Suited Connectors, Implied Odds, and You (Theory/Math)

[Jamougha]

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.

[ilya]

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.

[Shroomy]

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

[DonkBluffer]

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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).

[/ QUOTE ]

Any chance you can make this program available to the public (or just me [img]/images/graemlins/smile.gif[/img])?

[c_strong]

Goofy,

Really nice post, thanks.

[ QUOTE ]

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

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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.

[nextgenneo]

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?

[ianlippert]

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.

[Jouster777]

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?

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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
Subtract a bit for draws on bad boards (maddog)

[avfletch]

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.

[Jouster777]

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.