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Shamrock
Posted: Tue Aug 04, 2009 2:39 pm Reply with quote
Joined: 15 Feb 2007 Posts: 162 Location: Plano
Here's the problem: You have to construct holecards for two players, X and Y, and four community cards (i.e. as if the turn had been dealt but not the river) such that:

(1) If the hands were turned over at this point (before the river card is dealt), Player Y would win at showdown.
(2) Player X has the most equity possible given constraint (1). For the purposes of this calculation, equity for Player X can be computed as (river cards that give Player X a win + 0.5 * river cards that chop the pot) / 44. (The 44 is the number of cards remaining in the deck; anyway, it's irrelevant, all you have to do is maximize the numerator.)

As a warm up, suppose we give Player Y 2 Spade 2 Club and Player X Q Heart J Heart and the board is T Heart 9 Heart 9 Diamond 4 Club .

In this case, condition (1) is satisfied since Player Y currently has two pairs, nines and twos, while Player X just has a pair of nines with QJT kickers. In this example, Player X has 8 flush outs (the 2 gives Player Y a full house), 6 additional straight outs, 6 natural pair outs, and 5 more outs to double pair the board and counterfeit Player Y's 2s. Thus Player X has a total of 26 outs, so his equity is 25/44 = 56.8%.

The first challenge is to beat this number and then the second challenge is to figure out what the maximal possible equity is for Player A and how to achieve it.

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Azreal
Posted: Wed Aug 05, 2009 2:18 pm Reply with quote
Joined: 06 Mar 2007 Posts: 44
yeah couldn't find a better way to msg you... you and dori play the jack and jill tourney anymore recently? amy and i planning on heading up and hopefully having some fun at it this weekend.
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Shamrock
Posted: Fri Aug 07, 2009 5:49 pm Reply with quote
Joined: 15 Feb 2007 Posts: 162 Location: Plano
Azreal,

We haven't playedey in one together recently, but Merlot did go play the last one they had up at Choctaw. Lets just say they had some issues to iron out. For instance they had all of the guys play first, and then the girls. This kind of defeats the purpose. They asked Merlotgirl for ideas on how to run a good J&J tournament and she gave them the info, it's yet to be seen if they took her ideas and implemented them.

Good luck

Shamrock

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Shamrock
Posted: Sun Aug 09, 2009 8:00 am Reply with quote
Joined: 15 Feb 2007 Posts: 162 Location: Plano
Based on the huge response I've decided to end all of this wild discussion on the topic, and post the answer.

If player X has 5 Heart 6 Heart and player Y has 7 Club 2 Diamond and the board reads 3 Heart 4 Heart 3 Spade 4 Spade we have the optimum result. Player Y is ahead at the moment by virtue of his 2 pair with 7 high kicker. However, Player X has 71.59% equity. There is no card that could come out which would make X lose the hand. Any 8 - A is a split pot. Any 2 or 7 gives X a str8 and the win. Any 5 or 6 gives X the win with a higher 2 pair than Y. Any Heart and X wins with a flush. Any 3 or 4 puts a boat on the board, and splits the pot.

So X has a 43.18% chance of winning the pot and a 28.41% chance of chopping it. Giving X 71.59% equity compared to the 28.41% equity that Y has to chop.


Last edited by Shamrock on Sun Aug 09, 2009 12:24 pm; edited 1 time in total

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sgx2000
Posted: Sun Aug 09, 2009 12:15 pm Reply with quote
Joined: 15 Nov 2007 Posts: 61 Location: dallas, tx
that's what i was going to say!
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