Sorta game theory question, I guess.

Daliman · #1 04-21-2005, 02:06 AM

Let's say you are playing a hand of poker, and you have a very good hand all the way to the end. At the end, however, a card hits that makes your hand a bit vulnerable. Your opponent checks, and let's just say for the sake of argument you WILL have the best hand 85% of the time. If you bet and have the best hand, you may or may not get paid off, but if it helps the exercise, let's say 60% of the time that you bet and are winning, you will get paid off. If you bet and get raised, you will call every time. Do not factor for getting checkraised with a worse hand, as that can be offset by you 3 betting with the worse hand, so for these purposes, let's not use it.

Given no additional info regarding betting patterns, tells, etc, would it then be proper to bet it 100% of the time? Or 85%? Is there a specific formula?

TheShootah · #2 04-21-2005, 02:14 AM

Are we to assume every time you get raised you lose?

jdl22 · #3 04-21-2005, 02:23 AM

Just so I'm clear -
I'm ahead 85% of the time,
out of this 85%, 60% of the time he's playing check call
the 15% of the time I'm losing, I'm getting check-raised and foolishly calling

EV of check is clearly zero.
EV of bet:
.15*(-2)+.85*.6 = -.3+.51 = .21

bet every time here since this is greater than zero. Clearly the best line is bet/fold given the way he's playing though that is of course not an equilibrium (he would improve by check raising losing hands).

jdl22 · #4 04-21-2005, 02:30 AM

I discovered that you are asking a different and more deep question.

When considering what you should do in any game, poker being one example, you should consider the EV of each alternative. If the EV of one strategy is greater than the EV of all the other strategies then that's what you should do 100% of the time. In the case of game theory there is some confusion at times due to the common use of mixed strategies in games. In these games players only use mixed strategies when the payoff to each pure strategy being used in the mix is equal. Otherwise this player would improve by playing whichever strategy yields her the best payoff.

What you are referring to is known as probability matching. It's a terrible strategy but in a lot of experiments subjects have been shown to play something like this. For example, suppose I flip a weighted coin and it comes up heads 75% of the time. If we are flipping the coin and I'm offering you even odds you should always go with heads due to it being +EV but many players will choose heads 75% of the time.

Daliman · #5 04-21-2005, 04:21 AM

[ QUOTE ]
I discovered that you are asking a different and more deep question.

When considering what you should do in any game, poker being one example, you should consider the EV of each alternative. If the EV of one strategy is greater than the EV of all the other strategies then that's what you should do 100% of the time. In the case of game theory there is some confusion at times due to the common use of mixed strategies in games. In these games players only use mixed strategies when the payoff to each pure strategy being used in the mix is equal. Otherwise this player would improve by playing whichever strategy yields her the best payoff.

What you are referring to is known as probability matching. It's a terrible strategy but in a lot of experiments subjects have been shown to play something like this. For example, suppose I flip a weighted coin and it comes up heads 75% of the time. If we are flipping the coin and I'm offering you even odds you should always go with heads due to it being +EV but many players will choose heads 75% of the time.

[/ QUOTE ]

Ok ,now we're on to what I was talking about. Now, in the instance of the weighted coin, wouldn't be EV work out exactly the same if you found the proper fulcrum,(which is 75%)?

I guess part of what I am also saying is that if you are winning 85% of the time, wouldn't it be sort of axiomatic that if it were strictly an even money bet, you should DO it 85% of the time?

I guess I don't understand WHY not doing it 100% of the time can't be more profitable.

Nicmavsfan28 · #6 04-21-2005, 04:50 AM

one more question friend, is there any situation in which you can think of that probability matching is advisable? Seems to me that you would have to go with heads 100% of the time to ensure that my positive expectation is fulfilled. Thoughts? [img]/images/graemlins/spade.gif[/img]
Sincerely, nic

Nicmavsfan28 · #7 04-21-2005, 05:06 AM

#If this thought is misguided please tell me why.# Utilizing the weighed coin example: 75% of the time heads comes up:
If you kept count of the amount heads came up over the course of 100 flips and you reached your positive expectation at, lets say, 83 flips. That is to say heads showed up 75 times in about 83 flips on a particular round of 100 flips, here is my question...
Since every time you bet with your crooked acquaintence, heads hit 75 times every time you completed a full round of 100 flips, would it not be more profitable to switch immediately to tails and therefore attempt to win more than your alotted 75% guaranteed heads results. Is it a bad play considering the consistency of heads this round of betting, & what's to stop the same exact coin from hitting heads until the 100th flip and then hitting tails on the next round of betting for the first 31 of 50 times before resuming the pattern? [img]/images/graemlins/spade.gif[/img] [img]/images/graemlins/wink.gif[/img]

morello · #8 04-21-2005, 05:24 AM

[ QUOTE ]

I guess part of what I am also saying is that if you are winning 85% of the time, wouldn't it be sort of axiomatic that if it were strictly an even money bet, you should DO it 85% of the time?

[/ QUOTE ]

Because you can't choose to bet only the 85% of the time that you're ahead. Betting 100% of the time has a positive expectation. Betting less than this will have a less positive expectation.

Of course, the BEST strategy is the bet the 85% of the time that you are ahead, and check the 15% that you are behind.

morello · #9 04-21-2005, 05:28 AM

[ QUOTE ]

Since every time you bet with your crooked acquaintence, heads hit 75 times every time you completed a full round of 100 flips, would it not be more profitable to switch immediately to tails and therefore attempt to win more than your alotted 75% guaranteed heads results.

[/ QUOTE ]

Each flip is an independant event. The fact that it's been heads 75 out of 83 times does not mean it will be tails the next 17. You can't be guaranteed that after 100 flips, you will have exactly a 75/25 breakdown.

Nicmavsfan28 · #10 04-21-2005, 06:03 AM

Yes, yes- i do understand that every flip is an individual event, but i am treating the 100 flips as an individual event, and taking a certain amount of consistency as a given. If you read the end of that excerpt you will see i note that there is no guarantee that the stats will be fulfilled.
What I am getting at is that once the 75% has been fulfilled early (and if it occured at say 96 flips this hypothetical situation would not apply.) then due to the inevitablity of statistics, that you are due a certain amount of losses if you continue to pick heads. Once you have about 21 flips left and you have only flipped tails 3 times then it is reasonable to expect over half of the remaining flips should turn out to be tails 12/21 to be exact. If what im thinking is right then you would be putting yourself in a position to win around 85% rather than 75%. [img]/images/graemlins/spade.gif[/img]