I Used The Whole Time Clock On This River

[gila]

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Correct me if these numbers are wrong (i'm pretty sure some are since I was up all night researching office chairs), but, at any rate.

The SB's holdings:

Hands that beat you: 77 three ways, 75 three ways, k5 three ways, q5 three ways, and a5 four ways (Not counting KK or QQ which I am assuming he doesn't have). So, that's 16 hand combinations he could have that you lose to assumming he does not have a high pocket pair.

Now you have to figure what hands he would 3-bet here (if any) that you would beat. Again, lets assume he does not have pocket aces. Would he 3-bet kq, k7, and ak? If so, then that is 12 ak's, 9 kq's and 9 k7's.

If he 3-bets all these hands that is 30 combinations you beat vs. 16 that beat you (and of course we are not even considering the hands that would tie yet).

So, easy call here if he would 3-bet these. What if he would only 3-bet the kq and k7. You still have 18 wins vs. 16 losses and still have a fairly easy call.

If he only 3-bets the kq then you become a 16-9 dog (again, we are throwing out the ties for now) to have the best hand but still have a call getting 4.5-1 odds.

So, the way I see it, the only way you have a fold is if you think the sb will NOT 3- bet the kq or worse. And if that is the case you will need to caculate the number of wins vs. losses. vs. ties and see how that stacks against the pot odds. Which, in this small pot, would probably make it a fold.

So, what I think this hand comes down to, is: will the sb 3-bet kq or worse in this spot? If yes, call, if no, fold.

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I am pretty sure this is a bit off as you are not considering all the (very likely) hands that make this a split: 52, 53, 54, 56, 58, 59, 5T, 5J. Too tired to figure out how many combinations this is but quite a few obviously.

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I was just considering the wins vs. losses. But, the ties are very easy to figure. You had them all there. Only one five left, so there is 4 52's, 3 53's 4 of every thing else 54's, 56's, 58's, 59's 5T's 5J's.

That should be it. 31 ties if the sb will play ANY hand. I don't really think these change the decision though since they are pushes. What is the difference if you consider winning 30 hands and losing to 16, or if you consider winning 30, losing 16, and tieing 31? Still makes for an easy call if your conclusions about what he will 3-bet are correct.

[krishanleong]

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That should be it. 31 ties if the sb will play ANY hand. I don't really think these change the decision though since they are pushes. What is the difference if you consider winning 30 hands and losing to 16, or if you consider winning 30, losing 16, and tieing 31? Still makes for an easy call if your conclusions about what he will 3-bet are correct.

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Tying makes a big difference. Theoretical spot. Assume you are losing 9 out of 10. Pot lays you 4-1. You fold. Give yourself 30 split hands and you can call. Split equity helps bridge the gap when pot odds aren't quite there.

Krishan

[gila]

Yes, it does matter in the math and in many decisions, but I don't believe it matters in THIS decision with only 31 ties. Of course, it depends what spot you are in and how big the pot is. If your are the favorite, then obvioulsy the ties will make you a smaller favorite, and if you are a dog, the other way.

But, for ties to make a 16-9 dog NOT call a 4.5-1 bet, I would think there would have to be in the hundreds of ties, at least. If somebody could do the math for this, I would sure like to see it.

At any rate, I still do not believe 31 ties turns a 16-9 dog hand getting 4.5-1 from a call to a fold, but please prove me wrong.

Edit: I'm trying to figure out the effects of the ties here, and, actually, I don't think any number of ties would change any of the call/fold decisions in this particular problem. I guess, on that last statement I made, the more ties you could have the BETTER your call, is that correct? And on the hands where you are a favorite, no amount of ties would make the call -ev either (in this situation).