Ask The Wizard #106

While in northern Michigan I came across a new blackjack rule on splitting aces. Instead of resplitting you still only receive one card but you may double on it if you like. Can you tell me the effect of this rule?


I’ve never heard of this rule before. According to my analysis, being allowed to double after splitting aces decreases the house edge by 0.08%. However not allowing resplitting any pair, compared to resplitting to four hands, increases the house edge by 0.06%. So the combination of the two rules decreases the house edge by 0.02%. Following is the basic strategy of when to double after splitting aces, assuming 4 to 8 decks and the dealer stands on soft 17:

Soft 12 to soft 16: double against anything
Soft 17: double against 2 to 9
Soft 18: double against 3 to 6
Soft 19 to 21: never double

What happens if two players get a royal flush, both of who made the progressive side bet, in Caribbean Stud Poker?


I believe what happens in this situation is the player to the dealer’s right would win the progressive jackpot and the other one would win only $10,000. This is because the dealer pays players from right to left so player to the right would be paid first, the meter reset to $10,000, and then the second player paid. However I think the second player would have a legitimate complaint on his hands. The probability of this happening in a full table is 1 in 20,103,110,301. So I would doubt this has ever happened or ever will happen.

I’m a pit boss at an Indian Casino in Northern California and I’ve been following the discussion about Tip Sharing vs. Going For Your Own (April 4, May 13 columns) and I have to say from what I’ve seen, dealers much prefer the go for your own. In fact, because we’re a go for your own house, we have dealers from all over the state (and even from all over the country) trying to get a job here because we’re so close to the Bay Area. Even dealers from far bigger casinos such as Thunder Valley (near Sacramento) and Cache Creek (also near Sacramento) are trying to get a job here because they don’t pool their own tips. I also experienced something similar with another Northern California casino that wasn’t as nice as the one I’m currently at. There was almost a dealer mutiny whenever it was discussed about going to a pooled system.

In Scottsdale, the hottest casino to work at right now is a go for your own joint that has over 100 tables. The dealers there are consistently making several hundred dollars per day working there and everyone from across the country wishes they were there.

The only dealers that I see that wish it were pooled are those that lack personality or have poor dealing skills (or both). The only way those dealers make any money is to pool their tips. And just for the record, the top moneymakers at the casinos I’ve been at are ALWAYS men, and not even very attractive men. While some of the really attractive ladies do indeed make good tips without even trying (or so it seems), the best dealers are truly entertaining personalities with a fast, clean game.


Thanks for your comments.

I disagree with your answer about using the Martingale with an infinite bankroll (May 22, 2004 column). If I had an infinite amount of money and time, and the casino would take any bet, then could I ensure a profit by playing the Martingale (doubling after every loss until I win) on a fair bet on the toss of a coin? The question writer proposes a random walk on a fair bet. The expected value is indeed zero, as you say. But the probability of ever being ahead is 1, as long as you are willing to quit after being ahead some finite amount. The probability of eventually achieving that finite amount with an infinite bankroll and infinite time is 1.... for ANY finite level of winnings. Even if the game is unfair, infinite bankrolls can ensure that eventually you can receive a positive result... and then quit. Pick a level of winning you want... $1 million. Bet a million. If you lose, bet $2 million. If you lose again bet $4 million. In an infinite number of flips, even with the game as unfair as you like, you will eventually win. Take your $1 million and go home. Come back tomorrow and repeat.

Jonathan Falk, actuary

I had a feeling one of my fellow actuaries might disagree with me on this one but I stand by my answer. I see this as a question of expected value rather than probability. The writer used the word "ensure", which is related to the word insurance. An insurance policy would have a fair cost of 1, which is simply the product of the probability (1/2infinity) and amount covered (2infinity). As I said in my original reply, 2infinity/2infinity = 1. So the player would give up his one unit win to pay for the insurance policy. You might argue that the insurance company would never have to pay because they could claim an infinite number of flips have not occurred yet, but I’m assuming a timeless quality in the question. If we did consider time I would be even more right because the player would never live long enough to play an infinite number of flips, and any finite number of losses is definitely possible.

First off, I love your site. I occasionally play Three Card Poker at Grand Victoria Casino in Elgin, IL. They have a Pairs Plus Pay Table that isn’t listed in your Three Card Section:

Pair 1:1
Flush 3:1
Straight 6:1
Three of a Kind 30:1
Straight Flush 50:1


Thanks. This pay table has a house edge of 5.10%.

Do you have a book on various versions of video poker, or can you recommend a book where can I get strategies for Bonus Poker, Double Bonus, Tripple Bonus, Double Double Bonus, and Tripple Double Bonus?


Video poker does not suit itself well to books. There are so many different games and pay tables, and they add new ones so quickly, that a book would be dry and quickly outdated. I recommend getting video poker software that can produce a strategy for almost any game. Two examples of such software are Video Poker Strategy Master and Frugal Video Poker.