Results not important, please critique flop and turn play

[LearnedfromTV]

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Thus the call can only be correct if hero could have such a good read that the majority of the time the villain would not have a straight.

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This is way wrong.

Hero has to call $88 into a $301 pot.

When the Villain has the straight Hero's EV is $301*10/42 = $72

When the Villain doesn't have the straight, let's say 50% of the time he semibluffing and has on average 8 outs to a straight, and 50% of the time he's either drawing dead (or drawing to one card, the extremely unlikely, given the action, lower set)

So when villain doesn't have the straight, Hero's EV is $301*0.5 + 301*(34/42)*0.5 = $272

72*(1-x) + 272*x = 88 -----> x = .08.

So he has to have the straight greater than 92% of the time to make the call incorrect.

(Even if Villain has an average of ten outs (i.e. he *only* makes this bet with big straight draws and *never* with two pair or as a bluff), he still would have to have the straight about 90% of the time to make a call incorrect.)

[BluffTHIS!]

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Hero has to call $88 into a $301 pot.

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Learning from TV can be hazardous to your poker career. The pot was only $301 after hero called villain's bet on the turn and villain was allin.

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The pot was only $301 after hero called villain's bet on the turn and villain was allin.

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The way he did the math, this is taken into account. he showed that the call is worth more than $88 as long as the opponent doesn't have the straight 8% of the time or more.

[BluffTHIS!]

That is not true. Hero is being offerred odds of $213 for calling a bet of $88 on the turn. His call does NOT count in the EV calculations. He can either win $213 or lose $88 for making that $88 bet.

There are 5 cases:

1) Villain has the straight and hero does not draw out;
2) Villain has the straight and hero draws out;
3) Villain does not have the straight but does have a straight draw and draws out;
4) Villain does not have a straight but does have a draw but does not draw out;
5) Villain does not have a straight and is bluffing or drawing dead or only to 1 card.

Calculate the probability of each case that is possible with the river board, determine each case's payoff/loss (expectation), multiply the probabilities of each case by its expectation, and add them up for an overall EV.

With the other assumptions that poster made as to percentages of time villain has a draw or is drawing dead when not having the straight on the turn, you will find that the villain has to not have the straight on the turn >73% of the time for hero's call to be +EV. However this would change if you gave a substantially greater probability to villain playing a lower set/overpair in a funny manner with no straight draws to go with it.

[LearnedfromTV]

[ QUOTE ]
That is not true. Hero is being offerred odds of $213 for calling a bet of $88 on the turn. His call does NOT count in the EV calculations. He can either win $213 or lose $88 for making that $88 bet.

There are 5 cases:

1) Villain has the straight and hero does not draw out;
2) Villain has the straight and hero draws out;
3) Villain does not have the straight but does have a straight draw and draws out;
4) Villain does not have a straight but does have a draw but does not draw out;
5) Villain does not have a straight and is bluffing or drawing dead or only to 1 card.

Calculate the probability of each case that is possible with the river board, determine each case's payoff/loss (expectation), multiply the probabilities of each case by its expectation, and add them up for an overall EV.

With the other assumptions that poster made as to percentages of time villain has a draw or is drawing dead when not having the straight on the turn, you will find that the villain has to not have the straight on the turn >73% of the time for hero's call to be +EV. However this would change if you gave a substantially greater probability to villain playing a lower set/overpair in a funny manner with no straight draws to go with it.

[/ QUOTE ]

You are wrong. If he calls and wins he gets $301 dollars, including his $88 back.

The question is how often he has to be ahead on the turn for his equity in the $301 pot to be $88. If his equity is $88 the call is neutral EV. If his equity is > $88 the call is + EV. His equity is what I calculated. The algebraic expression in my first post gave his equity as a function of x, the probability he Villain did not have the straight. I set that expression equal to $88 to solve for the value of x that gives neutral EV.

Calling the pot 213 and thinking of the bet as -88 instead of 301 and 0 is fine, but all this will do is reduce the left side by 88. You have to set that expression equal to 0 before solving for x though, because the expression has become an EV function instead of an equity function. The value of x will be the same.

OK, in summary about TV's post:

- math is correct
- use of "EV" is wrong

Based on EV:

Pot = 213

cost of call = -88

% to win if villain has straight = 10/42
% to win if villain has lower set = 41/42
% to win if villain has AA45 = 27/40

AA45 (or AA35) is the best draw that doesn't have a straight already.

If villain has set or worse:
EV = -88/42 + 213*41/42 = +206

draw:
EV = -88*13/40 + 213*27/40 = +115

straight:
EV = -88*32/42 + 213*10/42 = -16

50/50 split between draw and underset yields:

x(115+206)/2 + (1-x)*-16 >= 0
x >= 0.09 (9% "bluffing")

if all bluffs are draw the maximum draw ...
x(115) + (1-x)*-16 >= 0
x >= 0.12 (12% "bluffing")
This is the worst case scenario.

Finally, if we change the draw to 8 outs and assume a 50/50 split as TV did, x >= 8%.

So TV was correct.

[LearnedfromTV]

[ QUOTE ]
OK, in summary about TV's post:

- math is correct
- use of "EV" is wrong


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Good post Acorns. I only count ten outs for AA45/AA35 though (two A, 8 straight making cards). I don't think any hand has more though. I think open-ended is the best he can be without a made staight. I could be wrong there though.

In my first post, using the phrase "Hero's EV" was misleading. I should have said Hero's equity. But the difference is a semantic one - these two sentences:

The expected value of Hero's stake in the pot is $88 if Villain has the straight 92% of the time.

and

The expected value of the $88 call is $0 if Villain has the straight 92% of the time.

are both appropriate. When one speaks of +EV and -EV decisions, the context is that of the second case (evaluating a wager), but expected value is still a meaningful term in the first case (evaluating an expected stake, or equity). In poker discussion, the convention is that people usually mean the second case.

Either way, a significant source of error (in poker and many other areas) is people making off-the-cuff statements like "has to not have the straight a majority of the time" that seem reasonable without thinking them through. Clearly we are nowhere close to needing a majority.

[BluffTHIS!]

I asked 2+2's resident probability expert Bruce Z to review this thread and give his response below. Note that when he says you/your he is referring to my (Bluff's) method. (Thank you Bruce for your time on this.)

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LearnedfromTV is correct. You have described the correct method of computing the expected value of the amount won, where you consider the two possible outcomes +213 and -88, and you compare this EV to zero to determine whether or not to call. His method is a valid alternative which computes the expected value of the final amount of chips in hand, where the two possible values are +301 and 0, and he compares this final amount to +88 instead of zero, since this is how many chips he would retain if he folds.


Your method:

EV = P(win)*213 + [1-P(win)]*(-88) > 0


His method:

P(win)*(213+88) + [1-P(win)]*0 > +88


As you can see, these methods are equivalent, as your method simply subtracts P(win)*88 from the first term, and then adds [1-P(win)]*(-88), which has the net effect of adding -88 to the left side, and so your right side is 0 instead of +88. His method has the advantage of only having to do 1 multiply, since the probability of losing is multiplied by zero. Both methods give the same answer.


His method:

$301*10/42 = $72

$301*0.5 + 301*(34/42)*0.5 = $272

72*(1-x) + 272*x = 88 -----> x = .08.


Your method:

$213*10/42 = $50.71

-$88*(1 - 10/42) = -$67.05

$213*0.5 + 213*(34/42)*0.5 = $192.71

-$88*(1 - 0.5 - 34/42*0.5) = - $8.38

($50.71 - $67.05)*(1-x) + (192.71 - 8.38)*x = 0 -----> x = .08.


I would simply compute the odds of winning, and then compare this to pot odds.


My method:

x is the probability that your opponent does not have a straight, so (1-x) is the probability that he does have it:

P(win) = (1-x)*(10/42) + x*(0.5 + 0.5*34/42) > 88/(213+88)


As you can see multiplying both sides by 213+88=301 gives his method. When you compute the pot odds, you do not include your own bet, but then you compare the pot odds 213:88 to the odds against winning. An alternative is to include your own bet, and then compare the fraction 88/(213+88) to the probability of winning rather than the odds, as I have shown above.

-Bruce

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Well, if we have shown anything, it is that calling this a no-brainer was probably a bit of a misnomer! [img]/images/graemlins/laugh.gif[/img]

This last method mentioned by Bruce is the one that I most frequently use during a hand, mostly because I find it easier to estimate the probability of winning and compare that to the ratio of my bet to total pot on the fly.

So, basically it comes down to whether or not you think there is a ~10% chance that villian has less than a straight in this case. I agree with Bluff in that most opponents would have check/raised with two pair on the flop. However, I have seen Villians line equal a naked 1 pair or 1 pair + weak draw on the flop and 2 pair on the turn enough for me to justify making the call against most opponents (facing a 2/3 pot all-in turn bet).

[Tilt]

I still think that call is a no brainer. There is almost always a 10% chance that an opponent in this position will be bluffing the straight.

You don't need to do the heavy math on the fly. Just ask yourself, when your set appears busted and you have to make a call, am I getting 3:1 on my money? If not, is it real close, like within 10% of 3:1? If so I would almost always make the call. Even if it turns out for that particular player that there was no chance he was bluffing, your lost EV has metagame benefits. If you get bluffed off big pots at the river often you will lose a lot of money at this game.