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# Betting Both Sides: Who's Outfoxing Whom?

5 October 1998

More often than you might think, gambling guys and girls get caught in brainstorms which precipitate schemes to bet both sides of the same proposition. Plenty of permutations are possible, depending on the game and the goal. Here are illustrations:
o Drop equal amounts on Pass and Don't Pass at craps, then bet the Odds on just one side after the come-out roll. The purported purpose is to nullify the house advantage. The reasoning: cancel out the flat money, on which everyone knows the casino has an edge; bet only the Odds, where the sages say players are on fair footing with the bosses.
o Bet big on Red at roulette while a covert cohort a few seats away makes equal wagers on Black. The ostensible objective is to risk essentially nothing, while persuading pit people into laying high roller treatment on both of you.
o Wager on Player and Banker at baccarat simultaneously, one side slightly more than the other; the imagined idea is to bet only the difference, letting you loiter around the elite on a bare-bones budget.

Do solid citizens who use these ruses know a secret to circumventing the system? Or are they outfoxing themselves? Examining a typical "both sides" strategy will answer these questions, while also showing how the casino earns its money.

Assume Johnnie and Connie play roulette at the same table, each betting \$100. Johnnie on red, Connie black. They endure 380 spins then request and get "comps" for the bounteous Bon Vivant Buffet.

Johnnie and Connie can't possibly get ahead. When a red or black number hits, one wins and the other loses so together they push. When the ball lands in the green 0 or 00, each loses \$50 - \$100 overall. So after 380 spins, our dour duo may be even if 0 or 00 never appear, or up to \$38,000 behind if they pop every time.

These extremes, of course, are highly unlikely. The loss expected from the law of probability is \$2,000 because 0 and 00 should average 20 hits in 380 trials. And it's this statistically expected result, inherent in the structure of the game, on which casinos dispense what looks like largesse to players. So who got the best of whom? Johnnie and Connie with a free gourmet feeding frenzy? Or the casino which can't lose and expects a \$2,000 win?

What happens if Johnnie and Connie get gutsy and go for the gold? Suppose they bet \$200, the same total, on red for 380 spins. They could lose \$76,000 in the unlikely event the ball stops on a black number each time. They could win \$76,000 in the equally remote case that the ball lands in 380 successive red numbers. And they could break even in various ways, such as red and black occurring 190 times each. However, expectation based on the laws of probability is 180 reds and 180 blacks - netting to zero, and 20 greens costing (you guessed it) 20 x \$100 or \$2,000.

Picture all such situations like this. With \$100 on a proposition having 1 percent house advantage, the casino has a \$1 expected win. With two \$50 bets, each on wagers having 1 percent edge, the casino has an expected win of \$0.50 each - \$1 total. The result is the same whether the propositions are complementary, opposing, or totally unrelated... simultaneous or sequential.

Patrons' potentials for contributing to casino earnings are rated using statistical expectations rather than actual results. The reason is that huge numbers of bets are booked, so players doing better than the theoretical average balance those doing worse, and casino profits from the games converge on the amounts predicted by the law of probability.

On an individual basis, spreading a fixed sum across both sides of a proposition limits bankroll swings. This may suit a person, but doesn't alter what the casino expects to extract from the action. Rather, it raises the chance a player will finish close to the predicted average. As Sumner A Ingmark saw the situation:

Though complicated betting is your game,
The house earns its percentage just the same.

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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.