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Would You Rather Get Rebates on Your Action or Your Losses?11 February 2003
Pretend you play 1,000 rounds at $1 each on a slot machine with 94 percent payback. The casino calculates its theoretical profit as 100 - 94 or 6 percent of the $1 x 1,000 or $1,000 you put through the machine. This comes out to $60. A normal rebate is a third of the house's theoretical gross, in this case $20.
Few folks whine when they win and the casino credits them for the action
anyway. But bettors bawl when their bankrolls bust briskly in cold
games, then get thanked for their patronage by the laws of statistics
rather than of subtraction. As a simple example, say someone starts with
$200, keeps betting $10 on the five at craps, and goes belly-up after 40
decisions. The real damage is $200. But the theoretical loss on this bet
is 4 percent of the $10 x 40 or $400 handle, which equals $16. If the
casino rebates a third of this, the player "earns" $5.33 -- not enough
for an all-you-can-eat buffet, which the loser laments just cost $200.
Refunding a fraction of the house's theoretical win amounts to a straight discount on the edge. If the casino rebates a fraction of its statistically expected win, its advantage is cut in equal proportion. With a 1/3 promotional allowance, the 4 percent edge on the bets on the five at craps drops by 1/3, to 2.67 percent.
The math for loss-based rebates is more complex. For one thing, the effective reduction in edge depends on how many rounds you play; this, in turn, hinges on whether the casino calculates the reimbursement at the end of a session of arbitrary duration, after a predetermined interval such as five hours at the machines or tables, or for a calendar period such as a month or year. The discount also varies according to the details of what and how a person plays, as well as the fraction of the losses forgiven.
Again imagine a bet on the five at craps, now in a casino that credits solid citizens 10 percent of their losses. Wager your entire stake once and you have a 2 percent edge in the game. Advantage reverts to the casino when you stay for two outcomes, then climbs gradually toward the "retail" 4 percent level. On the 17th decision, edge reaches the 2.67 percent mark characterizing the present rating system. Play more, and you're worse off than with the traditional method. Not that day, of course, if you happen to lose $200 in 40 coups and get a $20 refund instead of $5.33, but prospectively and certainly in the long run.
Betting on the four rather than the five, the nominal house advantage is 6.67 percent. A credit equal to 1/3 of the casino's theoretical win would cut the effective commission to 2/3 of 6.67 or 4.44 percent. A rebate equal to 10 percent of your losses makes this a "fair bet" for one decision and gives the bosses an edge below 4.44 percent for one to seven tries. The approaches are a wash at eight, the loss-based edge hits an unpleasantly ugly 5.46 percent at the 40th round, and it inches toward the undiminished 6.67 percent for the casino thereafter.
The bottom line is that if you're planning limited enough action -- and the bounds depend on the details of the game and the casino's policies -- a loss-based refund might be attractive. As your gambling grows more extensive, and it needn't stretch too far, the familiar formula for recovering a fraction of the handle becomes the superior choice. Sumner A Ingmark, whose poetry, short or long, requires no discounting, created this caveat to consider before you make a deal that looks too much like a steal:
Offers which seem too alluring,
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