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Best of Alan Krigman

Gaming Guru

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The Enduring Effect of Match Play Coupons on House Edge

4 February 2003

"Match play" coupons are common casino promotional incentives. The idea is to combine chips and coupons of equal face value into a bet worth twice the real money actually set out. Losing costs both the chips and coupons. Winning pays according to the total of the two parts, returning the chip portion but not the coupons.

Monetarily, a coupon is worth somewhat under half its denominated value. And you can get the cash if you'd rather not gamble. A simple way to do this is at baccarat. Bet your coupons with an equal amount of chips on Player, and three-fourths of the total in chips on Banker. This might be two $10 coupons plus $20 in chips on Player and $30 in chips on Banker. A Player win nets $40 minus $30, or $10; a Banker win nets $30 minus $1.50 commission minus $20, or $8.50. The $20 in coupons is therefore converted to $10 or $8.50 in your pocket. Chances of Banker or Player wins average the soft $20 to a hard $9.24, 46.2 percent of face value.

A different take on match play is that it reverses or discounts edge. The extent varies with game, wager, and duration. Solid citizens have the upper hand in rounds using coupons. With the coupons gone, the edge reverts to the house on each subsequent coup. But players retain an overall advantage on the aggregate bet until they reach a crossover. At this point, enough rounds have transpired that the house's percentage on additional money offsets the bettors' initial advantage. Further play brings the house edge gradually up toward the nominal edge for the game.

To see the effect, picture an even-money bet at single-zero roulette. For instance, $10 to win $10 on red. The house normally has 2.7 percent edge. With match play, say $5 and a coupon to win $10, players get a giant 45.9 percent edge on the cash at risk.

Assume that after betting all their coupons, players continue to make even-money single-zero roulette wagers at the previous chip level. The crossover where the house regains the edge is at 17 times the number of bet units represented by the coupons. Pretend a player has $25 in match play and bets it with $25 in chips on red, then keeps going at $25 per spin -- betting on red or some other even-money proposition. The player has an overall advantage for 17 more rounds. A bettor who used $75 in match play then continued at $25 would have a crossover at 3 x 17 or 51 rounds.

Casinos generally restrict match play bets to even-money wagers. You can see the reason in terms of edge on bets on individual numbers at single-zero roulette. These pay 35-to-1 and normally also have 2.7 percent house edge. Match play gives bettors a huge 91.9 percent edge on rounds involving chips and coupons of equal value. More, the crossover for the casino to later regain the overall edge is 34 times the number of coupon units bet. A heavy hitter, such as a $100 bettor with five $100 coupons, could go 5 x 34 or 170 rounds at $100 on a single spot and still have an effective edge over the casino on the gross bet. This is about three hours at a typical table. The casino would be the theoretical underdog if this high roller played for less time.

The following list shows the lingering effect of coupons on the nominal 2.7 percent edge at single-zero roulette. Figures are for bets on red and on a single spot, using coupons denominated at two bets. Crossovers are at 34 rounds for red, 68 for one spot.

Effect of two bet-equivalent match play
coupons on edge for wagers on red and on
a single spot at single-zero roulette

additional
bets after
coupons are
exhausted

edge
(+ favors player
- favors house)

red
one spot
0
+45.9%
+91.9%
5
+11.2%
+24.3%
10
+ 5.4%
+13.1%
25
+ 0.9%
+ 4.3%
50
- 0.8%
+ 0.9%
100
- 1.7%
- 0.8%
500
- 2.5%
- 1.8%
2,500
- 2.7%
- 2.7%

Most players think they've blown their chances once they've used their match play coupons and are entirely back to chips. Now you know that the effect on edge is enduring. The matchless poet, Sumner A Ingmark, anticipated just such situations when he wrote:

We may think the past long dissipated,
But its remnants foretell how we're fated.

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.