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The [0,1] game and Derivatives: A Study of Some Poker-Like Games Bill Chen/ Jerrod Ankenman Part 9: A comparison of game values and proving these strategies are optimal. This is part 9 in a many-part investigation of what we will refer to as the [0,1] game, which can in some ways be thought of as analogous to poker ... May 2 2003 by Jerrod Ankenman - 1 message - 1 author |
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Jerrod Ankenman <jerrodanken...@yahoo.com> wrote: The [0,1] game and Derivatives : A Study of Some Poker-Like Games Bill Chen/Jerrod Ankenman Are these articles available in html or pdf (or printed book) form? Usenet plain-text is a bit hard to read. I do have a sort of far-reaching plan to html-ize or potentially ... Mar 7 2003 by Jerrod Ankenman - 22 messages - 5 authors |
The [0,1] Game: Part 8Group: rec.gambling.poker
OK, so this is our solution: y*_1 and x*_1 are both 1-a, or p/(p+1). x1 is (1-a)
^2/(1+a) y1 is (1-a)/(1+a) ...bluffing thresholds are both ... Interesting...
looking at the 'pot-limit' case of p=1, how with both players playing optimally
in this, the action would go 'check-check' (1 - 1/6 - 1/12) x (1 - 1/3 - 1/6)
...
Mar 7 2003 by Jerrod Ankenman - 22 messages - 5 authors
The [0,1] Game: Part 8Group: rec.gambling.poker
We could create this table like this: Y's hand X bets X checks [0,x1] -1 -1 [x1,
y1] p+1 p+1 [y1,y*_1] p+1 p [y*_1,y0] p p [y0,1] p p+1 But since we're only
concerned with the differences here, we simply shortcut by ignoring the size of
the pot when it doesn't matter. Note that when there is bluffing, as for example
...
Mar 6 2003 by Jerrod Ankenman - 22 messages - 5 authors
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The [0,1] game and Derivatives: A Study of Some Poker-Like Games Bill Chen/ Jerrod Ankenman Part 7: The finite pot This is part 7 in a many-part investigation of what we will refer to as the [0,1] game, which can in some ways be thought of as analogous to poker and is actually interesting in its own right . ... Feb 14 2003 by Jerrod Ankenman - 1 message - 1 author |
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X's hand Y's hand X's result Probability [0,r] [0,r] special* r^2 [0,r] [r,1] 0 r(1-r) Shouldn't X's result here be 1? (X bets and Y calls with a weaker hand.) Sorry, I see why this isn't clear. What we're looking at here is the additional bets (past the first one). We know that since both players are to the left ... Jan 29 2003 by Jerrod Ankenman - 3 messages - 2 authors |
The [0,1] Game: Part 6Group: rec.gambling.poker
Jerrod Ankenman jerrodanken...@yahoo.com rec gambling poker The [0,1] game and
Derivatives: A Study of Some Poker-Like Games Bill Chen/Jerrod Ankenman Part 6:
The value of the full infinite pot game Recap to this point: In parts 1-5 we
have solved a number of different games with infinite pots, finding optimal ...
Jan 28 2003 by Jerrod Ankenman - 3 messages - 2 authors
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Jerrod Ankenman jerrodanken...@yahoo.com rec gambling poker The [0,1] game and Derivatives: A Study of Some Poker-Like Games Bill Chen/Jerrod Ankenman Part 5: The full infinite pot game and Game #5 This is part 5 in a many-part investigation of what we will refer to as the [0,1] game, which can in some ways be ... Jan 24 2003 by Jerrod Ankenman - 3 messages - 3 authors |
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However, in investigations that will show up later, we've found that the value of the check-raise becomes far more prominent in at least two cases: 1) When the players have different distributions of hands. Say X gets a number from [0,10] while Y gets a card from [0,1]; it's correct for X to check ALL the time and ... Jan 22 2003 by Jerrod Ankenman - 8 messages - 6 authors |
The [0,1] Game: Part 4Group: rec.gambling.poker
Jerrod Ankenman jerrodanken...@yahoo.com rec gambling poker The [0,1] game and
Derivatives: A Study of Some Poker-Like Games Bill Chen/Jerrod Ankenman Part 4:
Check-raising and Game #4 This is part 4 in a many-part investigation of what we
will refer to as the [0,1] game, which can in some ways be thought of as ...
Jan 21 2003 by Jerrod Ankenman - 8 messages - 6 authors
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