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Re: BBJ EV
 Originally Posted by Jibalob
At what point does the BBJ become +EV? Assuming that for every raked hand an extra $0.50 is taken to contribute to the BBJ, and that 70% of the BBJ is distributed among the 6 players at my table if hit, how high does the BBJ need to be before this becomes +EV? I did some really scrappy calculations last night and came up with a ball-park figure of $500,000 but am not so sure now.
Any good mathematicians wanna try and come up with a figure?
I'm not sure I'm a good mathematician, but here's some probabilities. Of the (52 choose 7 = ) 133,784,560 possible 7-card hands possible, exactly 134,044 of them are quad 8's + (needed to qualify for BBJ at UB), 1 per thousand hands.
To occur twice in the same NLH hand, both players would use the same community cards which makes the calculations very intractable, so consider the following:
1. Two 7-card stud hands are dealt at random from two different decks.
2. Both hands dealt are quad 8's or better.
The probability of this occurring is (1/1000)^2, or 1 in a million. However, this OVERESTIMATES that likelihood of these hands occurring simultaneously in NLH for several reasons. The most obvious reason is that there are 5 community cards in NLH which limits the total number of combinations possible. But your odds of being in a hand that wins the BBJ are no better than 1 in a million.
The "big winner" of the BBJ gets 25% of the jackpot (at UB), and $0.50 worth of EXTRA rake is taken from each raked hand. So per hand, hero is taking a 1 in a million shot at 1/4 of the BBJ, and pays $.50 out of every raked pot he takes down to do so. Among equally talented players at 6-max, each person would win 1/6 of the raked hands. Assuming 90% of hands get raked, this would mean hero is paying $0.075 per hand for a shot at the BBJ.
Since 0.075 x 13.333 = 1, we can convert the 4 million to 1 odds into odds per-hand-played by dividing 4 million by 13.333. This estimate gives a BBJ of $300,000. Note that this is conservative, because the probabilities of winning are overestimated and because GOOD players pay more rake than bad players (and hero, here, is assumed to be good). Your half million estimate is reasonable, given the assumptions I just outlined.
A GOOD player wishing to profit should play the HIGHEST limit BBJ tables. The cost-per-hand is the same regardless of level, but the extra rake will erode regular poker earnings much less at higher limits.
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