KQ .5/1 hand

[Aaron W.]

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Here's some additional thoughts about my raise on the river; I sat down and figured out the math.

Assuming everything else in the hand plays out the same way, each time,

1) If he is bluffing with his bet, maybe 10% of the time i will win 12.75BB unimproved.
2) If he will fold to a raise, maybe 10% of the time, i will win 12.75BB.
3) Maybe 80% of the time he will win 12.75BB, including when he re-raises, which I would fold to.

So, in 10 times i will gain 25.50BB by wagering a total of 10 extra big bets on the river, which means i will have a net profit of 15.50BB by betting on the river. Again, let me know what you think.

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I think you are overconfident on your ability to fold out villain. If he's bluffing, he's not calling -- he's folding to your raise. It's highly doubtful that he's folding any hand that is better than yours. I think you've got about a 5% chance of winning this pot, not the 20% you envision. Don't forget that there are still players left to act, who may still call with hands that beat you.

[imported_adhoc]

Well, here's something else that occured to me. I think that, because the pot is large by the river, one could call his bet in my position unimproved, even though this could only hope to beat a bluff. Such a call might win perhaps 10 percent of the time. So, using the same assumptions I made, this would mean I would gain 10.75BB once in 10 times, which is less than the 15.50BB I might win by raising. Thoughts?

[Aaron W.]

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With QK I figured I had 6 outs because the flop was ragged and checked to me. I would otherwise count it as 3 outs. With the backdoor straight worth 1.5 outs, I guessed I had 7.5 outs, similar to an open ender or flush draw; giving me something like 2 1/4 to 1 to make a hand by the river.

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You are overestimating your outs just a little bit. You've got to knock down your overcard outs because of the flush draw and the large field. I'd give you about 5-6 outs here.

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I bet on the flop because I figured it would be good to try and take 2 free cards against a table of passive opponents, as one would do with a flush draw - which worked. There was also the possibility that I might win unimproved, so it could also be construed as a value bet.

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Don't think of this as a value bet. K-high isn't a value betting hand as flush draws are. If you hit one of your overcard outs, there are still many redraws against you (two pair, trips, an ace). If you hit a flush, the liklihood of someone having a redraw to beat you is much much smaller.

How often do you estimate you have the best hand here?

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The bet on the river was a bluff. I hoped the villain might think I was trying to trap him with the 4's and fold, and did not think I could win with anything by calling after he bet, for the reasons already mentioned. Do you still think this is so bad?

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Yes, it's still very bad.

[Aaron W.]

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Here's some additional thoughts about my raise on the river; I sat down and figured out the math.

Assuming everything else in the hand plays out the same way, each time,

1) If he is bluffing with his bet, maybe 10% of the time i will win 12.75BB unimproved.
2) If he will fold to a raise, maybe 10% of the time, i will win 12.75BB.
3) Maybe 80% of the time he will win 12.75BB, including when he re-raises, which I would fold to.

So, in 10 times i will gain 25.50BB by wagering a total of 10 extra big bets on the river, which means i will have a net profit of 15.50BB by betting on the river.

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And another thing... you're wagering 20 BB total on the river, not just 10.

[Aaron W.]

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Well, here's something else that occured to me. I think that, because the pot is large by the river, one could call his bet in my position unimproved, even though this could only hope to beat a bluff. Such a call might win perhaps 10 percent of the time. So, using the same assumptions I made, this would mean I would gain 10.75BB once in 10 times, which is less than the 15.50BB I might win by raising. Thoughts?

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I think you're too focused on picking off a bluff, and you don't know how weak your hand is in this spot. Too many hands beat you here.

Calling with a pair would be fine. But calling with king-high is not.

[imported_adhoc]

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And another thing... you're wagering 20 BB total on the river, not just 10.

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By 10 extra bets, I mean the extra bet of raising rather than just calling, which I would do otherwise. If you assume all of my guesses about the different percentages of things happening are correct, which another poster said were not realistic, would this play still be unprofitable? Could you give me your breakdown in the same fashion I tried to offer mine? Maybe I counted incorrectly, and I'm curious as to how you see the likelihood of the different results vs. the extra bets.

[Aaron W.]

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And another thing... you're wagering 20 BB total on the river, not just 10.

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By 10 extra bets, I mean the extra bet of raising rather than just calling, which I would do otherwise. If you assume all of my guesses about the different percentages of things happening are correct, which another poster said were not realistic, would this play still be unprofitable? Maybe I counted incorrectly.

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This is a bad EV calculation. You cannot neglect the investment you are making with the call because you are not calculating what the 'extra' bet is doing. You are calculating what a *RAISE* will do. The 'extra' bet is folding out weaker hands and getting called by better hands. The 'extra' bet is *NOT* winning the pot for you.

[imported_adhoc]

OK, but what would be a realistic EV calculation for this river play vs. calling? That is, why is it unprofitable in your opinion, and how unprofitable would it be over a sample size like, for instance, 10 hands?

[Aaron W.]

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OK, but what would be a realistic EV calculation for this play? That is, why is it unprofitable in your opinion, and how unprofitable over a sample size like, for instance, 10 hands?

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It's not a sample size issue, since you're making up the probabilities on your own. In theoretical terms, it's an exact value.

Here's a full EV calculation:

When it is your action, the pot has 9.75 BB in it. We'll round it up to 10 just for simplicity (you can do it with the exact value on your own).

Case 1: You fold.

When you fold, your EV is 0 since every time you end up having lost no money and having gained no money.

Case 2: You call.

What can happen?

a) There is no raise and you have a losing hand (maybe villain has it, maybe one of the other players has it) or there is a raise and you fold. This happens x times out of 100 (so x/100 is the percent). In both situations, you lose 1 BB.
b) There is no raise and you have the best hand. This is the only remaining possibility, so this happens 100-x times out of 100 and you win 10 BB. (You may think, "what if another player overcalls? Then the pot will be bigger." But if a player overcalls, he has king-high beat.)

Now we need to estimate the various probabilities. This is where things become highly subjective. I think you've got the best hand about 5% of the time. So we set x = 95.

Finally, we compute EV:

EV = (prob of event a)*(Value of event a) + (prob of event b)*(Value of event b)
= .95*(-1) + .05*(10)
= -.45

So every time you call, you lose about half a big bet.

Case 3: You raise

a) You get called by a better hand, or there is a raise and you fold. This happens x times out of 100. In both situations, you lose 2 BB.
b) You get called by a worse hand. This happens y times out 100 and you win 11 BB (only one more from villain, since you don't count your own bets as profit).
c) You win with no showdown. This is the last possibility, so it happens 1-x-y times out of 100. You win 10 BB.

Again, we estimate. Since we estimated that you have a 5% chance of having the best hand in the previous case, it must not change when we consider this case. But you fold out lots of those hands that you beat with your raise. So let's say y = 3. Let's say you fold out a better hand 5% of the time, so that 7% of the time you win with no showdown. This gives x = 90 and 1-x-y = 7

EV = .9*(-2) + 11*(.03) + 10*(.07)
= -1.8 + .33 + .7
= -0.77

Therefore, folding is better than calling, and calling is better than raising.

You would need to pick off a better hand about 10% of the time for a call here to be profitable. But this is dubious since

1) There are 4 opponents on the river, which makes the chances that *NOBODY* has a pair very small.
2) It's not often that someone bluffs into 4 opponents, so villain often has *SOMETHING*.
3) There are some bluffs that will *STILL* beat you, namely ace-high hands (say A2 or A5 that missed the gutshot).

[SteveL91]

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So, in 10 times i will gain 25.50BB by wagering a total of 10 extra big bets on the river, which means i will have a net profit of 15.50BB by betting on the river. Again, let me know what you think.

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Since I'm a veritable math-moron, I won't even touch that. I will, however, ask you to think about this logically. You raise PF and bet the flop (not a good idea, in my opinion). You then check the turn that pairs the board. What do you think you're going to fold by raising another brick? While it does complete a straight-draw, people tend to put PFRs on things like AK and not 56. There's no way you're getting a better hand to fold anywhere near often enough to make this raise profitable. You need to try this move on someone capable of folding, and even then, this isn't the spot to try it, in my opinion. The board just isn't scary enough and to reiterate, the river was a brick from the villain's point of view.