Match Play Can Give You an Edge, Even in Extended Sessions

14 June 2004

By Alan Krigman

Match play is funny money casinos use to reward and encourage patrons who gamble at appropriate levels. In general, bettors can augment their wagers with up to an equal match play amount. Wins are paid based on the sum of the two elements. And they get back their initial cash outlays, but not the match play tokens, with the earnings. Losses cost both the genuine and the ersatz dough.

Match play is typically restricted to wagers paying essentially 1-to-1. These include the flat portions of Pass, Come, Don't Pass, and Don't Come at craps; Banker and Player at baccarat; outside bets at roulette; and starting wagers at blackjack. The even-money restriction and the one-time use of the tokens make the equivalent cash value of match play somewhat under half that of its denomination, the offset depending on the edge of the bet.

Everybody likes match play. Solid citizens because it increases how much they can win with the same funds at risk. Casino bigwigs since they don't actually have to spend anything, can talk about face value that overstates true worth, and figure they'll recover what's won with it from players who don't know when to quit. Few bettors or bosses tend to appreciate the impact that match play has on the statistical advantage in the games.

On a single-round basis, The effect is huge. Take, for example, bets on Player at baccarat. These have 49.32 percent chance of winning and the complementary 50.68 percent chance of losing. The house advantage is the theoretical loss to the bettor per dollar wagered; since wins and losses are each $1, this equals 0.4932x1 - 0.5068x1 or -1.36 percent (the minus indicates that the house is favored). With maximum match play, the win for a true $1 bet becomes $2 while the loss stays $1. Edge is accordingly 0.4932x2 - 0.5068x1 or a whopping +47.96 percent, favoring the bettor.

The edge effect carries over after the match play is history. Say you have $1 in match play. Bet $1 on Player plus a $1 token for the first hand. Then bet $1 in cash on the next. Together, $3 can be won and $2 lost so edge drops to 0.4932x3 - 0.5068x2 or +46.6 percent. Continuing, as more real money is bet relative to bogus bucks, the combined edge approaches the nominal -1.36 percent.

Of particular concern is the total in real money that must be bet per dollar of match play before edge reverts to the house. For those who enjoy a bit of algebra, assume PW is the probability of winning, PL that of losing, E the nominal edge, and B the handle at which the advantage is zero. The equation is PWx(B+1) - (PL)xB = 0. Solve to get B = PW/(PL - PW), or alternately, B = -PW/E.

For Player at baccarat, B is 0.4932/0.0136 or $36.26. For outside bets that lose on green at double-zero roulette, PW = 18/38 and PL = 20/38. B is 18/(20-18) or $9.00. Outside in a single-zero game, PW = 18/37 and PL = 19/37 so B is 18/(19-18) or $18.

Craps gets stickier when dice doyens take or lay odds on Do or Don't "matched" Pass or Come bets, and the overall edge in the game depends on everything on the table rather than just the even-money part. But, considering flat Pass or Come bets alone, PW = 0.4929 and E = -1.41 percent. With these figures, bettors have the advantage until their handle is $34.71 per match play dollar. Blackjack is also messy, owing to doubles and splits, as well as 3-to-2 payoffs for naturals. However, with perfect basic strategy and the rules now widely offered, nominal edge is 0.004 percent -- equivalent to PW = 0.498 and PL = 0.502; using these figures, the zero-edge handle is 0.498/(0.004) or $124.50.

Multiply these figures by the total you get in match play for a full assessment. For instance, pretend you're a blackjack buff with $50 in match play. Using it all at once or as something like two $25 or five $10 matches, you'd have the advantage until you'd bet $124.50x50 or $6,225 of your own money. Betting an average of $25 at a table with three active spots other than your own, this would be 249 rounds and would involve over two hours. With such action, you could easily enjoy an edge for your whole session. Recalling this rhyme by the prudent poet, Sumner A Ingmark:

Being in the catbird seat,
While a situation sweet,
May not circumvent defeat.