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# How to Maximize Your Edge when You Act as Banker

13 May 2003

In most casino table games, the house functions as Banker. This means that the dealer opposes all patrons, who act as Players, paying winners and collecting from losers. The casino earns its profit in these games by one or both of two means: a) payoffs are slightly below the odds bettors must overcome to win, or b) a commission or "vigorish" is collected from participants either on wagers when they are made or on winnings when they are paid.

In some situations, patrons get an opportunity to bank, usually in sequence around the table. The classic example is in chemin de fer -- a version of baccarat now rarely seen. Modern casinos have patron banking in "Asian games" such as pai gow. In some venues it's also employed on games like blackjack, in set-ups where the house deals but has no "gambling interest" in the result. Solid citizens serving as Bankers often have an edge under these conditions. The bosses still get their due, to be sure, through the vigorish on individual Player wins and Banker nets.

The edge faced by Players in patron-banked games depends entirely on the likelihood of winning or losing, the payoff, and the size of the commission. As an example, picture an even-money game with probabilities of 51 and 49 percent for Banker and Player, respectively, where the house rakes 5 percent off each Player's winning bet. Per dollar wagered, Players have 49 percent chance of clearing \$0.95 and 51 percent of losing \$1. Edge is therefore an adverse (0.49)x(0.95) - (0.51)x(1) = -4.45 percent.

The edge associated with the Banker's hand is a function not only of the probability of winning or losing, the payoff, and the commission, but also of how many Players are in the game and the relative amounts they bet. The simplest case involves one Player. With the parameters of the previous example, per dollar bet by the Player, the Banker has 51 percent chance of netting \$0.95 and 49 percent chance of losing \$1. The edge is still negative, but a much lower (0.51)x(0.95) - (0.49)x(1) = -0.55 percent.

What happens when the Banker confronts two Players, each betting \$1? Now, the Banker has (0.51)x(0.51) = 26.01 percent chance to net \$1.90, (0.49)x(0.49) = 24.01 percent chance to lose \$2, and the remaining 49.98 percent chance to push. The edge is accordingly ((.02601)x(1.90) - (.02401)x(2))/2 = +0.70 percent. The "plus sign" indicates that the Banker has the upper hand.

With three Players betting \$1 each, the Banker's chances are 13.27 percent to win \$2.85, 38.23 percent to win \$0.95, 36.74 percent to lose \$1, and 11.76 percent to lose \$3. As with two Players, edge with three is +0.70 percent. Similar reasoning shows that when all Players make equal bets, the Banker is favored by 1.01 percent for four or five opponents, 1.17 percent for six or seven, and 1.26 percent for eight or nine. The specific figures would vary although the trends would be the same for alternate probabilities of winning and values of vigorish.

The edge on the Banker's action likewise changes if Players bet differing amounts. To illustrate, say that three Players bet \$1 each and one bets \$2. The Banker's edge drops from 1.01 percent for four Players betting equally, to only 0.82 percent. If the maverick bets \$3, edge falls further, to 0.70 percent. At \$5, it's 0.39 percent. The least propitious position for the Banker pertains when one Player bets at the table maximum and the rest at the minimum. If this occurs at a limit spread of 10-to-1, the edge for the Banker would be only 0.03 percent. At a 25-to-1 spread, the Banker would be at a 0.28 percent disadvantage.

Knowing these factors can help you make the most of the option to bank. Shop for low commission if there are distinctions among casinos competing for your business. Bank as often as you can. And use whatever cunning you can contrive to sway the suckers (aka Players) into betting as high as possible consistent with what you can afford to book per coup, but to all wager the same amount. How? Four ways: finesse, finesse, finesse, and by heeding the hortation penned by the persuasive poet, Sumner A Ingmark:

When dealing with the public, exhibit all your charm,