Quiz#20 Same Concept

[DpR]

[ QUOTE ]
[ QUOTE ]
ace is a good card

[/ QUOTE ]

yea. i think stox played this well.

[/ QUOTE ]

thirded :-)

[emerson]

[ QUOTE ]
emersons post is interesting. i dont know what to make of it.

[/ QUOTE ]

I made a logical and mathematical error in that bluff frequency calculation. If he has about 36% equity with a small pair against our range, meaning that 64% of the time we will have him beat and bet, then the chance that we are bluffing cannot be greater than his pot odds to be optimal. He is getting 6.25 to 1. So the correct bluffing default, before we take opponent tendencies into account, would be about 10.25%. To get that frequency we bluff about 28.5% here, not the 40% that I posted previously. (10.25% /36%)


I agree with those who don't like the river bet. We already beat most of the missed draws.

[bboy_]

how did you get that 28.5%?

[greatwhite]

[ QUOTE ]
[ QUOTE ]
emersons post is interesting. i dont know what to make of it.

[/ QUOTE ]

I made a logical and mathematical error in that bluff frequency calculation. If he has about 36% equity with a small pair against our range, meaning that 64% of the time we will have him beat and bet, then the chance that we are bluffing cannot be greater than his pot odds to be optimal. He is getting 6.25 to 1. So the correct bluffing default, before we take opponent tendencies into account, would be about 10.25%. To get that frequency we bluff about 28.5% here, not the 40% that I posted previously. (10.25% /36%)


I agree with those who don't like the river bet. We already beat most of the missed draws.

[/ QUOTE ]
I don't think that the passive player who has been calling down with his pair of 4's understands this. Against a TAG this hand is most likely played differently postflop. You'd think that a TAG would raise on the flop or turn with a low pair to protect his hand, driving you out of the pot.

[disjunction]

IMHO loose passives are loose passives because they chase their aces and/or other draws too much, not because they can't make teh big laydowns when the situation calls for it.

[emerson]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
emersons post is interesting. i dont know what to make of it.

[/ QUOTE ]

I made a logical and mathematical error in that bluff frequency calculation. If he has about 36% equity with a small pair against our range, meaning that 64% of the time we will have him beat and bet, then the chance that we are bluffing cannot be greater than his pot odds to be optimal. He is getting 6.25 to 1. So the correct bluffing default, before we take opponent tendencies into account, would be about 10.25%. To get that frequency we bluff about 28.5% here, not the 40% that I posted previously. (10.25% /36%)


I agree with those who don't like the river bet. We already beat most of the missed draws.

[/ QUOTE ]
I don't think that the passive player who has been calling down with his pair of 4's understands this. Against a TAG this hand is most likely played differently postflop. You'd think that a TAG would raise on the flop or turn with a low pair to protect his hand, driving you out of the pot.

[/ QUOTE ]

This is really the same issue that Harmon discusses in the limit section of Super System 2 when she says not to bluff with AK high. The rationale is that you already beat the missed draws and those that made small pairs along the way are not going to fold once they get to the river very often. In this case an AK is on the board, so Q high would be about the same thing. True, this is not the nut no pair. That would be QJ. But there are only three better hands that have a high likelihood of folding here. I think that bluffing any more than the optimal amount would be a mistake here, and I really don't think you should bluff here with any hand better than jack high.

[emerson]

[ QUOTE ]
i think it has merit against a thinking opponent rather than a loose passive.

it's also possible that us betting and him calling are -ev for both parties, correct?

[/ QUOTE ]

That's not really possible. You can have a situation where there is negative log growth for both parties. That happens when you make a positive expectation bet that is more than twice the Kelly fraction relative to your bank. It is negative log for both. But both sides of a bet can't have negative ev in poker unless it is related to the rake. That is not the case here. If you ran this situation a billion times they can't both lose money. There is no place for the excess to go.

[emerson]

[ QUOTE ]
how did you get that 28.5%?

[/ QUOTE ]

Okay, here is the math. We determined that a small pair has approx 36% equity against hero's open raising range from the button. This means that 64% of the time the small pair is beat on the river. He is getting pot odds of 6.25 to call. If we bet here every time it would be profitable for him to call in such situations. For an optimal bluff we want his chance of winning to be no better than his pot odds. So we divide 64% by 6.25. That comes to 10.24%.

So this means that we are betting about 74.25%. Checking behind 25.75%. Of the times we are betting, if the small pair calls, he wins less than once out of 6.25 times. So it is not profitable.

Now, we arrive at the decision point of whether to bluff or check 36% of the time. In order that our total bluff % is 10.25%, we bluff 28.5% of that 36%.

.285 * .36= .1026

This gives us just about the total percentage we are looking for. This is just a default, however. You bluff either more or less frequently depending on your read of the opponent. I think in this situation we bluff less, not more frequently, than optimal.

[bboy_]

interesting stuff. this is 'game theory' math right?

i don't understand the math in the first example but the second one got me thinking.

[emerson]

[ QUOTE ]
interesting stuff. this is 'game theory' math right?

i don't understand the math in the first example but the second one got me thinking.

[/ QUOTE ]

That's good, cause there was a flaw in the logic I used in the first example.