Match play promotions are better than you may think

Make believe your friendly neighborhood casino wants to boost its minibaccarat action. So the joint sends you and some other specially-selected solid citizens $100 in “match play” coupons. The coupons are good only for $10 or higher bets on Player at minibaccarat.

In case you’re foggy about the fine points, match play is funny money the casino gives you to bet along with equal face value of your own wampum. When the proposition loses, the bosses take both parts of the wager. When it wins, you get paid according to the total of yours and theirs and recover your portion of the original outlay, but the house keeps the match play dough.

Player pays even money; discounting pushes, chances are 49.336 percent to win and 50.664 percent to lose. On individual bets, match play doesn’t affect the prospect of winning; it’s always 49.336 percent. Since the coupons are once-through and worthless unless you also put up real scratch, and you’re apt to keep gambling when they’re gone, the whole idea may seem chintzy. Using it changes the edge in your favor however. And the effect long outlasts the coupons.

Normally, ignoring rounds that push, edge on Player is (0.49336 x $1 - 0.50664 x $1)/$1, or -1.33 percent, the minus sign denoting that the house has the advantage. With match play, you can win $2 for every actual $1 at risk, so edge is (0.49336 x $2 - 0.50664 x $1)/$1, or +48.01 percent, the magnitude and plus sign indicating that you have a tremendous leg up. Not recovering the match play outlay is irrelevant because it has no direct redemption value. You can go for broke on a single bet. Without match play, risking $100, your chances are 49.336 percent of a $100 profit and 50.664 percent of a $100 loss. With your C-note plus $100 match play, the probabilities are 49.336 percent of a $200 profit and 50.664 percent of a $100 loss.

Another option is to make 10 bets, each with a sawbuck of legal tender. You have a 49.336 percent chance of winning each hand, with or without the match play. Possible cumulative results for the 10 rounds are as shown in the accompanying table for both types of wager.

Wins    Probability       profit or loss	
                     without match   with match
0          0.11%        -100          -$100
1          1.09%        -80            -$70
2          4.75%        -60            -$40
3         12.35%        -40            -$10
4         21.04%        -20             $20
5         24.59%          0             $50
6         19.95%         20             $80
7         11.10%         40            $110
8          4.05%         60            $140
9          0.88%         80            $170
10         0.09%        100            $200

Without match play, the median (the point where half of all results are above and half below) and the most likely numbers of wins and losses are five each – at break-even. The monetary average is a $1.33 loss. With match play, the median and most likely results are also five wins and five losses, but this tally yields a profit of $50. The average for this action is a $48.01 gain.

Would it be preferable to bet $100 at once, or to parcel the same stake out in 10 $10 hands? Outcomes for the casino over many patrons would be the same. Set aside whether or not a person is concerned about buying time in the thick of the action. Then, from a particular bettor’s perspective, the answer depends on an individual’s willingness to risk the total in one fell swoop on a 49.336 percent shot at doubling a bankroll, versus favoring a range of possible gains or losses – each with its own chance of occurring. Overall, in 10 $10 rounds, the probability of earning anything from $20 to $100 without match play is only 36.07 percent while that of finishing with a $20 to $100 loss is 39.34 percent, the 24.59 remaining percent being of breaking even. The corresponding figures with match play are 81.70 percent hope of a profit from $20 to $200, 18.30 percent fear of a loss from $10 to $100, and no pushes.

But wait. There’s more. The casino wants you to keep on trucking after your match play coupons are history. Pretend you do. The edge on the total of all your action drifts down from the 48.01 percent you got with the coupons, toward the establishment’s nominal 1.33 percent. Say you use your match play for 10 rounds at $10 each then continue, betting your own cash. You’ll get 361 such rounds before the edge reverts to the house. The burden grows slowly heavier thereafter, reaching 1 percent only after 1,495 hands. And it approaches but never quite gets to 1.33 percent.

The figures cited are particular to bets on Player at baccarat. Values would differ somewhat for match play with other wagers. Trends, however, would be analogous. Don’t tell the casino honchos they lose their edge for sessions or visits of relatively long duration when bettors use even modest match play, though. It’s a secret sophisticated players don’t want the bosses to know. Here’s what the muse, Sumner A Ingmark, muttered about keeping mum: