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

[rakemeplz]

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.

[HebbNH]

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bumped 1 last time.

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

[roll]

This thread owns.

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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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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.

[FlyingStart]

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

[kozyanski]

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:

<ul type="square">[*]3 4 x[*]3 x 4[*]4 3 x[*]4 x 3
[*]x 3 4[*]x 4 3[/list]
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 &amp; 6, 5 &amp; 7, 6 &amp; 7, 6 &amp; T, 7 &amp; T, 7 &amp; J, T &amp; J, T &amp; Q, J &amp; 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 &amp; 6 and look at all of the other "good two cards" containing either 5 or 6, those are 5 &amp; 7, 6 &amp; 7 and 6 &amp; T. 7 and T are cards you don't want.
5 &amp; 7: The list of other good two cards that contain 5 or 7 is: 5 &amp; 6, 6 &amp; 7, 7 &amp; T and 7 &amp; J, bad cards are 6, T and J.
6 &amp; 7: 5 &amp; 6, 5 &amp; 7, 6 &amp; T, 7 &amp; T, 7 &amp; 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!

[Dr_Jeckyl_00]

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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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what is the 5/10 rule ?

[Chaos_ult]

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?

Edit: apologize if someone has already asked this, I didn't read the whole thread.