Analysis of when to call down to a turn raise

[jtr]

Hi, all.

I've done some basic maths on when you have the odds to call down to a turn raise in limit hold'em. Would appreciate comments / criticisms.

(This was originally posted over in small stakes, as a response to an old thread, but hasn't got a lot of attention so far. I'm hoping that's just because the forum is busy, but if you think what I've written is crap, please feel free to say so.)

First, a few caveats:

1) By default I'm talking about Party Poker 2/4 games. The assumptions I'm making about my opponents' postflop passivity will need to be altered for bigger games, I'm sure.

2) I do realize that these decisions are contextual / hand-specific. I intend the following as a rough guideline to get started.

So, here are the two cases I've thought about. Case one: you've got a big overpair, let's say AA. You raise, you bet the flop, you bet the turn, and get raised (possibly check-raised) by a single opponent. Case two is the same except you've got AK and have hit top pair, top kicker.

Hopefully everyone will agree that a decision on whether to fold or continue must be dependent on the size of the pot. In a truly huge pot, you have to continue; in a small one, you'd lean towards folding.

To simplify things, let's look at the EV for folding now (zero, obviously) versus calling the turn raise and calling the assumed-to-be-inevitable river bet. I know real life is more complicated than this, but given that in these situations you won't really know which cards are your outs (especially if the river card pairs the board) I think this is a decent starting point.

Again, keeping it simple: let's say there are three categories of hand that the opponent may have.

1) A set or monster made hand better than a set, against which we have zero outs, or 2 outs at best in the case of AA versus a set. Call the probability of this case M (for monster hand).

2) A typical raggedy two-pair situation; the opponent having hit on the turn or hit on the flop and slowplayed a little. Against this we have 8 outs in the AA case and 9 outs in the AK case, although we won't know which cards are our outs. Call the probability of this holding T (for two pair).

3) The hand we really hope he has: a complete bluff, top pair with a worse kicker, some crappy semi-bluff draw. Call the probability of this holding B (for BS hand). M+T+B=1, obviously.

Now, after we bet the turn and get raised we assume we're going to pay 2 big bets to see a showdown. Call the number of big bets in the pot at the start of the turn N. So your turn bet makes N+1, the raise makes N+3, and you stand to win N+4 bets for your 2 bets to call down.

Here are two formulas suggesting a minimum size for N to make calling down the right policy.

In the AA case, N(crit) = ( 92 / ( 2M + 8T + 41B )) - 6. In the AK case, there are no outs against the monster, so it's simpler: N(crit) = ( 92 / ( 9T + 43B)) - 6.

I know there are some simplifications in there, but I think those numbers are pretty close, so bear with me.

Now to the real point of my post. At Party 2/4 (or for whatever game you play) what do you think are reasonable values of M, T and B for the typical opponent? What about for a known passive fish? What about for an aggressive, thinking opponent?

I've made a pessimistic start at describing the average passive 2/4 player with M = 0.6, T = 0.35, and B = 0.05. I didn't just pull these out of the air. The two pair number is low-ish because of the number of times the really passive guys just call down with their raggedy two pair. The B number is very low because they just don't raise on the turn much without decent hands. These assumptions lead to cutoff points for N of 9.2 BB in the AA case and 11.3 BB in the AK case. Note that N is the number of big bets in the pot at the beginning of the turn (I did it that way so I can look at the pot size before I even bet the turn and think about whether it's big enough for me to call down if raised).

9.2BB or 11.3BB represent pretty big pots when heads-up on the turn, and imply that most times on 2/4 you'll be folding to a turn raise from a typical opponent. However, it's all very sensitive to the values you choose for M, T, and B -- especially B. If we imagine an aggressive opponent who is equally likely to have a set, two pair, or a semi-bluff draw in this case, we would conclude that N is actually a negative number, meaning that you absolutely call the guy down every time.

Thoughts on the logic very welcome, but also anyone's estimates for M, T, and B at different games. (Speaking selfishly, especially interested in hearing from 2/4 and 3/6 players.)

Cheers,
--JTR.

[D. Andrew]

I think this post deserves at least a reply. You have put some time into this and it is appreciated.

First, I do not think your estimates of M,T and B are accurate. Posters in the other post thought they were. It really does not matter much, as these numbers are dependant on the player and situation.

You have a major flaw in your logic. Simply put, assuming that you will always pay two bets is incorrect. When faced with the decision on the river when you do not improve (assuming your opponent has bet which is not 100%), you will be evaluating your decision soley on B. Using your B=.05, this would be never as the pot will not be laying you 19-1.

[jtr]

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I think this post deserves at least a reply.

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Thanks.

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First, I do not think your estimates of M,T and B are accurate. Posters in the other post thought they were. It really does not matter much, as these numbers are dependant on the player and situation.

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Fair enough. I realize there are many games where my estimates would be way off, but from a moderately detailed study of some hand histories, I came up with those estimates for typical players in the Party 2/4 game.

[ QUOTE ]
You have a major flaw in your logic. Simply put, assuming that you will always pay two bets is incorrect. When faced with the decision on the river when you do not improve (assuming your opponent has bet which is not 100%), you will be evaluating your decision soley on B. Using your B=.05, this would be never as the pot will not be laying you 19-1.

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This is an excellent point. Certainly if you had reason to believe that 2-pair was especially likely to be your opponent's holding, the strategy of calling the turn raise and then folding on the river unless you'd spiked trips or seen the board pair could be very viable. My logic certainly didn't include this: I went with the habit that many of us seem to have (rightly or wrongly) of thinking of the 1BB to call the turn raise, and the 1BB to call on the river, as a package deal. Assuming you've got a voice in your head that says "Don't fold for one bet on the river", as many SSHE readers do, I think it's quite realistic to imagine the two bets as necessarily linked. However, I do take your point -- thanks for the input.

[umdpoker]

in a big pot, i would call down. in a smaller pot, i think this is one of those times that is mostly read dependent. if the guy is a maniac, then i 3-bet and call down a cap. against a slight lag, i probably just call down. against a tight-mr no bluff, then i fold tptk on a coordinated board. with an overpair, i pretty much have to call down unless the guy has never shown down a loser. if i have no notes on somebody, then i lean towards calling down if its close, just because i prefer to have some info on a player.

[D. Andrew]

I went with the habit that many of us seem to have (rightly or wrongly) of thinking of the 1BB to call the turn raise, and the 1BB to call on the river, as a package deal. Assuming you've got a voice in your head that says "Don't fold for one bet on the river", as many SSHE readers do, I think it's quite realistic to imagine the two bets as necessarily linked.

I am not sure if you are trying to defend you model with this or insult me. If for some reason you believe that knowledgeable players are routinely calling river bets as a 19-1 dog when they are only receiving 8.5-1 then I think you are mistaken. I find it much more plausable that the players are calling the river bet when they are better than a 1 in 9.5 favorite; hence B is going to be at least appx 10.5% in your examples of an overpair and TPTK. Then I think you could say "it's quite realistic to imagine the two bets as necessarily linked"; otherwise...

[jtr]

I am most definitely not trying to insult you, D., and I apologize for anything in the post that gave that impression. If I've said something specifically offensive then let me know what it was.

I do feel you're being a little uncharitable here, however. Of course a knowledgeable player will not knowingly call a river bet when he believes himself not to have the pot odds to do so. But on the river it is often difficult to be precise about your chances of holding the best hand. (In contrast to earlier streets in which you can often be quite precise about your chances of drawing to the nuts or thereabouts.) So I do feel that for many players of reasonable experience, calling the turn raise is often done in the knowledge that, disastrous river cards excepted, a river bet will probably be called as well. The reason being that you won't know what your outs are. So it can make sense to look at the odds to call both as a package deal in the way I described. I completely agree with you that this analysis is incomplete and approximate, and that a better analysis would certainly include the option to call the raise and check-fold the river unimproved. If your thinking at the table always covers all of these options then more power to you; mine sometimes does not and I am looking for some speedy heuristics to help with the decision-making process.

In my defence, I'm pretty sure there's a page in SSHE in which the noted poker authority spells out some similar logic. I'll look it up if you think it would help.

And finally, yes, you're right, B of about 10% or more is going to be the threshold at which a strategy of calling down becomes clearly viable.