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# Playing it smart - There's more than one honest way to leave a casino in a limo

7 May 2007

It's easy to make big bucks at a casino if you're a high roller. Go to a baccarat table with \$50,00d. Bet it all at once on Player. The chance is about 49.3 percent, slightly under half, you'll win \$50,000 and leave with \$100,000. Of course, the flip side is a 50.7 percent chance, just over half, you'll bust out.

What about solid citizens with more typical betting budgets? Say, \$200. Finishing with \$100,000 turns out to be far less likely than 49.3 percent. And, not just because the casino has the advantage on the action it books.

If a game had no edge, and time was not a constraint, the likelihood of gambling \$200 up to a \$100,000 would be 0.2 percent two out of a thousand regardless of how the money was bet. Think of it like this. A thousand people start with \$200 each, \$200,000 total. Of these, 998 bite the dust while two win \$99,800 and leave with \$100,000 each, \$200,000 total. That's two out of a thousand. It's a wash for the bosses owing to the zero edge.

Absent house advantage, prospects of success wouldn't be affected by the way wampum was wagered. A \$200 bet with a probability of 0.20 percent would return the \$100,000 or wipe you out in one fell swoop; there would be no turning back. As another option, the \$200 could be parlayed on a 50-50 even-money proposition. Winning the first bet would leave you with \$400, the next \$800, then \$1,600, \$3,200, \$6,400, \$12,800, \$25,600, \$51,200, and finally \$102,400. After nine wins in a row, you'd have just over \$100,000. The chance here is 50 percent multiplied by itself nine times, which equals 0.195 percent or 1.95 out of a thousand; this differs from two out of a thousand because of the extra \$2,400. More, you have eight opportunities to change your mind about the \$100,000 goal and lock up some or all of the profit.

In a real casino, the house does have an edge. How much tougher does this make either of these betting strategies to have you arrive on a bus with \$200 and depart in a limo with \$100,000?

Say the longshot was an all-or-nothing slot machine paying 500-for-1. If the game had 95 percent return, meaning the house kept an average of 5 percent as a result of its advantage, chance of winning would drop from 0.20 to 0.19 percent. A difference of one in 10,000. Not enough to notice on any given day.

Were the edge on the even-money bets also 5 percent, chance on any round would decrease from 50 to 47.5 percent. The shot at nine in a row would be 47.5 percent multiplied by itself nine times or 0.123 rather than 0.195 percent. A difference exceeding seven in 10,000. More than one in 10,000 but still subliminal.

Of course, you may not have the guts to go for broke. Maybe you want to bet \$10 per round on the machine and hope for enough more hits than misses to amass the \$100,000. The best that could happen would be 20 straight wins returning \$5,000 each. But many combinations of winning and losing rounds could also get you to your target. On the 95 percent game, with the 0.19 percent chance to win 500-for-1 on any round, combining all the possibilities puts your chance at about 0.06 percent six out of 10,000.

Betting on the even-money proposition, \$10 at a time, the best you could do would be 10,000 successive wins. Multiplying 47.5 percent by itself 10,000 times yields a probability that the math mavens say "approaches zero." If the house had a much smaller edge, say 0.5 percent as in blackjack, the chance is still essentially zip. And figuring the combinations of wins and losses that total to \$100,000 doesn't change this conclusion. Betting \$200 flat each time, you're still off the scale at 5 percent edge but have a chance of 67 out of a million at half a percent.

One lesson here is that if you want to make big bucks with a small bankroll, your chance is low no matter how you address it. Another is that the more aggressive you are, the better your chance becomes. So, in planning your goals for a casino visit, ponder this piece of profundity from the poet, Sumner A Ingmark:

Know the subtle correlations,