Match Play Coupons: What’s the House’s Best Bet?

Author’s note: Match play (MP) coupons or chips are extremely costly to the casino when used in the capacity of “game starters,” or as a motivation to “play” on a table game. In almost every situation, MP coupons/chips used as a game starter do not provide the casino with a positive return through additional revenue over cost.1­­ On the other hand, MP coupons/chips that are used as player reinvestment, and have their cost (face value or actual) subtracted from the possessing customers reinvestment account, are doable.

In past articles, I’ve mentioned that an easy method for calculating the cost of “match play” (MP) coupons/chips is to take one half of the MP value and subtract the return from the mathematical house advantage charged on the total of the coupon and the amount of matching casino value chips. For example, a $10 MP’s value when played on the “player” hand in baccarat would be calculated as:

$10 / 2 = $5 – ($20* X 1.23%) = $5 – $0.25 = $4.75
* $10 MP coupon + $10 casino chip

As illustrated in Table 1, this calculation has been conducted with the player and banker wager, as well as the “tie,” and the costs to the casino for the use of a $10 MP coupon/chip are $4.75, $4.79 and $2.12, respectively.

Based on the effect of applying the different mathematical house advantages (H/A) to the individual wagers, the higher the H/A, the lower the cost of the coupon. However, this method might be the easiest in calculating MP cost, but it is subject to several flaws that mislead the casino executive as to the exact cost of the MP used on the three baccarat wagering options. As long as this calculation is used on “even money” wagers, the results are fairly accurate. When this calculation method is applied to MP wagers where winning bets are paid in multiples, the method results in serious, if not costly pricing errors.

The best method for calculating the cost of an MP coupon/chip is to use the win percent, multiply it by the MP total payoff, and subtract this amount by the loss percent time the actual values chips lost. For example, the same player wager in baccarat would be calculated as:2

49.31% X $20* – 50.69% X $10 = $9.86 – 5.07 = $4.79
* $10 MP coupon + $10 casino chip

The other baccarat wagers are calculated using this more accurate method of determining cost, and are shown in Table 2.Table 1: Calculated Cost of Match Play Coupons/Chips in Baccarat
Table 1: Calculated Cost of Match Play Coupons/Chips in Baccarat

When comparing this more accurate cost number with the previous calculation, it is apparent that the actual cost of the MP coupon/chip wagered on the player is slightly higher, while the actual cost of the MP wagered on the banker bet is slightly low. Other conclusions can be drawn, such as:

• The difference between the player and banker MP wagers in the two calculations is insignificant unless the casino is distributing a high-dollar volume of coupon/chips.
• The result from this comparison indicates that the actual cost of the MP for both the player and the banker is inverse the previous calculated cost. This is primarily based on the percentage of win/loss occurrence and the banker payoff of 19 to 20 (5 percent commission).
• When averaging the costs, the cost is about the same ($4.77 versus $4.75).
• The biggest difference is noted with a MP wagered on the 8 to 1 “tie” bet.

Table 2: Actual Cost of Match Play Coupons/Chips in Baccarat
Table 2: Actual Cost of Match Play Coupons/Chips in Baccarat
The tie wager clearly illustrates the effect of the MP coupon/chip when winning wagers are paid based on a multiple payout schedule, and the resulting volatility. If one used the previous “easier” form of calculating the cost noted in Table 1, he or she would automatically jump to the conclusion that the baccarat tie wager would only cost the casino $2.12. When using the more accurate method, one can see this is far from true. In Table 2, the accurate calculation indicates that the tie is far from the best MP bet at a cost of $6.18. Even though the tie wager wins only 9.5 percent of the hands, because of the MP, a winning result is paid double times the multiplier of 8. Based on this information, the casino is better served by limiting the MP coupon/chip to be played only on the player or the banker, or “even money” bets. This principle holds true for all table games.
Note: In EZ Baccarat, the banker cost when wagering a MP coupon/chip is 0.4755 or $4.76. This MP wager is slightly more costly because winning banker wagers are paid 1 to 1 (no commission) even though the banker wager wins less often (48.43 percent).

Table 3: Actual Cost of Match Play Coupons/Chips in Roulette
Table 3: Actual Cost of Match Play Coupons/Chips in Roulette
The Roulette Promotion That Cost Too Much
A general manager at a Midwestern casino wanted to increase his table game play on his double zero roulette games. Why not? The double zero games support a mathematical H/A of 5.26 percent, one of the highest mathematical edges held by any casino game. If more of his table game players learned how to play roulette, then his revenue potential should increase. In order to attract more roulette play, the GM decided to utilize a promotional program anchored around the issuance of “roulette only” match play coupons mailed out to his better table games players. He had marketing send out $50 in MP coupons, in $10 increments, to the top 200 table games players in his player database. Using the standard “half the coupon value minus H/A” formula, the GM calculated the cost per coupon to be $3.95. In addition, since all bets on the layout are subject to the same H/A (except the 5 number bet which has a 7.89 percent H/A), the coupons could be wagered anywhere on the layout. The GM estimated the cost of the promotion would be $3,950 if all the coupons were wagered. Was he correct in his assumption?

The answer is a big no. What the GM needed to do was calculate the cost of the coupons based on the same principles used in the previous baccarat tie bet situation (see Table 3).

While the true calculation of the 1 to 1 payoff bets of black, red, even, odd, first 18 and second 18 are slightly higher than the “short cut” method, the remaining wagers get more expensive as the pay schedule increases. If every one of the coupons were wagered on a single number straight-up, the cost of the program would be $8,680, more than double the GM’s original projections.

Understanding the true cost of the promotion might encourage the GM to limit the use of the coupons. Would allowing the players to wager only on even money wagers still attract “sustained” play on roulette that the GM had envisioned?

Table 4: Return from Match Play on Player Only (Baccarat)
Table 4: Return from Match Play on Player Only (Baccarat)
Offsetting Wagering is Actually OK­
A husband and wife both have $10 match play coupons. They step up to the baccarat table and proceed to place one coupon along with $10 in chips on the player wager, and place one coupon along with $10 in chips on the banker wager. The floor supervisor watching the couple place their wagers views the two bets as “offsetting” and refuses to allow the couple to wager in that fashion. The wife removes her coupon and chip bet off the banker wager and places it along with her husband on the player wager. The floor supervisor approves and the dealer starts calling the hand. Was the floor supervisor correct in his decision?

Many casino executives believe that offsetting wagering with coupons and promotional chips cost the casino money. It’s their understanding that the offsetting strategy provides the conspiring player(s) an “automatic” win. Although the offsetting strategy does guarantee the player(s) a return for their coupon play, this situation is not any different if the wife waited until the next hand and then proceeded to place her coupon and chips on the banker. Both wagers, no matter what their intended relationship is to each other, are still treated mathematically as two separate wagers, both subject to independent mathematical house advantages.­

Table 5: Return when Offsetting Match Play with Match Play (Baccarat)
Table 5: Return when Offsetting Match Play with Match Play (Baccarat)
In fact, forcing both husband and wife to wager on the player bet cost the casino slight more money than allowing them to offset. Based on the calculations given in Table 4, the expected cost of a $10 MP coupon and $10 in chips on the player wager is $4.79. If both the husband and wife wagered simultaneously on the player bet, they would expect a theoretical return of $9.78 (2 X $4.79). Of course there is no guarantee the couple would walk away winners, but over the long term, the cost would remain the same to the casino.

Conversely, if the floor supervisor would have allowed the couple to wager as they originally intended, the theoretical cost to the casino would have been $9.49, as illustrated in Table 5. This decrease in cost, from $9.78 to $9.49, is attributed to one of the MP wagers being placed on the less costly banker bet. [Note: If both the husband and wife had chosen to wager on the banker bet, the theoretical cost to the casino would actually be slightly less, calculated to be $9.12.]

This same principle holds true for wagers made on any table game that would allow the MP coupons to play against each other such as red/black, even/odd, and first/second 18 in roulette, and Pass/Don’t Pass & Come/Don’t Come in craps.

[Note: There is some tremendous information to be found on match play, single play and multiple play coupons/chips in James Grosjean’s self-published paper, Beyond Coupons (see footnotes). Grosjean is an advantage player who has analyzed promotional coupon/chip play, as well as all table games and side bets. Grosjean is considered one of the top advantage players in world.]

Footnotes
1 Kilby, Jim; Lucas, Anthony (2008). Principles of Casino Marketing. Norman: Okie International. www.principlesofcasinomarketing.com.
2 Grosjean, James (2008). Beyond Coupons. Self-published paper. www.beyondcounting.com/pdfs/beyondcouponsbjfo.pdf.

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