Freeze out calculations

There is a well known a story about a freeze-out competition between a Japanese high roller,Kashiwagi, and Donald Trump that took place 20 years ago. The Donald agreed to cover all costs for a fairly large retinue of hanger ons for Japanese businessman (code: Japanese mafia). In exchange Kashiwagi was not allowed to play more than $200K per hand at baccarat. The game would be over when either the casino or the player were ahead by $12 millon (60 units). He was required to play at least 8 hours per day.

Assume that Kashiwagi always played banker (house edge is 1.06%), and always plays the maximum, what is the ratio of probabilities that Trump wins to the probability that Kashiwagi will win?

The math works out easily only on the Player bet. I work out a similar problem in roulette at my mathproblems.info site, problem number 116. For even money bets, the general formula is ((q/p)^b-1)/((q/p)^g-1), where:

b = starting bankroll in units
g = bankroll goal in units
p = probability of winning any given bet, not counting ties
q = probability of losing any given bet, not counting ties

In the case of the Player bet the values are:

b = 60
g = 120
p = 0.493175
q = 0.506825

So the answer is ((0.506825/0.493175)^60-1)/(( 0.506825/0.493175)^120-1) = 16.27%.

It is much more complicated on the Banker bet, because of the 5% commission. That would result in the distinct possibility of the player overshooting his goal. If we add a rule that if a winning bet would cause the player to achieve his goal, he could bet only what was needed to get to 120 units exactly, then I estimate his probability of success at 21.66%.

Pretty canny move by the Donald to keep the whale gambling while still subjecting him to the relentless house advantage, while not having too much of a risk himself.

Guess that's a reason why he is so successful -- he knows a good deal by instinct when he sees it.

Quote: teddys

Pretty canny move by the Donald to keep the whale gambling while still subjecting him to the relentless house advantage, while not having too much of a risk himself.

Guess that's a reason why he is so successful -- he knows a good deal by instinct when he sees it.

Thank you Wizard

Akio Kashiwagi’s won a record breaking US$6 million from the Trump Plaza in Atlantic City in February 1990. In May 1990, Akio agreed to the freeze out competition that was the subject of this question. Donald J. Trump is quoted as saying that Akio was up more than US$10 million before he started losing. After 6 days Akio lost all of the US$10 million and broke the agreement.

Akio paid back the $6 million he had just won in February, and stood up Donald for the remaining $4 million. Trump had to write off the debt in January 1992, when Akio was found dead at his Mount Fuji home with 150 stab wounds without ever paying Donald the balance.

So, Donald's canniness is subject to some question. If you play with mobsters, you are going to get burned sometimes.

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