In casino math, does 60 minus 50 equal 10?

Mollie and Ollie have been pooling their pin money and playing $10 minibaccarat. They've found that a $300 stake is usually enough to outride the inevitable downswings of the game. They enjoy the thrills and chills, and typically finish slightly ahead or not far behind after a few hours. One thing they miss is that this modus operandi doesn't garner them much in comps.

They coveted the royal treatment accorded to fat cats with bulging bankrolls, who made large bets, and occasionally took heavy hits. So they devised a plan to get in on the goodies.

Their brainstorm was to take $2,000, split it down the middle, sit as far apart as possible at the same nine-spot minibac table, and not openly acknowledge one another. Mollie would then bet $50 per round on Player while Ollie put $60 on Banker.

Both bets pushed when the hands tied. Otherwise, one always won and the other lost. They therefore figured they were collectively still only risking $10 per round. But, separately, they'd be betting a lot and looking like high rollers. More, if one took a serious dive, the other would soar. Between them, they'd be close to break-even, but the loser could likely get a sizeable comp.

Will this work? Casinos make their moolah by means of the edge they have on every bet, because this sends cash in one direction only – from the bettors to the bosses. Casinos gain nothing from the downswings some solid citizens suffer as a result of volatility, since this can cause moves up as well as down and averages out to zero. In the admittedly special case of Mollie and Ollie betting oppositely, the factors that raise one's fortunes simultaneously cut the other's. However, the same effect governs the averages across many folks acting independently.

Edge at baccarat – basing the calculations on every round including those in which the hands tie – is 1.24 percent on Player and 1.06 percent on Banker. Say, arguendo, that participants get 100 hands in an hour of minibaccarat.

With bets of a straight $10 per hand, the gross wager in 100 rounds is $1,000. Were all the action on Player, the casino figures it earns, on the average, 1.24 percent of $1,000 or $12.40. Were the $10 all on Banker, the joint's statistically expected earnings would be 1.06 percent of $1,000 or $10.60.

If Mollie bets $50 per hand on Player for 100 rounds, her gross wager is $5,000; 1.24 percent edge represents $62.00. Likewise for Ollie with $60 on Banker, the gross wager is $6,000; 1.06 percent edge accounts for $63.60. Together, the action has a theoretical value to the house of $62.00 + $63.60 or $125.60.

Were the 100 hands to strictly follow the proportions calculated from the laws of probability, $125.60 would be the casino's real profit. Short-term deviations from the projected results change the numbers, but not excessively except under rare circumstances.

Here's a tangible way to think about it. Pretend that in the 100 hands, Mollie wins 45 and loses 50, Ollie wins 50 and loses 45, and ties occur on the remaining five. Where do they finish?

Mollie picked up 45 x $50 or $2,250 and dropped 50 x $50 or $2,500 so she's $250 in the red. Ollie grabbed 50 x $60 or $3,000 but gave back 5 percent or $150 in commissions, and he's dropped 45 x $60 or $2,700. He's accordingly $3,000 - $150 - $2,700 or $150 in the black. Between them they lost $250 - $150 or $100 in the hour. Depending on the actual mix of hands encountered, the total would vary. Here, the net loss is less than the theoretical $125.60. Other times, it might be somewhat more.

So, let's see. With straight $10 bets, the casino is rating the play at $21.20 to $24.80. With Mollie and Ollie being clever, they're worth $251.20. Were you a pit boss who noticed the team effort, would you deny Mollie a comp because the couple could only lose $10 per hand, or "reward" her based on edge? Here's how the monetizing muse, Sumner A Ingmark, saw just such situations: