hey guys, i actually think he might have positive expectation:
he negotiated a .25% houe edge (roughly half of normal perfect play) and if he loses 500k he gets 20% back, each session independent.
check this analysis. he is +EV by martingaling his wins - 7/8 times he loses 400k with a 20% discount (400k x 7 x .80 = 2 240 000), 1/8 times he wins 400k x 8 with no reverse-discount = 3 200 000, so that's a mil in EV. if he pushes his martingale as far as he can his expectation grows superlinearly, which is why he martingales his wins until they cut him off.
is this math right? if he was -EV, the house would let him keep playing, hence telling him he can continue to play under normal rules. note he refused.
update: an easy way to see this (gross oversimplification) is if he plays only one hand/session he stands to win 100% of the money 49% of the time and loses 80% of the money 51% of the time.
This explanation seems most consistent with the limited information in the article.
We don't know whether he had several -$400K sessions before his big run. Gamblers and non-gamblers talk more about upswings than downswings.
There could be some other unmentioned factors that aided him a little, but the capped downside, a lucky run, and selective reporting are probably a sufficient explanation.
That's funny, I much prefer the story of mybiggest loss in an hour of blackjack than any of my winning stories, just seems more entertaining and less boastful perhaps.
It depends on how he expects to be taxed. If this is his only session during the year, he actually wins 60-70% of the money vs losing 80%. So he needs to either be way ahead or way behind from other gambling activity for this to work out the way you described (assuming he's a US citizen).
that's interesting, but i'm not sure i follow or agree - i can't put numbers on it, but intuitively his variance feels a bit like, but less than, poker's variance. Poker graphs look like a sawtooth of small losses and big wins. This means he would have to get spectacularly unlucky to be down after 50 sessions, given his positive pre-tax expectation[1].
so it depends how he structures his taxes. if he can get his taxes calculated yearly instead of per session, taxes make him a bit less of a winner. if his taxes are calculated per session, he is -EV. this is the same problem that poker players face, IIRC the precedent there is that if you file as a small business you can sum your wins and deduct your losses annually.
(/me used to be a small-time poker player)
[1] expectation in blackjack is computable because perfect play is deterministic, expectation in poker is harder because it depends on human factors like your mood and your opponent's skill level and his mood. you can only measure past expectation. A lot of players think they are winners but are really breakeven or losers, but blame it on bad luck.
His rebate is cumulative with the casino according to the article, except that they allowed him to reset it when he started this streak. He effectively only has one session per casino for rebate purposes.
Taxes are always computed on net winnings annually. Filing as a pro can affect the rate and allow deductions for expenses, but even amateurs can deduct losing sessions against winners if they have documentation.
he negotiated a .25% houe edge (roughly half of normal perfect play) and if he loses 500k he gets 20% back, each session independent.
check this analysis. he is +EV by martingaling his wins - 7/8 times he loses 400k with a 20% discount (400k x 7 x .80 = 2 240 000), 1/8 times he wins 400k x 8 with no reverse-discount = 3 200 000, so that's a mil in EV. if he pushes his martingale as far as he can his expectation grows superlinearly, which is why he martingales his wins until they cut him off.
is this math right? if he was -EV, the house would let him keep playing, hence telling him he can continue to play under normal rules. note he refused.
update: an easy way to see this (gross oversimplification) is if he plays only one hand/session he stands to win 100% of the money 49% of the time and loses 80% of the money 51% of the time.