by Richard Burke
In our local poker room, we often have to wait for tables for a half-hour or more. If we want to play the slots or another game while we wait, then the poker room lends us a pager which vibrates when our seat becomes available. Fred signed up for a few games last Saturday and headed for a blackjack table after he got his pager. Fred just loves action, so he not only plays Twenty-One, he also makes Lucky LuckyTM proposition bets.
Many other casinos offer Lucky Lucky prop bets. The last time we went to the Strip we saw it at Excalibur, New York New York, Rio, Treasure Island, the Venetian, and others. Casinos and Racinos in California, Illinois, Indiana, and Minnesota also offer it, so beware. Fred figured that if he hit three sevens suited or the three-card straight flush of 6-7-8, then for a measly dollar he could win his buy-in at either $4-8 limit or $1-2 nolimit hold’em. Lucky Lucky works this way: in a six-deck shoe if three cards, your first two cards and the dealer’s upcard, sum to nineteen, twenty, or twenty-one, then you win; otherwise you lose. The odds table nearby shows all the winning combinations.
If the dealer dealt you a pair of sevens and the she also dealt herself a seven for her upcard, then you win $50 for a $1 bet. If all three sevens belong to the same suit, then you win an additional $150. If your first two cards and the dealer’s upcard sum to nineteen, then you win $2 for a $1 bet, and so on per the table.
We deal with big odds and low probabilities using the concept of expectation. We use mathematics to imagine that we bet $1 a zillion times and then tally how often the bet pays off. Our friend from high school and college, Hal Holcomb Wyman, CalTech Mathematician, did the heavy lifting in figuring these Lucky Lucky expectations.
Using combinational mathematics we obtain 5,013,320 possible tripletons from a six-deck shoe, so we divide the numbers of profitable combinations by that number and multiply by their payouts to arrive at their expectations. We always express expectations in dollars, the amount you should expect to win for one dollar risked each time. The table shows that Fred should expect to win 73.6 cents for every dollar he risked – the casino holds 26.4 percent of the handle. No wonder so many casinos offer Lucky Lucky: it offers the player about the same crumby returns as Keno!
Fred argued that he played only for a quarter-hour or so, just while waiting for a seat at the poker table, so it didn’t matter that the expectations showed a big leak. But he played every day almost, roughly seventy-five hours a year. Twenty-One dealers average 70 hands an hour using a six-deck shoe. Over the course of a year Fred played about 5000 hands while waiting for a poker seat. His $5000 in Lucky Lucky prop bets returned $3680 on the average, for an out-of-pocket loss of $1320. Fred couldn’t believe it. “Thirteen hundred dollars just for those prop bets, not even counting the beatings I took at regular blackjack? Phooey, I’m not doin’ that no more!” Good thinking.
Do Puts and Calls interest you? Check out Mr. Burke’s revolutionary new equations at http://www.postalnet.com/OptionValueEquations.html. E-mail your Hold ’Em questions to firstname.lastname@example.org