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Ask the Wizard #180
John from Shakopee, NM
Before considering the bonuses, the house edge is lower on the over bet at 6.55%, as I show in my blackjack appendix 8. The probability of three suited cards is 4×combin(78,3)/combin(312,3) = 4×76076/5013320 = 0.060699. The probability the player’s two cards are suited, but the dealer’s card is not, is (4×combin(78,2)×234)/(combin(312,2)×310) = 2810808/15039960 = 0.186889. Let’s assume the action chips are worth 49.5% of face value. Then the bonuses are worth 0.495×(0.060699×$10 + 0.186889×$5) = $0.76301. The expected loss on the over bet is $10×0.0655 = $0.655. So each $10 over 13 bet is worth $0.76301 - $0.655 = 10.8 cents. The overall player advantage is 1.08% on a $10 over 13 bet.
James from Genting, Malaysia
Yes, you should. If you see the dealer has a 2 to jack the odds favor raising on anything. Using this strategy does result in a player advantage. I get into the details in my book Gambling 102.
kemprolemslev from Los Angeles
The probability of winning exactly 92 games and losing 70 is 162!/(92!×70!)×0.5592×0.4570 = 0.056868. To get the exact probability of winning at least 92 you would need to sum this formula for all wins from 92 to 162. The answer for at least 92 wins is 0.353239.
I assume by "dutching" you mean hedging. The sixth of my ten commandments of gambling is "Thou shalt not hedge thy bets." The only time I would make an exception is when the hedge bet itself has a positive expected value, or life changing amounts of money are at stake.
Allan from Toronto, Canada
Thanks for considering them. Bodog has their corporate headquarters in Vancouver. They feel it legally questionable whether they can take bets from their fellow Canadians, so they choose to be beyond reproach and not do so.
Samantha from Belize
The two suits can be divided either 4 and 1 or 3 and 2. Let’s look at the 4/1 split first. There are 4 suits to choose from for the one with 4 cards, and 3 left for the one with 1 card. There are combin(13,4)=715 ways to choose 4 ranks out of 13. There are 13 ways to choose a single rank. So there are 4×3×715×13=111,540 ways to have a 4/1 split between the two suits. By similar logic there are 4×3×combin(13,3)×combin(13,2)=267,696 ways to have a 3/2 split. So the overall probability is (111540+267696)/combin(52,5) = 14.59%.
My question isn’t about winning long term with systems, as we know that’s impossible. But might systems have a usefulness in ’tailoring’ the losing experience? For example, player A prefers that each trip to the casino he will either win or lose a moderate amount of money (of course he’ll lose slightly more often than win). Player B prefers a chance to make a little money 4 out of 5 trips, and lose lots of money 1 in 5 trips.
Both will lose money in the long run, but is there a betting system that might help each accomplish his goal?
Yes. While betting systems can not change the house edge, they can be used to improve the probability of achieving trip objectives. Player A wants as little risk as possible. To minimize risk he should flat bet. Player B wants a high probability of a trip win. He should press his bets after a loss. Such a strategy carries the risk of a substantial loss. Although you didn’t ask, a player who wants to either lose a little or win big should press his bets after a win. This kind of strategy will usually lose, but sometimes will have a big win.
The probability two bingo cards have no numbers in common is (combin(10,5)/combin(15,5))4×(combin(11,4)/combin(15,4)) = 1 in 83,414. The probability two bingo cards have all 24 numbers the same is (1/combin(15,5))4×(1/combin(15,4)) = 1 in 111,007,923,832,371,000.
Kevin from Massapequa
Thanks. (45-4)/combin(52,5) = 1020/2598960 = 1 in 2,548.
Nathan S. from New Plymouth
The probability of making a flush, with exactly three cards to the same suit as your hole cards, is combin(11,3)×combin(39,2)/combin(50,5) = 122265/2598960 = 0.057706. The probability of making a flush, with four more cards to the same suit as your hole cards, is combin(11,4)×combin(39,1)/combin(50,5) = 2145/2118760 = 0.001012. The probability of making a flush, with five more cards to the same suit as your hole cards, is combin(11,5)/combin(50,5) = 462/2118760 = 0.000218. The probability of making a flush on the board in another suit is 3×combin(13,5)/combin(50,5) = 3861/2118760 = 0.001822. Add this all up and you get 0.057706 + 0.001012 + 0.000218 + 0.001822 = 0.060759.
Kristine from Tacoma
It seems he doesn’t want to buy the cow because the milk is free.