a bit on game thoery

[timmer]

It is the river in a full ring stud high game (discount the antes and bring in for this ?)

I am heads up against an open pair of aces I hold an A high 4 flush and the final A was folded in a way my opponent couldnt see but I could.

obviously there are 9 cards that make my hand out of 36 cards remaining in the pack.

there is 8 BB in the pot as is.

my opponent checks .

it is certain that 9 out of the 36 times I improve I should bet out.

How many times out of the 27 times I dont improve should I also bet? considering game theory, the 9:1 pot odds I am offering my opponent, for my bluffing frequency to be optimal?

should and how would I take into account the number of times my opponent may catch 1 of my suit ?

Im am thinking an additional three times but suspect only once may be correct.

just wandering

timmer

[Iceman]

You do need to count the antes and bring-in.

Discounting the possibility that he has a hidden full house:

He's getting 9:1 odds on a call. If more than 10% of your bets are bluffs, he should always call, and you're wasting your money on the extra bluffs. If less than 10% of your bets are bluffs, he can safely fold to your bets, and you could take more advantage of that fact. So the answer is that you should bluff only 1 out of the 36 times that you miss.

In practice, you should only use game theory against very expert players, and instead tailor your bluffing frequency to your opponents. Against calling stations, you should tend to almost never bluff. Against weak-tight players, you should usually bluff much more often than game theory would indicate.

[Jerrod Ankenman]

[ QUOTE ]
In practice, you should only use game theory against very expert players, and instead tailor your bluffing frequency to your opponents. Against calling stations, you should tend to almost never bluff. Against weak-tight players, you should usually bluff much more often than game theory would indicate.

[/ QUOTE ]

Why would you only use game theory against "very expert" players? What if you don't have a particularly good read on an opponent's play? Most players don't get to see enough hands shown down to reliably conclude that a player is a calling station or weaktight, and even these players do not play these ways 100% of the time. Sure, you can overvalue a little bit of evidence, but arguing that you should only use game theory against "very expert" players is a little bit silly. I mean, how many "very expert" players are there in the world, anyway?

Using game theory in these spots assures you of a minimum equity and provides an excellent "base" strategy. Then, as the amount of information you have about the other player increases, you can edge toward exploitive play.

Jerrod

[timmer]

huh? you make you flush 9 times for every 36 tries

so if you are offering 9:1 and you chances of hitting are 25% so you should bluff an amount equivalent to 1/9th of 25% or 2.77% of the time you miss. so you should bet 27.77%
of 36 cards which is 9.9972 cards. 9 of which are flush cards and .9972 which are misses.

this is what I get from pg 174 & 175 of TTOP.

I was wondering if my interpolation was correct

9 good cards to 1 bad card to "make[ing] the odds against my bluffing identical to the odds my opponent would be getting from the pot" TTOP pg 172

I discounted the antes and bring in to make the query simpler. athough for most stud games the number of misses correctly bet would be *roughly* similar

just wandering

timmer

[timmer]

[ QUOTE ]
[ QUOTE ]
In practice, you should only use game theory against very expert players, and instead tailor your bluffing frequency to your opponents. Against calling stations, you should tend to almost never bluff. Against weak-tight players, you should usually bluff much more often than game theory would indicate.

[/ QUOTE ]

Why would you only use game theory against "very expert" players? What if you don't have a particularly good read on an opponent's play? Most players don't get to see enough hands shown down to reliably conclude that a player is a calling station or weaktight, and even these players do not play these ways 100% of the time. Sure, you can overvalue a little bit of evidence, but arguing that you should only use game theory against "very expert" players is a little bit silly. I mean, how many "very expert" players are there in the world, anyway?

Using game theory in these spots assures you of a minimum equity and provides an excellent "base" strategy. Then, as the amount of information you have about the other player increases, you can edge toward exploitive play.

Jerrod

[/ QUOTE ]

the quote is "Against an opponent you think is better than you or against an opponent you dont know, game theory can sometimes enable you to overcome the others judgemental edge" Pg 166 CPT 19 TTOP

this passage makes no mention to "expert players"

just my few cents

timmer

[SumZero]

You make your flush 9 times out of 36. Assuming that your opp will win when ever you don't hit, you'll win when ever you do, and he'll never reraise, and assuming he knows how often you'll bluff and is an optimal player then:

You will bet 9 + x times, where x is the number of times you are bluffing (assume for a second that you will use "miss" cards to decide if you should bluff. So if x were 3 and all the 2's were live you might say you will bluff on any 2 (since there are 3 2's that "miss" you. The 4th 3 is the flush). This means that you can only bluff in multiples of 1/36).

If x is 0, he'll fold every time you bet. In this case you'll win 9*8 = 72 BB. And will lose nothing. So you'll net 72+0 = 72 BB.

If x is 27, he'll call every time you bet. In this case you'll win 9*9 = 81 BB. And will lose 27*1 = 27 BB. So you'll net 81-27 = 54 BB. Clearly this is worse.

If x is 2, and he folds to every bet then: In this case you'll win (9+2)*8 = 88 BB. And you will lose nothing. So you'll net 88+0 = 88 BB. This is clearly good, but what if he always calls you? Now you'll win 9*9 = 81 BB. And will lose 2*1 = 2 BB. This will net you 81-2=79 BB, and is clearly the right strategy if x = 2. So x=2 is better than x=0.

If x is 1, and he folds to every bet then: In this case you'll win (9+1)*8 = 80 BB. And you will lose nothing. So you'll net 80+0 = 80 BB. This is clearly good, but what if he always calls you? Now you'll win 9*9 = 81 BB. And will lose 1 BB. This will net you 81-1 = 80 BB. So here it doesn't matter if he calls you or folds to you, either way you net 80 BB, and is the optimal play against an optimal player.

[Iceman]

In large pots on the river in limit poker, game theory says your bluffing frequency should be very low, like in the example. Given the pot odds you're receiving, and the way players in that particular game and level tend to play, even if you know nothing about your opponent you can usually bluff profitably in that spot much more often than game theory would indicate.

[BruceZ]

[ QUOTE ]
huh? you make you flush 9 times for every 36 tries

so if you are offering 9:1 and you chances of hitting are 25% so you should bluff an amount equivalent to 1/9th of 25% or 2.77% of the time you miss. so you should bet 27.77%
of 36 cards which is 9.9972 cards. 9 of which are flush cards and .9972 which are misses.

[/ QUOTE ]

You mean 2.777...% of the total time, not just of the time you miss. If you didn't round off, you would find that 27.777...% of 36 is exactly 10, not 9.9972. So you should bet on 9 flush cards plus exactly 1 other card. But of course you don't have to go through all of this. Your bet gives your opponent pot odds of 9-to-1, so you want the odds against your bluffing to be 9-to-1. Since 9 cards make your hand, you will bluff on exactly 1 card.

[timmer]

not if you have a scientific calculator it isnt. [img]/images/graemlins/smile.gif[/img]

[BruceZ]

[ QUOTE ]
not if you have a scientific calculator it isnt. [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]

Sure it is. (0.25/9 + 0.25)* 36 = 10. Scientific calculator or not.