What If You Could Buy Gaming Chips at a Discount?

26 July 2004

By Alan Krigman

What if you could buy gaming chips at a discount? Say, 10, 20, or even 25 percent. Special chips you bet at face value, get back with your payoff when you win, and redeem at cost if any are left when you quit. Not a pipe dream. A deal you can get on ships in Florida that sail past the three-mile limit then open the games. And, anything being possible in the gambling galaxy, you might one day find it at your favorite punting parlor, too.

Here's the Florida gambit. You buy the discounted chips, for table games only, using an "In Good Taste" (IGT) card. With most participating operators, you can go for $100 or $250 face value; IGT bills you through a regular credit card at 25 percent off -- $75 or $187.50. You can use the privilege from twice a week on some boats to once a month on others. The minimum bets required with the chips are $10 and $25 for the $100 and $250 sets, respectively. You're therefore purchasing 10 discounted units for bets at the lower limit. Of course, solid citizens usually stake themselves for more than 10 units, bridging the gap with standard chips. The casinos may be thinking that 10 marked-down chips won't last long, so they'll soon have the edge on the action.

Will they, though? Or will the bettors keep the catbird seat?

Players have an edge over the house on individual coups using the discounted chips. A huge edge, because $7.50 or $18.75 at risk are paid as though they were $10 or $25. Here are comparative expectations for a few representative cases. Normally, per dollar bet flat on Pass at craps, the house averages $0.014 profit; with chips discounted by 25 percent, players expect to net $0.113 on $0.75. An outside bet such as Red at single-zero roulette is usually worth $0.027 on the dollar to the casino; with chips discounted by 25 percent, it favors the player to the tune of $0.101. Placing the four at craps, the figures are $0.067 for the house with real money and $0.100 for the player with discounted chips. And one spot at double-zero roulette -- a bet that pays 35-to-1 -- averages $0.053 for the bosses one way, $0.191 for the bettors the other.

Here's one flaw in reasoning based on the idea that the casino must only wait out 10 rounds as the underdog, then has the edge for the duration. The discounted chips are returned to players with payoffs when bets win, so they can be used again. The average number of rounds that can be bet with each chip varies from more than two for Lay bets, to just under two for even-money propositions, to slightly more than one for longshots.

More importantly, per round, players' expected profits with the discounted chips greatly exceed the house's theoretical earnings under ordinary conditions. For instance, $0.113 for someone who bets a discounted dollar on Player at baccarat versus $0.013 for the casino with hard money. So, in this instance, about nine customary bets are needed to offset one with discounted chips.

These factors mean that a person wagering discounted and regular chips can enjoy an extended session with a theoretical edge over the casino. The total number of favorable rounds a player can expect to bet at a constant 1-unit level turns out to equal the number of discounted units, times the discount, divided by the nominal house advantage. The accompanying table shows figures for typical wagers, assuming 10 units bought at 25 percent off.

Average number of rounds bet at a constant level during which Players are favored, with a bankroll including 10 units discounted by 25%

proposition	nominal house advantage	rounds at an advantage over the house
blackjack/perfect BS	0.4%	625.0
baccarat Player	1.3%	187.9
craps Line	1.4%	176.7
craps Place 6/8	1.5%	165.0
0 roulette outside	2.7%	92.5
craps Place 5/9	4.0%	62.5
00 roulette 1 spot	5.3%	47.5
craps Place 4/10	6.7%	37.5

Is this a secret the casino bosses don't want anyone to know? Or a secret they don't know themselves? To understand the root of this dilemma, you need delve no deeper than the venerable verse by the master muse, Sumner A Ingmark:

Absent analytic tools,
Sometimes intuition rules,
Other times it simply fools.