#1
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Same Problem Except All Cards Down
That's obviously easier. So someone do it quickly.
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#2
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I don’t know Why !!!
Defining x as Player1’s critical drawing hand.
Defining y as Player2’s critical drawing hand – given Player1 is NOT drawing. Two equations: Xy=3/8 (y-x)/(1-x)=(1-x)/2 Solving: x= 0,567381 * y= 0,660931 Why do I bother ??? Exercise: What is Player2’s critical drawing hand – given Player1 IS drawing ? Answer is implied in above. BB King’s ... Formerly known as the pokerplayer formerly known as Jack |
#3
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Re: I don’t know Why !!!
Just wondering, what's the rationale behind the first equation?
I got the same answer as you, but I did it the hard way, ie. I got the 2nd equation which was was the same as in the previous problem and then I made an expression for A's EV in terms of x and found its maximum by taking the derivative. That led to 3-4x-4x^3=0, the solution of which is exactly 0.567381 which is the same as what you got. |
#4
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Re: I don’t know Why !!!
Didn't David used to forbid you from these things because you were too good? [img]/images/graemlins/wink.gif[/img]
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#5
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Our solution is wright !?!
<font color="red"> Just wondering, what's the rationale behind the first equation?</font>
If you solve this … <font color="red"> Exercise: What is Player2’s critical drawing hand – given Player1 IS drawing ? Answer is implied in above. </font> … it should be fairly easy to see the rationale behind the first equation. I’m working on a short explanation !? If you need it ? <font color="red"> That led to 3-4x-4x^3=0, the solution of which is exactly 0.567381 which is the same as what you got. </font> Manipulating my two equation’s I got that equation too. This is the key-equation. You got it - I got it. It somehow proof that our solution is wright. BB King’s ... Formerly known as the pokerplayer formerly known as Jack |
#6
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Re: I don’t know Why !!!
[ QUOTE ]
Just wondering, what's the rationale behind the first equation? [/ QUOTE ] I think I can explain this one: Just as the second equation stems from determining player B's cutoff based on player A's cutoff, the first equation stems from player A's cutoff based on player B's cutoff. If A draws, B will draw with anything <0.5, and stand with anything >0.5. So, if A draws, then 50% of the time, when B draws, A will win 1/2 the time, while the other 50% of the time, when B stays, B will on average have 0.75, so A will win 1/4 of the time. So when A draws, he can expect to win (0.5)*(1/2)+(0.5)*(1/4) = 3/8 of the time. When A stands, his expectation is simply X*y (since A will lose whenever Y>y, and will have expectation X when B draws, which he will do fraction y of the time. So A's cutoff is related to B's cutoff by x*y = 3/8. |
#7
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Re: I don’t know Why !!!
Thanks guys, I get it now. (thumbs up icon)
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