Ask The Wizard #102

You’re welcome. To minimize the element of risk you should raise until the point where the expected value of raising is less than the element of risk for the entire game. The expected loss by raising on Q-6-2 is 1.24% and on Q-5-4 is 2.10% to 2.15% (depending on how the cards are suited). So to minimize the element of risk you should raise on Q-6-2 or higher.

Assuming the player plays the same number of hands regardless of results then the casino would make the same amount of money either way, over the long run. Yet if the player will quit early if he reaches a certain loss point then he will play less on average and consequently the casino will make less money. It sounds paradoxical but if you quit playing when you go broke then you will lose more at a low volatility game, because there is a smaller chance of ruin and thus the house edge will grind you down longer. So by increasing your probability of ruin your expected loss actually goes down. For example if player A bets his entire $100 bankroll by betting on red in one spin of roulette then his expected loss is only $5.26. If player B bets $1 at a time for 8 hours on red in roulette his expected loss is 60*8*5.26% = $25.26 (assuming 60 bets per hour). So although player A has a much higher probability of ruin his expected loss is much less. This lesson is especially applicable to Internet bonus playing. If you get the bonus up front I recommend betting everything in one hand to start. By sometimes going broke before completing the play requirement you expose yourself to the house edge less and thus save time and lose less playing over the long run.

The odds are exactly the same on a one line, 10 line, and n-line video poker machine. When you get a trash hand in 100-play you can expect to get about 36% of your original bet back. In 10-play it is still 36% but there is more volatility. In 1 play it is still 36% but you can get lucky and get a high paying hand on the draw. In other words you are more likely to hit it big on the draw in single play, but at the expense of lots more non-paying hands.

Thanks for the kind words. Assuming the pay table is the same the strategy and expected return are exactly the same. Be warned that multi-play games tend to have worse pay tables than single line games.

There is a lot written about card counting simply because the books sell. I suspect many people watch a movie like Rain Man and get interested in card counting. Then they buy a book and realize it is too hard or give it a try and get discouraged because they lose. Only the most patient, devoted, and well financed players stick with it.

You could test for how often the same card appears in two consecutive hands. Considering only the four initial cards dealt and assuming all four are different the expected number of those cards seen in the next hand is 16/52 = 0.307692, assuming the cards are shuffled after every hand. If you see fewer repeats than would argue that the cards are not shuffled after every hand. If the cards are not shuffled between hands the expected number of repeats seen would be 4*(4d-1)/(52d-4), where d is the number of decks. It is easier, but less reliable, to just ask customer support.

I have heard this allegation a lot of times but have yet to see any proof either way.

With the demise of Binion’s Horseshoe the number of true single deck games in Vegas has fallen by about 75%. Although it isn’t a priority of mine to keep up to date on this some that I know of are the Fiesta Rancho, Golden Gate, El Cortez, and the Western. Beware of single deck games that only pay even money or 6 to 5 on a blackjack, you are much better off at a shoe game that does pay 3 to 2.

1-(5/6)³⁶ = 99.86%

Each roll the expectation is that 5/6 of the dice will remain. So the expected number of dice remaining after n throws would be 36*(5/6)ⁿ. For example after 10 throws you would have 5.81 dice left, on average.