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# Playing it smart - When one plus one doesn't equal two at a casino

24 September 2007

It doesn't take a gambling guru to know that raising or lowering your bets will increase or decrease your up-and downswings. You'll win or lose more, and will do it faster.

Here's something relatively few casino aficionados realize. Some vital session statistics stay constant as long as you adjust your bankroll in proportion to bet size. In particular, your chances of weathering normal cold runs for a stated number of coups, or of reaching a profit level equal to a stated multiple of your bet before going bust, remain fixed.

The details vary among games because of differences in edge and volatility. But the general trends hold no matter what you play. Say, for example, you're used to betting \$10 on Red at single-zero roulette with a \$250 bankroll. You have a 79 percent chance to endure for at least 250 spins. And, if your win goal is \$100, the probability is 51 percent you'll make it rather than bust out.

Instead, suppose you bet \$20 on the same proposition with a \$500 bankroll.

The likelihood you'll survive for 250 spins is still 79 percent. And your prospects of being \$200 ahead before depleting your \$500 holds at 51 percent. Of course, your theoretical loss due to edge changes. In the first scenario it's 2.7 percent of the \$10 x 250 or \$2,500 gross wager, \$67.50; in the second it's the same percentage of the \$20 x 250 or \$5,000 handle, \$135.00.

One implication is that if two solid citizens each wager on identical propositions at the same table, together they're like one person with the combined bankroll betting the total amount.

What happens if the pair of punters plays synchronously but independently? For instance, pretend each bets \$10 on Red from a joint \$500 bankroll but at separate tables. After each experiences 250 spins, the gross wager for the two, together, is \$10 x 2 x 250 or \$5,000. The bosses accordingly figure their earnings from the action as worth \$135. The same as for \$20 on Red at one table. The good news is that the chance of the combined \$500 poke being enough for at least 250 parallel spins, however rises from 79 to 91 percent. The bad news is that the likelihood they'll earn \$200, between them, before biting the dust drops from 51 to 32 percent.

The question of independent, synchronized wagers isn't trivial. It can arise with a single player. A common case involves multi-line slot machines. On any given session budget, you're apt to last longer when luck is smirking but win less when it's smiling, the more lines across which you spread a fixed total wager. Another illustration can be found in craps. Although Pass, Come, and Place bets all lose on a seven, the correlation on wins is low enough so each can be considered essentially as its own game.

Tables at which participants play separate hands that have to beat the same dealer represent an intermediate situation. The hands aren't completely independent. In blackjack, for instance, weak dealer upcards help everyone; conversely for strong. Similarly, in Caribbean Stud, "called" hands all win even money on the ante when the dealer doesn't "qualify" with ace-king or better, and are almost sure to lose the ante plus the bet when the dealer has a straight flush, regardless of what each hand comprises. Playing multiple hands under such circumstances won't change the edge or the house's theoretical earnings from the gross wager in a specified number of coups, relative to the same total on one spot. But it tends to moderate the swings.

Spreading bets can't overcome the inherent edge in the games. But it can influence the tendency of bankrolls to swing during the action. And, while casinos earn their money on the edge over huge numbers of decisions, individual players realize their reveries or confront their nightmares on the swings. Here's how the celebrated songster, Sumner A Ingmark, saw this segmentation:

Casinos have answered all businesses' prayers, With statistical ways to forestall doom. The house can lose money on each of its players. But derive a good profit from volume.

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Best of Alan Krigman
Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.