
#7006464 - 08/21/06 07:27 PM

I've been too lazy to work all this out for a while now, thank you.

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maxtower
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: kitaristi0]
#7006708 - 08/21/06 07:51 PM

After reading goofy's analysis, it looks like you can profitably play suited connectors 45s - JTs with the 5/10 rule considering the implied odds.
One issue at hand is that the 5/10 rule assumes a reasonble chance you'll net an opponent's stack when you hit your hand. This is fine for the made hands because all of them are beating an over pair. The combo draws are not as good because if you push and your opponent folds, you are getting the correct implied odds to call preflop with the 5/10 rule in the first place. If you push and he calls, you'll hit your hand around 50-60% of the time. With the money already in the pot and the fold equity you might have, going all in with a combo draw is a fine play, however I question whether you have the correct implied odds preflop to get yourself into that situation. There is some math that needs to be worked out here, but it appears suited connectors are not as easy a call as pocket pairs using the 5/10 rule.
A good play may be to call with these in position only. That gives you an added advantage when your opponent checks the flop to you.

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carnivalhobo
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Jamougha]
#7006742 - 08/21/06 07:54 PM

12.6% chance of flopping a made hand or a big draw

10.8% chance of flopping a set with a PP, shouldnt we be calling the same raises (maybe more) with sc's as we are with PPs (which is most).

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: carnivalhobo]
#7006828 - 08/21/06 08:04 PM

I wrote a program to do these exact calcs over a year ago, and came out to the same ~25% you did, so your math is probably good (some of my numbers were also verified by BruceZ of the probability forum).

Because I wrote a program to do this, I ran through a number of other types of hands that you may be interested in. For instance, suited one-gappers come out to 23% to flop OESD+,2pair+. So basically, most anytime you're willing to play a suited connector, you should be willing to play a similar suited one-gapper also.

Summary of hands:
Suited connectors: 25%
Suited one-gappers: 23%
Suited two-gappers: 18%
Unsuited connectors: 17%
Suited aces: 17%

Note: This isn't the end-all, be-all, as it doesn't take into account draws to the nuts, etc. But it's a relatively decent gauge on the strength of those various types of hands to each other.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: carnivalhobo]
#7006871 - 08/21/06 08:10 PM

Quote:

10.8% chance of flopping a set with a PP, shouldnt we be calling the same raises (maybe more) with sc's as we are with PPs (which is most).

As he pointed out, your equity edge when you "hit" isn't nearly as big so your implied odds aren't nearly as high (as well as your draws are often obvious). A collary to this is that position becomes more important in the play of those hands.

These two factors combined mean you can't be playing in more pots with them than PPs based on the numbers you quoted alone.

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binions
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#7006968 - 08/21/06 08:22 PM

I looked at this long ago. My posts are somewhere in the archives.

If you factor out flopping flush draws on paired boards, and straight draws on paired and 3-flush boards against, I get 23.5% or 3.25:1 against flopping 2 pair or better made hands or at least an 8 out draw for suited max stretch 0-gap connectors.

21.3% or 3.7:1 against for max stretch 1-gap suited connecttors.

18.5% or 4.4:1 against for max stretch 2-gap suited connectors.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: binions]
#7006997 - 08/21/06 08:25 PM

I used to just subtract ~2% to account for those situations where you flop a draw but it's on a bad board or whatever. Looks like that was a pretty good guesstimate. Thanks for those.

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bhudson
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: maddog2030]
#7007138 - 08/21/06 08:41 PM

Quote:

Unsuited connectors: 17%

Whoa... I think you just helped me plug a huge leak.

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goofyballer
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: maddog2030]
#7007192 - 08/21/06 08:46 PM

Quote:

Suited aces: 17%

That too. People generally talk about suited aces in the same way they talk about SCs, when suited aces appear to be much weaker except for two things:
1. Flush draws are always to the nuts
2. They have three more outs on their flush draws when up against KK- than SCs do.

I wonder if those two properties make up for the fact that you're flopping good hands/draws 1 in 6 times instead of 1 in 4.

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bhudson
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#7007273 - 08/21/06 08:52 PM

My take on suited aces is they are fantastic to raise with and terrible to call raises with unless the implied odds are huge. Always been that way. However I used to consider unsuited connectors as negligibly weaker than suited connectors on the order of 1 or 2%.

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Antinome
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#7007294 - 08/21/06 08:53 PM

vnh

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Jamougha
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#7007377 - 08/21/06 08:58 PM

goofy,

you will also flop some useful top pair hands with a SA; less so with the smaller connectors.

If you have e.g. A8s against a reasonably tight CO opening range (say 22+, 2 broadway, A8o+, Axs, 65s+, 86s+, two suited cards 9 or higher) then you are 49:51 with their range and typically getting good pot odds + position. With 65s you would be 37:63 and it would be rather harder to judge where you are. Your call is justified more by pot odds than implied odds.

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ilya
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#7007943 - 08/21/06 09:44 PM

Nice post. However you failed to factor in the Fun Equity of gamboooooling it up with a draw. Sets are so boring and stressful in comparison...mostly you're just sitting their praying they don't hit their runner runner. Whereas when you have a draw and they call you, things can usually only improve.

Edited by ilya (08/21/06 09:46 PM)

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Shroomy

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: ilya]
#7010066 - 08/22/06 12:39 AM

I would even add a few percent if there were several players calling or raising before me to account for the good chance that they have each others outs.

good post

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DonkBluffer
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: maddog2030]
#7012272 - 08/22/06 05:13 AM

Quote:

I wrote a program to do these exact calcs over a year ago, and came out to the same ~25% you did, so your math is probably good (some of my numbers were also verified by BruceZ of the probability forum).

Any chance you can make this program available to the public (or just me )?

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c_strong

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: maxtower]
#7012667 - 08/22/06 07:14 AM

Goofy,

Really nice post, thanks.

Quote:

A good play may be to call with these in position only.

This is really important. With a small PP you don't mind being OOP so much, as you'll usually be playing fit or fold on the flop. Extraction is easier in position, but you should still be able to get stacks in with a set OOP against an overpair, TPTK etc.

With an SC, though, most of the time when you're continuing on the flop you'll have a draw. These are so much easier to play in position, where you have the option of checking behind for a free card if it's checked to you, betting or raising the flop to disguise your hand and possibly take a free card on the turn, etc. Much harder to play them OOP where none of your options are great: check/call looks like a draw, you have no FE and may not get odds to draw; leading may mean you get raised or floated so you can't take a free card; check-raising may mean you put a lot of money in to draw etc.

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nextgenneo
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: c_strong]
#7012712 - 08/22/06 07:32 AM

Here is one thing to think about, if you put someone on aces and you have a pocket pair if you hit a set your very unlikely to get drawn out upon, however with a SC if you flop a 2 pair then its more likely that they will outdraw you so should this be accounted for in the math?

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ianlippert
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: c_strong]
#7012715 - 08/22/06 07:33 AM

Another thing to consider is that SC dont hit against TPTK as easily as PPs do. Lets say you are against AK, what are the odds of you both hitting that flop? If you hit a straight they missed, if you hit 2pair they are less likely to have hit. I think when people think about implied odds they forget that a lot of the time you hit your hand and dont get paid off. What happens when you are playing against players that play more than top hands, if you are going to flop or fold I believe you are giving up a lot of money to these players.

Anyways this is interesting, I almost never call raises with SC and dont feel as though I am giving up as much as if I dropped PPs from my calling range.

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Jouster777
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#7012744 - 08/22/06 07:42 AM

Really great post Goofyballer. I am no math-head but I wanted to work on this part a bit:

Quote:

So, a question from me to all you math-heads: How do you combine these preflop odds with the odds of hitting your hand postflop to figure out the implied odds required to call with SCs preflop?

I used the 5/10 rule in the set mining situation as a benchmark to what % of villain’s stack we should expect to capture (on average) when we flop a big made hand. We will flop a set = 11.8%, and need to call less than 7.5% of avg. villain’s stack/avg. situation to merit a call. If this is a EV neutral situation then: EV=0=.118*(.075S+I)-.882*(0.075S)
Where S=effective stack size, I = implied money to be added to pot
This leads to: I=.49S…so our expectation when we hit a set is to capture 50% of villain’s stack

There are caveats below but I’ve tried to apply this benchmark to the situations that Goofyballer worked out:
1. you have a 5.6% chance of flopping big made hand, ~90+% equity => Expectation 50% of effective stack
2. you have a ~7% chance of flopping a strong (12+ outs) combo draw, ~50% equity => Expectation 20% of effective stack
3. you have a ~13% chance of flopping a standard OESD or FD, ~35% equity => Expectation 5% of effective stack

If you accept these estimates then our EV calculation becomes:
EV = .056*.5S+.07*.2S+.13*.05S-.75B = 0
Where B = size of preflop bet to be called

.028s+.014s+.0065s=.75B
B=.065S

This means that our preflop bet size should be 6.5% of the effective stack for the average situation as compared to 7.5% for PP’s. Until someone tears apart my estimates, I will use a 4/8 rule for SCs instead of the 5/10 rule for PP’s.

Should these caveats further alter the expectations estimated based on set mining?:
SC made hands are not as hidden as sets
SC made hands are usually stronger than sets

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avfletch
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Jouster777]
#7012893 - 08/22/06 08:27 AM

I'm at work at the moment so I've only had time to scan read the stuff so take this with a pinch of salt but I think there's a problem with the assumptions you've made.

You've worked backwards from the most powerful draws but I don't think you've discounted them when considering their weaker versions. Eg OESD + flush draw is a subset of the combinations that have a flush draw. The fact that they're not independent may throw the numbers off a bit from what you have.

Apologies if this is utter rubbish, its just thinking out loud on my lunch break. I'll give it some proper thought when I get in.

Cheers for doing the leg work on this though.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: avfletch]
#7013150 - 08/22/06 09:22 AM

If I read Goofyballer's calculation correctly, she(?) subtracted out made hands from combo draws and combo draws from standard draws. If that is true, the top groups should not be subsets of the lower groups.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Jamougha]
#7013189 - 08/22/06 09:27 AM

NVM

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fizzle
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Jouster777]
#7013573 - 08/22/06 10:18 AM

Quote:

Until someone tears apart my estimates, I will use a 4/8 rule for SCs instead of the 5/10 rule for PP’s.

This should probably work since a standard PFR is 3-4 BB of a 100 BB stack (3-4%).

However, I don't think your estimates work for when you're OOP for reasons mentioned in a post above. The implied odds are much worse and you won't be able to take nearly as much of the effective stack.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: fizzle]
#7013610 - 08/22/06 10:23 AM

Nice post. This one belongs in the next SSNL digest and should be added to the sticky.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: fizzle]
#7014097 - 08/22/06 11:13 AM

Great point on position fizzle. It also applies to sets but it is just part of the considerations that adjusts your range toward the 5 rather than the 10.

You are right the effect is much greater when potentially drawing. I'll throw out some more estimates and maybe you or others can refine them:
1. you have a 5.6% chance of flopping big made hand, ~90+% equity =>
Expectation 60% of effective stack in position
Expectation 40% of effective stack OOP
2. you have a ~7% chance of flopping a strong (12+ outs) combo draw, ~50% equity =>
Expectation 25% of effective stack in position
Expectation 15% of effective stack OOP
3. you have a ~13% chance of flopping a standard OESD or FD, ~35% equity =>
Expectation 7% of effective stack in position
Expectation 2.5% of effective stack OOP

EV(IP) = .056*.6S+.07*.25S+.13*.07S-.75B = 0
EV(OOP)= .056*.4S+.07*.15S+.13*.025S-.75B = 0

IP situation: 0.08*S=B or our preflop bet should be <8% on average
OOP situation: 0.05*S=B or our preflop bet should be <5% on average

IP 5-10 rule
OOP 3-7 rule

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fizzle
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Jouster777]
#7014250 - 08/22/06 11:29 AM

Quote:

IP 5-10 rule
OOP 3-7 rule

Your numbers seem ok I guess, as guestimates.

For OOP, that rules basically lets you always call with SC's in the BB to a standard raise. This makes sense, especially to a steal raise, where you have some maneuverability with 1 pairs or air as well.

I suppose extra callers would also help immensely with both your pot odds and implied odds, but I've never seen any math done with that. I suppose that's something else you can factor in when the number is inbetween the upper and lower bounds.

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BukNaked36
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Jouster777]
#7014419 - 08/22/06 11:43 AM

Quote:

If I read Goofyballer's calculation correctly, she(?) subtracted out made hands from combo draws and combo draws from standard draws. If that is true, the top groups should not be subsets of the lower groups.

Just an fyi - Goofyballer is male.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#7014507 - 08/22/06 11:51 AM

OP is tl;dr. J/k. I read it all. OP is the nuts. Thanks for doing the hard work. I wanted to expand and share some thoughts on playing these speculative hands: sooted connectors, sooted one-gaps, sooted aces, and small PPs effectively. I think this advice is solid. Oh yeah, I just now came up the % of stack worth calling with these hands. Those numbers could be wacko. I'm not sure. Feedback is welcome.

Sooted Aces:
Value #1 Can make nut flush and stack people with non-nut flush.
Ideal Pot Type: Multiway unraised.
Good Flop: NFD.
Way to Play the Hand: Hopefully see the draw for free or cheaply. Bad to push out worse draws flush draws and get heads up with TPTK-type made hand.
Importance of position: Very high. Being in a multiway unraised pot is infinitely easier from late position. Seeing draws cheaply is much easier, too. A lot of the implied odds of making flush over flush gets killed when having to call a preflop raise so I don't like to take a sooted ace into a multiway raised pot.

Value #2 Flopping two pairs and winning a large pot from someone holding AK or AQ.
Ideal Pot Type: Heads up. Raised. Villain with TPTK will fear two pair and sets much more in a multiway pot. Implied odds are not as good there.
Good Flop: Top two pairs.
Way to Play the Hand: If only the ace flops, call a small bet and fold to further action. With two pairs try to start building a pot as soon as possible. Make modest bets and raises whenever possible to facilitate getting all-in.
Importance of Position: Very important. Being heads up is important because TPTK is less likely to go broke multiway, fearing sets/2 pairs. Implied are much worse that way IMO. If the NFD is flopped, it's much easier to either see it for cheap or to semi-bluff villains out of the pot from position.

When to play sooted aces: I play weak sooted aces (AJ-ish and down) from late position. I limp after limpers. I call a raiser OTB if no one else has called and it isn't likely to get reraised behind. If the pot is unopened, I raise from CO or OTB to steal the blinds. I'd only call a raise from the blinds if the raise was small and I thought I was getting good implied odds.

How much are sooted aces worth paying to play preflop? I don't have OP printed so I'm going from memory but I think the chances of flopping the NFD or two pairs+ is 9% + 3% = 12%. I'd guesstimate winning about 1/3 of the effective stacks when these hands hit (NFD is just a draw after all). Thus, I wouldn't be willing to call more than 4% of my stack to see a flop with a sooted ace.

Sooted connectors and sooted one gaps
Okay. So I got sick or formatting stuff.

Caveat: These cards are very profitable but I think they must be played in a high variance way in order to make that money. Talk to Doyle.

Obvious observation: Many times these hands flop non-nut draws. It is exceptionally important to either fastplay or fold non-nut draws in multiway pots. I can't think of a quicker way to go broke than overcalling flop bets with a six-high flush draw. I don't take free cards when I flop flush draws or flush draw + other outs when my flush draw could break me.

Another obvious observation Don't draw when the hand could be dead. Doesn't matter if it's possibly live. Let the pot go.

Trickiness: I like OESD on two-flush boards because I can get paid a lot when someone thinks I'm over-betting a busted flush draw on the end.

Preflop: I'll usually take a flop the cheapest way possible in any pot that hasn't been reraised or raised big. I don't care if I'm playing multiway or heads up. Don't care about in position or out of position. I'll open limp from EP or sometimes I'll raise. Same goes for almost all positions. I'll open raise a little more as I get closer to the button, but I mostly like to limp these cards. Oh, sometimes I throw in a reraise if I think the OR is light and will lay down.

Flopping one pair: I've got to be heads up to care. Otherwise I'm folding all one-pair hands to any reasonable bet. If I'm heads up and in position I'll call one bet with middle pair and try to steal the pot on the turn or maybe play for a showdown. It varies. If I'm OOP I just fold. If I flop top pair, I'll call a bet in position or OOP and play for a showdown. I'll lay down to a second barrel, usually, though. Some might say this strategy is exploitable but I'd play TPTK the same way (only not folding it to the second barrel very often).

The strategy I have one cardinal rule that I try never to violate. If I flop any of those 20-25% percent of hands we've been talking about in this post, I play to get my money all-in, but I do it in PSB increments. I don't care if I'm in position or OOP. If I bet and get raised, I 3-bet. If I'll have less than a PSB left for the next street then I push. Simple. If I get called, I pot it on the next street. If I'm still called and I've got a lot left for a river bluff I'll frequently fire as big as I can there too. It takes STONES to call three PSB with top pair. A hidden gem about this strategy is that it tends to push out better flush draws so I don't hit and lose big pots. It also tends to get people giving me lots of money and then folding without a showdown. Try it.

Leading into the raiser: I'll almost always do it. I'm not trying to c/r very often unless the stacksizes are right for c/r all-in. Even then I'd rather bet sometimes. I don't want a free card coming off. If he's weak enough to give one I'd rather steal the pot. If he's got one pair I want to put him in a game theoretic bind.

Modifications: Some players I know won't raise the flop without a HUGE hand. I'm not 3-betting that player. I'm calling if I think I have enough implied odds to try to hit. If not, I'll tuck my tail and fold.

If I get raised on the flop and I think this player is testing me then I'm definitely 3-betting and potting it into him on the next street. I actually like being OOP here just as much as being in position.

Bluffing the river: If I just know the other guy isn't laying down, I don't burn my money. I'll give up with a busted draw much of the time. However, he only has to fold 50% of the time for a roughly PSB bluff to be the right play. I'll make sure to make PSB value bets when I think I've got him. Even if he doesn't pay off when I've got a made hand, that means he's folding to me when I did have a busted draw and decide to bluff.

The corollary: Small pocket pairs. Preflop I'll play the same way as suited connectors when I have a small pocket pair. When I flop a set I'll play the same way as when I flop one of the 25% of good hands with a suited connector. Adding sets to my range of fastplay hands really puts someone with hands as good as AA in a bad spot.

I found this strategy to be very hard to play against with deep stacks. I think it's very strong from a game theoretic perspective. Thus, I adopted it.

Stack Depth Requirements: I'd like to be deep enough to fire three full PSB's if possible.

Say someone raises to 4BB from EP and gets two callers. After I call the pot with be 17BB. (Hero expendatures, potsize)

Flop(4BB, 17BB). PSB, call.
Turn(21BB, 51BB). PSB, call.
River(72BB, 152BB). PSB, call.
(Hero uses 224BB).

The preflop call is only about 2% on my stack but I'd call more up to about 5% because the pot is multiway and I could make some bigger \$\$\$ when I flop two pairs against an overpair type hand.

Say someone raises to 4BB, Hero is the only caller.
Flop (4BB, 9BB). PSB, call.
Turn (13BB, 27BB). PSB, call.
River (40BB, 51 BB). PSB, call.
(Hero uses 91 BB).

The preflop call is 4.5 or ~%5 of my stack.

I'm not sure how to quantify what the correct calling percent is but for me I want the number to be close to 5% of the effective stacks so I can play the most profitably after the flop.

I'm really interested to hear comments about my thought processes here. If you hate what I'm suggesting, I'd like to hear some counter strategies so I can use them against guys that play this way.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Jamougha]
#7014715 - 08/22/06 12:09 PM

great numbers.
you want better than 7-1 with a pp also, since you won't always get paid off.

i definitely want better implied odds with suited connectors, always at least 20-1 (if multiway that number goes down).

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mornelth
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#7014849 - 08/22/06 12:23 PM

Quote:

Quote:

Wow - crazy math. I hope you apply this analysis instead of just leaving it at this.

Me too, I just need someone like Pokey to help me figure out how to do that

Quote:

So, basically, it's a 12% chance (~7.5:1) to flop something you'll want to shove.

So, it's near the 6.5:1 that a pocket pair gives you, plus the little something extra for flopping the other kinds of draws.

I was trying to make the point that thinking this way is dangerous; if you get it in on the flop with a set you'll lose 1 out of 10 times, but if you get it all in on the flop with the made hands/combo draws you flop with SCs, you'll lose your stack 1 out of 3 times. For this reason, even though the odds of flopping a made hand/combo draw is about the same as flopping a set, you need better implied odds to call with SCs to account for the times you lose.

Yeah, but won't those EXTRA times when you flop a regular draw and able to play it profitably add some extra equity to your hand? Almmost to the point where SC equity ALMOST equals to the PP4SET equity?...

(I'm just wondering, not REAL big on math...)

Aslo, somewhat OT - what does "tl;dr" stand for?

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mornelth
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: maxtower]
#7014862 - 08/22/06 12:25 PM

Quote:

After reading goofy's analysis, it looks like you can profitably play suited connectors 45s - JTs with the 5/10 rule considering the implied odds.
One issue at hand is that the 5/10 rule assumes a reasonble chance you'll net an opponent's stack when you hit your hand. This is fine for the made hands because all of them are beating an over pair. The combo draws are not as good because if you push and your opponent folds, you are getting the correct implied odds to call preflop with the 5/10 rule in the first place. If you push and he calls, you'll hit your hand around 50-60% of the time. With the money already in the pot and the fold equity you might have, going all in with a combo draw is a fine play, however I question whether you have the correct implied odds preflop to get yourself into that situation. There is some math that needs to be worked out here, but it appears suited connectors are not as easy a call as pocket pairs using the 5/10 rule.
A good play may be to call with these in position only. That gives you an added advantage when your opponent checks the flop to you.

Yeah, if you flop a ready-made flush you're either not getting paid - or you're getting stacked...

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: ianlippert]
#7014960 - 08/22/06 12:34 PM

Quote:

Another thing to consider is that SC dont hit against TPTK as easily as PPs do. Lets say you are against AK, what are the odds of you both hitting that flop? If you hit a straight they missed, if you hit 2pair they are less likely to have hit. I think when people think about implied odds they forget that a lot of the time you hit your hand and dont get paid off. What happens when you are playing against players that play more than top hands, if you are going to flop or fold I believe you are giving up a lot of money to these players.

Anyways this is interesting, I almost never call raises with SC and dont feel as though I am giving up as much as if I dropped PPs from my calling range.

You: 6s 5s
Flop: 4s Ks 7c.

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linuxrocks
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: mornelth]
#7015087 - 08/22/06 12:46 PM

Quote:

Aslo, somewhat OT - what does "tl;dr" stand for?

Urban dictionary def.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: jskinn04]
#7015317 - 08/22/06 01:06 PM

Quote:

The strategy I have one cardinal rule that I try never to violate. If I flop any of those 20-25% percent of hands we've been talking about in this post, I play to get my money all-in, but I do it in PSB increments. I don't care if I'm in position or OOP. If I bet and get raised, I 3-bet. If I'll have less than a PSB left for the next street then I push. Simple. If I get called, I pot it on the next street. If I'm still called and I've got a lot left for a river bluff I'll frequently fire as big as I can there too. It takes STONES to call three PSB with top pair. A hidden gem about this strategy is that it tends to push out better flush draws so I don't hit and lose big pots. It also tends to get people giving me lots of money and then folding without a showdown. Try it.

So, basically you're saying that you fire out a PSB everytime you flop a flush draw (or straight draw) or better? And if in position and OR bets out, you make a PSB raise everytime? Will this strategy work at \$50NL?

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linuxrocks
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#7015372 - 08/22/06 01:11 PM

Great analysis, goofy.

One thing I wanted to add is the equity of playing the SCs after flopping a pair. The odds of flopping a pair that's not paired is 30%. The equity obviously is not that great, but there's certainly some value in backdoor draws, hitting your second pair, trips etc. This is especially true when we are the one raising or re-raising. This, I think is the big difference compared to small pairs. They are almost useless, if you don't hit the set.

Calculating equity of a middle pair against a pre-flop raiser is quite a hairy calculation, but I am guessing it's much higher than the equity when small pairs don't hit set on the flop.

P.S. BTW, I am the PPadala on TP.com forums

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: mornelth]
#7015444 - 08/22/06 01:18 PM

Quote:

You: 6s 5s
Flop: 4s Ks 7c.

I'm not sure what you are trying to say here. I mean If I got a flop like this every time I played a SC I would love them.

Someone can correct me if I'm wrong, but I'm pretty sure that if the raiser has AK and I have a PP the odds of flopping a set and my opponent flopping TPTK is 3%. I dont think people have calculated this into their posts. The majority of the time you are against 2 big face cards you will not be getting their entire stack let alone the 50% that is needed to make the call.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Rocco]
#7015471 - 08/22/06 01:20 PM

Quote:

Quote:

The strategy I have one cardinal rule that I try never to violate. If I flop any of those 20-25% percent of hands we've been talking about in this post, I play to get my money all-in, but I do it in PSB increments. I don't care if I'm in position or OOP. If I bet and get raised, I 3-bet. If I'll have less than a PSB left for the next street then I push. Simple. If I get called, I pot it on the next street. If I'm still called and I've got a lot left for a river bluff I'll frequently fire as big as I can there too. It takes STONES to call three PSB with top pair. A hidden gem about this strategy is that it tends to push out better flush draws so I don't hit and lose big pots. It also tends to get people giving me lots of money and then folding without a showdown. Try it.

So, basically you're saying that you fire out a PSB everytime you flop a flush draw (or straight draw) or better? And if in position and OR bets out, you make a PSB raise everytime? Will this strategy work at \$50NL?

I haven't played NL cash online for a while. I learned this strategy while playing "World Championship Poker" which has T.J. Cloutier's namesake. I was pretty much a break even player at \$25 NL before I starting playing this game. I was actually losing to the computer in this game. I vowed to improve. I reread Super System and I applied some of Doyle's advice about playing middling straight flush cards (SC's, S 1-gaps). After adding these hands and this strategy I absolutely owned.

It's pretty simple why. If they decide to run me down when I have a bare flush draw, I have a 35% shot at outdrawing the guy. If the guy has the stones to call all three bets then I lose 65-35= 30% of my stack every time this situation occurs. That's when I have a bare flush draw. When I have a set and he calls me down in this situation I win about 95% of my stack. When I have two pairs and he has and overpair or TPTK I win about 50% of my stack over the long run. If villain plays to stop me from bluffing him he pays off HUGE when I've got him dead and that's really really hard for him to recover from. Also, since I'm playing a wide range of hands preflop, it's very hard to put me on a hand. I could just as easily have two pairs or a set as I could have a flush draw. They both get played the same way.

What's even sweeter is when I get called on the flop and turn by someone holding TPTK and then I get a fold on the river. I make a ton of money ever time someone makes a bad fold for that many chips.

An even better benefit is that this style puts people on tilt.

If I find that I'm always getting called down then I'll c/f weak flush draws and straight draws and tailor my range more towards made hands. I think it's a great strategy to put someone holding 1 pair in a huge game theoretic bind. Either he's a little ahead or he's WAY behind and it's going to cost him his stack to find out.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: jskinn04]
#7016208 - 08/22/06 02:06 PM

quick question - aren't regular draws already included within the combo draws section?

For example, if hero has 9 8

are the "regular" draw odds excluding all the times it's a combo, or does it assume the flop is

7 A *non-6, non-T, etc. etc.*

versus

7 A *any card*

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: bestcellar]
#7016817 - 08/22/06 02:41 PM

vnh OP and jskinn about playing these speculative hands.

Something I find happens occasionally with SCs in multiway raised pots are when when you hit the straight and a TAG hits a set and can't wait to push the money in - and possibly sandwiching the PFR for a x3 stackathon.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: munkey]
#7020069 - 08/22/06 06:33 PM

Re: counting draws more than once, I made sure that I discounted subsets of draws that I'd already calculated; for example, in the tl;dr math section,

Quote:

Flush draw (9 outs):
Two clubs + a blank that does not complete a flush or pair your hand:
11/50 * 10/49 * 33/48 * 3 = 9.26%

Subtract 1.424 and 2.661 since we already counted the times where the flush draw gives you an OESD, and you get 5.175% non-combo flush draws.

I accidentally left out "and gutshot" after "gives you an OESD", but yeah, I accounted for all that.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: DonkBluffer]
#7020507 - 08/22/06 07:14 PM

Quote:

Any chance you can make this program available to the public (or just me )?

I wouldn't have a problem doing that, but it's pretty much the exact opposite of user friendly so it would be pretty hard for someone else to use.

I have no problem running sample hands through and posting the results. I just think that I posted the most interesting cases... anything worse isn't worth really playing pr studying anyway.

Also the program, as I wrote it, is limited in that it just figures out whether you hit a pair or not (doesn't differentiate between BP, MP, and TP) since my primary goal with the program was to get the numbers I posted. So it's really only useful for hands where you aren't concerned what type of pair you have.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: maddog2030]
#7020647 - 08/22/06 07:29 PM

Great post Goofyballer. I'm going to bookmarked this.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Barrin6]
#7021875 - 08/22/06 09:25 PM

jskinn04,

I am really interested in seeing some hand histories that you have played SCs in this way, just so I know exactly what you're talking about.

Max

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#7022365 - 08/22/06 10:04 PM

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: linuxrocks]
#7037034 - 08/23/06 10:28 PM

Quote:

Quote:

Aslo, somewhat OT - what does "tl;dr" stand for?

Urban dictionary def.

TY

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#7045304 - 08/24/06 03:19 PM

I think the conclusions are all wrong. You need to calculate how much you actually win when you flop a pushable hand. That's the key variable. That means calculating an EV for the pushable draws estimating your fold equity. If you assume 100% fold equity the EV of a combo draw is small. If you assume 0% fold equity, the EV of a combo draw is small.

I don't see how SC can be as profitable as pps.

Krishan

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Jouster777]
#7048258 - 08/24/06 06:55 PM

Quote:

Great point on position fizzle. It also applies to sets but it is just part of the considerations that adjusts your range toward the 5 rather than the 10.

You are right the effect is much greater when potentially drawing. I'll throw out some more estimates and maybe you or others can refine them:
1. you have a 5.6% chance of flopping big made hand, ~90+% equity =>
Expectation 60% of effective stack in position
Expectation 40% of effective stack OOP
2. you have a ~7% chance of flopping a strong (12+ outs) combo draw, ~50% equity =>
Expectation 25% of effective stack in position
Expectation 15% of effective stack OOP
3. you have a ~13% chance of flopping a standard OESD or FD, ~35% equity =>
Expectation 7% of effective stack in position
Expectation 2.5% of effective stack OOP

EV(IP) = .056*.6S+.07*.25S+.13*.07S-.75B = 0
EV(OOP)= .056*.4S+.07*.15S+.13*.025S-.75B = 0

IP situation: 0.08*S=B or our preflop bet should be <8% on average
OOP situation: 0.05*S=B or our preflop bet should be <5% on average

IP 5-10 rule
OOP 3-7 rule

Interesting analysis...... how are you coming up with these expectation percentages?

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: ata]
#7066596 - 08/26/06 12:22 PM

OP posted:

OESD + flush draw + pair (20 outs ZOMG):
You need a flop of 87(6/5), 7(6/5)4, (6/5)43, with two clubs each.
8c 7c 6/5x: 2/50 * 1/49 * 5/48 * 3 = .0255%
Multiply by 3 to get odds for all three flops = 0.07653%. Not very high.

Is this right? why is it 5/48 and not 6/48 and why is it multiplied by 3 two times?

could be my fault but please explain.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Elandriel]
#7069212 - 08/26/06 06:19 PM

Quote:

OP posted:

OESD + flush draw + pair (20 outs ZOMG):
You need a flop of 87(6/5), 7(6/5)4, (6/5)43, with two clubs each.
8c 7c 6/5x: 2/50 * 1/49 * 5/48 * 3 = .0255%
Multiply by 3 to get odds for all three flops = 0.07653%. Not very high.

Is this right? why is it 5/48 and not 6/48 and why is it multiplied by 3 two times?

You're right; it is 6/48, which bumps it up to about .09%. Fortunately I screwed up on one of least frequent draws so it doesn't mess with the results too much

The first time I multiply by three is because there's three different orders the cards come could in:
(8c/7c #1) (8c/7c #2) (pair card)
(8c/7c #1) (pair card) (8c/7c #2)
(pair card) (8c/7c #1) (8c/7c #2)

The second time I multiply by three is because we just calculated the odds of one specific flop coming, when there's three specific flops that could give us an OESFD.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#7169634 - 09/04/06 04:49 PM

Thank you:)

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Elandriel]
#7169840 - 09/04/06 05:09 PM

very nice, myself I'm very tight, maybe to tight, and I never call raises with sc's except 10-J occasionally.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: krishan]
#7266811 - 09/12/06 04:05 PM

Quote:

I think the conclusions are all wrong. You need to calculate how much you actually win when you flop a pushable hand. That's the key variable. That means calculating an EV for the pushable draws estimating your fold equity. If you assume 100% fold equity the EV of a combo draw is small. If you assume 0% fold equity, the EV of a combo draw is small.

I don't see how SC can be as profitable as pps.

Krishan

Krishan

I'd really like for someone to address this.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: ata]
#7267645 - 09/12/06 05:00 PM

Quote:

Quote:

Great point on position fizzle. It also applies to sets but it is just part of the considerations that adjusts your range toward the 5 rather than the 10.

You are right the effect is much greater when potentially drawing. I'll throw out some more estimates and maybe you or others can refine them:
1. you have a 5.6% chance of flopping big made hand, ~90+% equity =>
Expectation 60% of effective stack in position
Expectation 40% of effective stack OOP
2. you have a ~7% chance of flopping a strong (12+ outs) combo draw, ~50% equity =>
Expectation 25% of effective stack in position
Expectation 15% of effective stack OOP
3. you have a ~13% chance of flopping a standard OESD or FD, ~35% equity =>
Expectation 7% of effective stack in position
Expectation 2.5% of effective stack OOP

EV(IP) = .056*.6S+.07*.25S+.13*.07S-.75B = 0
EV(OOP)= .056*.4S+.07*.15S+.13*.025S-.75B = 0

IP situation: 0.08*S=B or our preflop bet should be <8% on average
OOP situation: 0.05*S=B or our preflop bet should be <5% on average

IP 5-10 rule
OOP 3-7 rule

Interesting analysis...... how are you coming up with these expectation percentages?

For #1 I used the 5-10 rule for set mining as a benchmark. If you look at that "rule" it expects you will capture 50% of villain's stack, on average, when you hit a big made hand. For SC's this number might be even higher because the made hands you flop are stronger than sets (though also more transparent) leading to me using the 50% number.
For #2 and #3 I extrapolated/guessed

Any fine tuning of those numbers/estimates and criticisms would be great.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: tubasteve]
#7270269 - 09/12/06 08:42 PM

Quote:

Quote:

I think the conclusions are all wrong. You need to calculate how much you actually win when you flop a pushable hand. That's the key variable. That means calculating an EV for the pushable draws estimating your fold equity. If you assume 100% fold equity the EV of a combo draw is small. If you assume 0% fold equity, the EV of a combo draw is small.

I don't see how SC can be as profitable as pps.

Krishan

Krishan

I'd really like for someone to address this.

This is the part that I need someone smarter than me to look into. There are so many complex factors that go into postflop play that determine how much FE you have, how often you'll get AI with the draw, etc. that it's really hard to come up with a figure of how much money you'll win playing these.

I tried to make a point of not making any conclusions based on the data. I just calculated all this so you guys would be more aware of the kinds of situations you can expect to be in postflop with SCs (and how often you'll find yourself in them), and in the hopes that someone would be able to extrapolate the data into more meaningful conclusions about how we should play SCs preflop.

Also, steve, I'm too busy looking into your avatar's eyes to figure this out: who is she?

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Re: Suited Connectors, Implied - JSKINN04? [Re: jskinn04]
#7286923 - 09/13/06 11:59 PM

Sure you dont end up with as much in the middle when you hit and they busto, but you dont give up as much when you have to let it go on the river. So, is it a wash either way?

Do you think added FE of a psb makes the difference?

What about in Little Green Book where Gordon talks about SpiritRock just pushing these same hands?

Do we beieve all three end up with about the same results?

Ive gone with 70%, because Ill be betting that way with just about everything on the flop. c-bet, TPTK, etc . . .
I used to apply your method, just to keep it simple. But I soon realized I didnt care for c-betting the pot, and gettin reraised the pot with TPTK.

Ret

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: goofyballer]
#7287414 - 09/14/06 12:49 AM

Well I checked my PT numbers on PPs(TT~22, no need to drag the big pairs) and compare that to SCs, I win alot more w/ PPs. I even lose money w/ SCs if I don't take AKs into account. I'm just not good enough to play SCs profitably. Even they make a hand, it's usually not the nuts. There will be higher staights/flushes, the board will pair... With PP hitting a set, I know exactly what to do.

Edited by ZingyDNA (09/14/06 12:49 AM)

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: ZingyDNA]
#8384938 - 12/11/06 09:14 PM

I just found this gem, and i think it deserves a bump to those people, such as myself, that missed it.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: VorShot]
#8385009 - 12/11/06 09:20 PM

Quote:

I just found this gem, and i think it deserves a bump to those people, such as myself, that missed it.

I really appreciate this. Great find.

Nice post Goofy.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: luke4130]
#8385682 - 12/11/06 10:01 PM

OMG, goofy got street cred yo. Also, anything > 8 outs = ARRIN!

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: carrotsnake]
#8387629 - 12/12/06 12:21 AM

Quote:

OMG, goofy got street cred yo. Also, anything > 8 outs = ARRIN!

Yuck.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: VorShot]
#8786974 - 01/16/07 07:59 AM

Quote:

I just found this gem, and i think it deserves a bump to those people, such as myself, that missed it.

I agree. Probably also deserves more analysis from people more capable than me.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: krishan]
#8787316 - 01/16/07 09:07 AM

This thread is a great find. In my latest adjustment to my game, I just cut out suited connectors because I suck hard with them. But I find the point below to be a good one: what is your goal with the suited connector when you flop your biggish draw against a raiser? I think that's what most of this thread is about, against a raiser. Are you purely playing for the metagame? IE if you're willing to push that hard with your draw, people will pay off your sets and made hands when you push them hard

Let's assume 100% continuation bets and \$100 stacks.
Raiser pops it to \$4, you call in position with your suited connector.
You flop a 12 outer. Pot is rounded to \$10
Preflop raiser leads out for \$6, You raise to \$20
Just to be arbitrary lets say it's 50/50 that the raiser has a hand worth pursuing and will eventually get it in with you on the flop or turn (argue with me if I'm horribly wrong here in my assumption)

Assumption 1: he folds, you win 12 dollars 50% of the time.

Assumption 2- he wants to get it in with you- let's say you have 45% equity with your 12+ out draw in these cases (sometimes these will be sets and two pairs and you could make your draw and lose as well, I am not sure if 45% is a super accurate estimate)
So you lose \$100 55% of the time= \$55
You win \$102 45% of the time= \$45.9
So 50% of the time you're -\$9.10.
so you win \$2.90 on average with my assumptions when you flop a big draw that you'd be willing to felt.

According to the original calculations, you flop your big draw about 7% of the times, which is 13:1. So, if you're calling a raise with these hands 13x-\$4, -42 + 1 hand when you flop your draw and make \$2.90 on average, but could also be stacked .

What happens when you play your simple 9 out flush or 8 out straight draw fast to get it in?
LEt's keep this assumption the same:
Raiser pops it to \$4, you call in position with your suited connector.
You flop your flush or OESD. Pot is rounded to \$10
Preflop raiser leads out for \$6, You raise to \$20
Just to be arbitrary lets say it's 50/50 that the raiser has a hand worth pursuing and will eventually get it in with you on the flop or turn (argue with me if I'm horribly wrong here in my assumption)

Assumption 1: he folds, you win 12 dollars 50% of the time.

Assumption 2: He gets it in with you somehow on the flop
Let's give you an equity of say 33%
So 67% of the time you lose \$100 here
33% of the time you you win \$102 here
So you lose -23 with the play here.

So seems pretty obvious I guess- you don't want to get it all in with a draw- so it seems pretty important to play these hard in games where people can fold TPTK or an overpair, because if you can't get them to fold, you're going to be a loser. I guess these hands allow you to apply big pressure to people to get them to make bad folds, like folding Queens with a King on the board when you push it hard, and they maybe also to pay you off if you do hit (how could that 9 have possibly helped him?) but you really don't want to make it look like a draw- ie shoving the flop with a 4 flush/combo draw on a raggy board might not be so great if the guy with aces puts you on the draw and calls- you don't really want to be called even if you have a gutshot to go with your flush draw, except to set the guy up for when you flop your set....

Quote:

I think the conclusions are all wrong. You need to calculate how much you actually win when you flop a pushable hand. That's the key variable. That means calculating an EV for the pushable draws estimating your fold equity. If you assume 100% fold equity the EV of a combo draw is small. If you assume 0% fold equity, the EV of a combo draw is small.

I don't see how SC can be as profitable as pps.

Krishan

Krishan

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Osprey]
#8787380 - 01/16/07 09:18 AM

Osprey:

The rounding and incorrect equity #'s make your post incorrect IMO. Equity with combos is >50% a lot of the time.

And preflop raisers usually arent leading 6 into a 12 pot. It would more like 9-10.

Edited by ImsaKidd (01/16/07 09:19 AM)

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: ImsaKidd]
#8787721 - 01/16/07 10:21 AM

I don't think it makes a huge difference.
Let's take a best case scenario

Let's assume 100% continuation bets and \$100 stacks.
Raiser pops it to \$4, you call in position with your suited connector.
You flop a 12 outer. Pot is \$10 to the flop heads up
Preflop raiser leads out for \$10, You raise to \$40
Just to be arbitrary lets say it's 40% that the raiser has a hand worth pursuing and will eventually get it in with you on the flop or turn (argue with me if I'm horribly wrong here in my assumption)

Assumption 1: he folds, you win 16 dollars 60% of the time.

Assumption 2- he wants to get it in with you- let's say you have 55% equity with your 12+ out draw in these cases
So you win \$102 55% of the time= \$56.1
You lose \$100 45% of the time= \$45
So 40% of the time you're +\$11.10
so you win \$14.04 on average with my assumptions when you flop a big draw that you'd be willing to felt with these better assumptions.

According to the original calculations, you flop your big draw about 7% of the times, which is 13:1. So, if you're calling a raise with these hands 13x-\$4, -42 + 1 hand when you flop your draw and make \$14.4 on average, so even with better assumptions, you're still losing quite a bit of money. It seems to be a lose lose situation if you call with these cards and your opponent folds immediately or gets you all in as the only 2 options- it really seems to me like they need to make big, incorrect folds. Or there needs to be multiway padding in the pot.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Osprey]
#8809498 - 01/18/07 02:43 AM

No one has any thoughts about how getting it all in with a monster draw is not a great thing?

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Osprey]
#8809622 - 01/18/07 02:53 AM

There is another thread that goes over it buried in one of the stickies somewhere. It basically said that getting it in with your monster draw is less +EV than if your opponent folds to your push. We push all in with our draws because we usually have a good deal of FE.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: blackize]
#8809735 - 01/18/07 03:05 AM

So then, really, what's the point of playing these suited connectors? To flop a made hand? Or to force bad folds on semi-bluffs in games where people can fold? It seems to me you don't make near the money back calling raises with these than you would if you just let them go in raised pots.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Osprey]
#8809997 - 01/18/07 03:41 AM

Quote:

It seems to me you don't make near the money back calling raises with these than you would if you just let them go in raised pots.

Accurately gauging your implied odds is a huge part of NLHE.

Typically we will be better than our opponents.

We can

1) Make them fold the best hand some of the time
2) Pick up the hand when they miss some of the time
3) Manage the pot size to either win a small pot or a huge one when we hit.
4) Often our unskilled opponents won't bet enough to give us improper odds to draw.

Position is key in this which is why almost all your play with suited connectors should be done in position.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Osprey]
#8810066 - 01/18/07 03:48 AM

i don't like calling raises with SC even in position with 100BB stacks. SCs are great to steal and re-steal with.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: iSTRONG]
#8810333 - 01/18/07 04:29 AM

Quote:

i don't like calling raises with SC even in position with 100BB stacks. SCs are great to steal and re-steal with.

Good point.

Against poor players who offer high implied odds, I don't mind calling in position with 100BBs. Against players who are much less likely to pay you off they are good for restealing.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: blackize]
#8810463 - 01/18/07 04:53 AM

Yeah, I've noticed in general that stealing in limped or sometimes even raised pots seems to be easy money at .5/1 NL

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Osprey]
#8822705 - 01/18/07 11:08 PM

bumped 1 last time

I think OP missed gutshot plus pair draws which are more infrequent than OESD but about as good. Excellent post though.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: rakemeplz]
#8872905 - 01/23/07 01:16 AM

Quote:

bumped 1 last time.

I'll give it one more. Not sure how I missed this until now. Very useful info. Thanks.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Osprey]
#10827845 - 06/18/07 12:08 AM

Quote:

I don't think it makes a huge difference.
Let's take a best case scenario

Let's assume 100% continuation bets and \$100 stacks.
Raiser pops it to \$4, you call in position with your suited connector.
You flop a 12 outer. Pot is \$10 to the flop heads up
Preflop raiser leads out for \$10, You raise to \$40
Just to be arbitrary lets say it's 40% that the raiser has a hand worth pursuing and will eventually get it in with you on the flop or turn (argue with me if I'm horribly wrong here in my assumption)

Assumption 1: he folds, you win 16 dollars 60% of the time.

Assumption 2- he wants to get it in with you- let's say you have 55% equity with your 12+ out draw in these cases
So you win \$102 55% of the time= \$56.1
You lose \$100 45% of the time= \$45
So 40% of the time you're +\$11.10
so you win \$14.04 on average with my assumptions when you flop a big draw that you'd be willing to felt with these better assumptions.

According to the original calculations, you flop your big draw about 7% of the times, which is 13:1. So, if you're calling a raise with these hands 13x-\$4, -42 + 1 hand when you flop your draw and make \$14.4 on average, so even with better assumptions, you're still losing quite a bit of money. It seems to be a lose lose situation if you call with these cards and your opponent folds immediately or gets you all in as the only 2 options- it really seems to me like they need to make big, incorrect folds. Or there needs to be multiway padding in the pot.

But the problem with this post is that there are huge, gaping holes in your EV calculation.

Sure 1 in 14 times you flop a combo draw and that adds \$14.4 that will be averaged over 14 scnarios, but what about the other 13 scenarios when you dont flop the combo draw?

Sometimes you will flop a pair, 2 pair, a regular flush or straight draw, trips, quads, broadway, royal, etc...

These non-combo draw scenarios need to be considered as you will be stacking sets and overpairs in some of them (as well as getting stacked once in a while and taking down small pots sometimes too).

So the situation is drastically more complex than you've shown it to be, and the EV is much higher than you've shown it to be.

If anyone is interested in a mathematical analysis similar to this one that includes the missing scenarios just respond and you shall recieve.

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: roll]
#12439584 - 10/10/07 08:04 AM

OP, do you have the numbers for a gutshot or better ? that would be one pair hands and gutshot added without counting twice

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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: FlyingStart]
#12441455 - 10/10/07 12:05 PM

Chances of hitting gutshot (and only gutshot) on flop:

Let's say you are holding A2. Flops that give you gutshot should contain 3 & 4, 3 & 5 or 4 & 5. If the flop contains 3 & 4 it shouldn't contain 5 and if it contains 3 & 5 it shouldn't contain 4 but if it contains 4 & 5 it could contain also 3. In that way we avoid double counting. And you also don't want to hit a pair (at least not yet - we'll look at it later) so you don't fancy flops with A or 2. All the possible ways of getting 3 & 4 on flop are:

• 3 4 x
• 3 x 4
• 4 3 x
• 4 x 3

• x 3 4
• x 4 3

x in the first four flops shouldn't be 3 or 4 just to avoid double counting.

Flop | cards you don't want* | number of cards that you don't want

3, 4 A, 2, 5; 3, 4 3*4 + 2*3 = 18
3, 5 A, 2, 4; 3, 5 3*4 + 2*3 = 18
4, 5 A, 2; 4, 5 2*4 + 2*3 = 14

Formula:

p(n) = 2*(4/50 * 4/49 * (48 - n)/48) + 2*(4/50 * (49 - n)/49 * 4/48) + 2*((50-n)/50 * 4/49 * 4/48)

where n stands for the number of cards that you don't want.

Therefore the probability for hitting a gutshot (and only gutshot) with A2 is:

pg = 2*p(18) + p(14) =~ 7,92%

Probability of flopping a pair or better (including gutshot) is:

pp = 2*(3/50 + 3/49 + 3/48) =~ 36,74%

Probability p of hitting gutshot or better is:

p = pp + pg

In this case p =~ 45%

* How to determine the cards you don't want?
First you should write down all of the two cards that help you, starting with lowest two. If you hold for example 98 those cards would be

5 & 6, 5 & 7, 6 & 7, 6 & T, 7 & T, 7 & J, T & J, T & Q, J & Q

You obviously don't want 8 or 9 becouse it would give you a pair which is already counted in pp.
Now start with 5 & 6 and look at all of the other "good two cards" containing either 5 or 6, those are 5 & 7, 6 & 7 and 6 & T. 7 and T are cards you don't want.
5 & 7: The list of other good two cards that contain 5 or 7 is: 5 & 6, 6 & 7, 7 & T and 7 & J, bad cards are 6, T and J.
6 & 7: 5 & 6, 5 & 7, 6 & T, 7 & T, 7 & J but the bad cards are only T and J. 5 is not a bad card becouse in the previous two steps we eliminated flops containing 5, 6 and 7 so we should coun't it now.

And so on

It's really not so complicated as it seems.

Hope it helps!

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Dr_Jeckyl_00
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: maxtower]
#12483378 - 10/13/07 08:33 AM

Quote:

After reading goofy's analysis, it looks like you can profitably play suited connectors 45s - JTs with the 5/10 rule considering the implied odds.
One issue at hand is that the 5/10 rule assumes a reasonble chance you'll net an opponent's stack when you hit your hand. This is fine for the made hands because all of them are beating an over pair. The combo draws are not as good because if you push and your opponent folds, you are getting the correct implied odds to call preflop with the 5/10 rule in the first place. If you push and he calls, you'll hit your hand around 50-60% of the time. With the money already in the pot and the fold equity you might have, going all in with a combo draw is a fine play, however I question whether you have the correct implied odds preflop to get yourself into that situation. There is some math that needs to be worked out here, but it appears suited connectors are not as easy a call as pocket pairs using the 5/10 rule.
A good play may be to call with these in position only. That gives you an added advantage when your opponent checks the flop to you.

what is the 5/10 rule ?

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Chaos_ult
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Re: Suited Connectors, Implied Odds, and You (Theory/Math) [Re: Dr_Jeckyl_00]
#12705292 - 10/28/07 03:30 PM

Bump because I don't think anyone has addressed the fact that you can win the pot without flopping anything. For example, lots of players who check out of position with initiative are weak 100% of the time (along the same lines you can try raising A high boards etc etc). Shouldn't this be included somewhere?

Edited by Chaos_ult (10/28/07 03:36 PM)

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