The Ins and Outs of Betting Both Sides

Some propositions at table games have an "either-or" quality about them. Player or Banker at baccarat, red or black at roulette, and pass or don't pass at craps are illustrations. You occasionally see players betting on both sides. Usually, but not always, in different amounts. Regardless of the rationale, one result is incontrovertible. The house advantage is based on the sum of and not the difference between the two bets.

Take craps. Solid citizens who bet both sides often believe they're outsmarting people who pay PhDs to analyze the games from every angle. Their brainstorms have forms such as betting $100 on both sides, then taking or laying double odds on one or the other after the point is established. The reasoning is that the flat bets will pretty much cancel each other out, leaving just the odds -- on which everybody knows the house has no edge at all.

Here's what actually happens. The house advantage on the pass line is 1.41 percent of the amount bet flat -- independently of the odds taken. The edge on don't pass is 1.36 percent of the flat bet. So, when you bet $100 on pass, the casino bosses credit themselves with a theoretical $1.41 profit. When you bet $100 on don't pass, they mentally rack up $1.36 in earnings. By betting both sides and taking odds on the pass, you're giving folks who need it less than you do a theoretical win of $2.77 -- $1.41 plus $1.36 -- for the privilege of betting $200 to win $240 on points of six and eight, $300 on points of five and nine, and $400 on points of four and 10. Simply betting $100 flat on the pass line would put you in the same position with odds for a theoretical commission of $1.41. Similar reasoning holds for don't pass. Sure, with $100 on both sides, your flat bets push after the come-out, they can neither lose nor win. Likewise, with $100 flat on both sides, you can only lose during the come-out if a 12 rolls, while lone pass line bets go down on twos or threes as well. But the two bets mean you never win anything on the come-out, while pass returns even money on seven or 11.

At other games where bets are made on two sides of the same coin, the motivation is generally to reduce a person's net exposure with unequal wagers. An example is $100 on Banker and $75 on Player at baccarat. Individuals might want to do this so they can play in the classy baccarat pits where the minimum bet is $50, yet they don't feel comfortable risking over $25 per round. Alternately, they may think of this strategy as a means of fooling the pit bosses into giving them black chip ratings for comps even though they're really only betting greens.

The problem, again, is that house advantage comes from the sum of the bets, while player win or loss is based on the difference. Consider baccarat. Per 1,000 decisions, Banker is expected to win 507 and Player 493. After 1,000 decisions with $100 each on Banker -- paying $95 because of the 5 percent vig -- a bettor therefore expects to win $95 x 507 = $48,165 and to lose $100 x 493 = $49,300. The net, a $1,135 loss, represents an edge of 1.135 percent. Likewise, after 1,000 decisions at $75 each on Player, a bettor expects to win $75 x 493 = $36,975 and to lose $75 x 507 = $38,025. The net, a $1,050 loss, represents an edge of 1.4 percent. Overall, expected loss on both bets is $2,185. In terms of the $25 net times 1,000 decisions, $2,185 represents a 8.74 percent edge -- a steep price for faux-elegance and high-roller treatment. And it confirms that casinos know what they're doing if they comp you like a $175 rather than a $25 patron. You've met criteria that matter most to the moguls, an edge based on a $175 bet, with the short term risk of a $25 patron if you happen to hit a run on Banker.

Should you bet both sides? No, if the edge is meaningful to you. Yes, if you think I make all this stuff up, the laws of nature don't apply to casinos, the PhDs missed an angle, gambling's more luck and hunch than knowledge and skill, high roller pandering is more important than winning, or it must be true because you read it on a $25 mimeographed "insiders' secrets" sheet. Your call. While cogitating, contemplate this couplet by Sumner A Ingmark: