Forum: Poker Theory
09-20-2007, 03:44 PM
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Replies: 102
Views: 439
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Forum: Poker Theory
09-20-2007, 11:05 AM
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Replies: 102
Views: 439
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Forum: Heads Up Poker
09-10-2007, 02:11 PM
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Replies: 49
Views: 191
Re: Why Position Matters Using Game Theory
With optimal play on both sides, player 2 will have a positional advantage, but under optimal play each player will be using a best response to the other players strategy.
In my example which...
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Forum: Heads Up Poker
09-10-2007, 01:19 PM
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Replies: 49
Views: 191
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Forum: Heads Up Poker
09-10-2007, 12:23 PM
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Replies: 49
Views: 191
Re: Why Position Matters Using Game Theory
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If player one bets with [0,0.1] and [0.8,1] then player two should/could call with [0.8,1] .
If player one checks with [0.1,0.8] then player two should/could bet with [1/3,0.8] and...
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Forum: Heads Up Poker
09-10-2007, 09:03 AM
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Replies: 49
Views: 191
Re: Why Position Matters Using Game Theory
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I have to change my formula set up to include the equity you get when both hands get checked .
Here is player 1's equity using a=3/7 with corrections .
The only profit player 1...
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Forum: Heads Up Poker
09-09-2007, 07:17 PM
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Replies: 49
Views: 191
Re: Why Position Matters Using Game Theory
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Mykey , you have my EV wrong .
If player one shoves with 1/4 + , then his
EV= 3*0.5*0.5 - 1 = -0.25
Just plug the numbers into my EV equation .
EV using your strategy is :
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Forum: Heads Up Poker
09-08-2007, 10:26 AM
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Replies: 78
Views: 291
Re: Heads Up Game Theory exercise
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to marv, mikey and other guys who study stuff way over my head:
can you please tell me why you have SB bluffing with his worst hands? Intuitively it seems like "bluffing" with your better...
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Forum: Heads Up Poker
09-07-2007, 09:50 PM
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Replies: 78
Views: 291
Re: Heads Up Game Theory exercise
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For the SB, the sum of all Jam fractions from 1 to 62 must total 37/2
In the case of
1..16 jam
17 mixed
15..59 fold
60..100 jam
The jam fractions for 1..16 and 60..62 (1/1 each)...
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Forum: Heads Up Poker
09-07-2007, 05:15 PM
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Replies: 78
Views: 291
Re: Heads Up Game Theory exercise
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I nearly agree with this answer.
This is a jam/fold problem with smallblind=1 bigblind=2.
With stacksize=6 (SB can raise to 3x BB) I get a solution of...
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Forum: Heads Up Poker
09-07-2007, 03:54 PM
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Replies: 78
Views: 291
Re: Heads Up Game Theory exercise
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[ QUOTE ]
I nearly agree with this answer.
This is a jam/fold problem with smallblind=1 bigblind=2.
With stacksize=6 (SB can raise to 3x BB) I get a solution of
SB:
1..16 jam...
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Forum: Heads Up Poker
09-07-2007, 03:41 PM
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Replies: 78
Views: 291
Re: Heads Up Game Theory exercise
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Marv there are many solutions to this . Yours is one of them and so is Mykey's as well as mine .
You can't do any better than folding 1-43, shoving with 44+ .BB would call with 63+ ....
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Forum: Heads Up Poker
09-07-2007, 09:49 AM
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Replies: 78
Views: 291
Re: Heads Up Game Theory exercise
I nearly agree with this answer.
This is a jam/fold problem with smallblind=1 bigblind=2.
With stacksize=6 (SB can raise to 3x BB) I get a solution of
SB:
1..16 jam
17 mixed
18..59 ...
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Forum: Internet Gambling
09-02-2007, 09:39 PM
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Replies: 44
Views: 672
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Forum: News, Views, and Gossip
07-24-2007, 09:34 PM
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Replies: 187
Views: 625
Re: Second Session Just Started
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2+2 should really dissect these research papers that the U of A is putting out.
http://www.cs.ualberta.ca/~games/poker/ (scroll down for publications)
i have read most of Morgan...
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Forum: News, Views, and Gossip
07-24-2007, 07:00 PM
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Replies: 187
Views: 625
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Forum: Probability
06-22-2007, 09:24 PM
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Replies: 10
Views: 79
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Forum: Probability
04-13-2007, 05:07 PM
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Replies: 62
Views: 309
Re: April 2007 IBM Ponder This Challenge
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I don't think you can deduce S is stationary from what you've done here. If t were restricted to say [-10,10], then we could easily construct a suitable X and S process.
[/...
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Forum: Probability
04-13-2007, 04:28 PM
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Replies: 62
Views: 309
Re: April 2007 IBM Ponder This Challenge
I don't think you can deduce S is stationary from what you've done here. If t were restricted to say [-10,10], then we could easily construct a suitable X and S process.
We can define a backwards...
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Forum: Probability
03-12-2007, 10:29 PM
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Replies: 13
Views: 101
Re: Sessions of random length and variance
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What are E(N) and Var(N) equal to here?
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E[N] = infty.
Let N be the first time |Z_n| > c, where c is at least 1. Let T(n) = min(n,N). Since (S_n)^2 - n is a...
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Forum: Probability
03-10-2007, 10:47 PM
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Replies: 13
Views: 101
Re: Sessions of random length and variance
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Okay, I think this is a valid non-anticipating counterexample. Let X_j be 1 or -1 with equal likelihood. Let N be the first time that |Z_N| > 2. By the law of the iterated logarithm, N is...
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Forum: Probability
03-10-2007, 01:29 PM
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Replies: 13
Views: 101
Re: Sessions of random length and variance
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Thanks, marv. That's a nice example. For the record, I will point out that your N not only looks into the future, but it is also not bounded by any fixed constant.
Nonetheless, you have...
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Forum: Probability
03-10-2007, 11:30 AM
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Replies: 13
Views: 101
Re: Sessions of random length and variance
Assume X_i = +1 or -1. If we can look into the future, just pick N = least s.t. X_{N+1} != X_N.
Then Z_N = sqrt(N) X_1. As N and X_1 are independent, E(Z_N) = 0 and Var(Z_N) = E((Z_N)^2) = E(N) =...
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Forum: Probability
03-01-2007, 09:46 PM
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Replies: 23
Views: 126
Re: 100 Prisoners
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oops. I didn't see Marv's post. Looks like he has solved it. Now can we prove his method works without the simulation?
PairTheBoard
[/ QUOTE ]
Yes. Think...
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Forum: Probability
03-01-2007, 12:54 PM
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Replies: 23
Views: 126
Re: 100 Prisoners
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I think this is a very nice puzzle which got buried under a pile of crap. So here it is with its own thread.
A prison contains 100 prisoners. In a special room are 100 boxes. Each box...
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