Sunday, April 29, 2012

The house always wins

Every day, tens of thousands of visitors go to casinos to gamble. Among all, a few leaves “the house” with a smiling face while many leaves the house with a lighter bank account. This is the way it is, scientifically.

Consider a simple bet on the red of a roulette wheel that has 18 red, 18 black, and 2 green slots. This bet is at even money so a $10 wager on red has an expected profit of

Expected Profit = (10) x (18/38) + (-10) x (20/38) = -.526

The negative expected profit says we expect to lose an average of 52.6 cents on every $10 bet. Over a long series of bets, the relative frequency of winning will approach the probability (18/38) and that of losing will approach (20/38) so a player will lose a substantial amount of money.

All other bets against the house have a similar negative expected profit. Or how else could a casino stay in business? Haven't you heard what they say about it : “the house always wins”?[1]

MBS - Source : Relax
And one of the two houses here, Marina Bay Sands, explodes this negative expected profit against many rich punters and countless not so rich gamblers successfully so that MBS' first-quarter operating profits is up 66 per cent compared to the same period last year.

During the soft opening of Marina Bay Sands,Las Vegas Sands CEO Mr Sheldon Adelson has said he expects the Marina IR casino to break even in just five years[3]. Looking back from now, it looks like he was very conservative about the gambling craze in this part of the world.

[1] - No Casino Game Has a Positive Expected Profit, Statistics Principles & Methods Sixth Edition
[2] - Marina Bay Sands rings up record profits last quarter
[3] - Marina Bay Sands Inside the casino

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