Ask The Wizard #59

Dear Wizard, First I want to say you are running a first class operation. Second, I was wondering about the prospects of gambling for a living or gambling to supplement one’s income either online or at a real casino. I can imagine it is probably a dubious enterprise for most, but for some, it could be rewarding. Second, I am wondering about the casino’s limits on the size off a wager and how that affects the expected return or how well one can do in a session. It would seem low limits would favor the casino, rather than the player, since statistically, the longer you play the more you will lose. Also, it would seem that it would be easier to start small and work your way up rather than start big and go higher. Also, do you think it is possible to tilt the odds in a players favor long term by a style of play in an online casino for a game such as blackjack?


Thanks for the kind words. I could talk all day about your first question. There are ways to gamble for a living. In my opinion the most viable ways are blackjack card counting, sports betting, and Internet bonus/advantage play. All three of these methods require a large bankroll to make enough to live on, ballpark $100,000, and that is just to get by. Most people have to start small and build their way up. Everyone has to bet relative to his own bankroll. Internet betting limits are high enough for most players. Not many people wish to bet more than $500 per hand. Boss Media’s single player game offers a small player advantage in blackjack, but it is so small it is not worth the time to play it.

Can you explain the numbers inside the slot machines. These numbers are usually seen on the right side of the window. There are three of them what do they mean? How can I use them to my advantage?

Bo from Wetumpka, USA

They are some kind of counter. As a player they won’t help you at all, just ignore them.

In Stanford Wong’s book, "Optimal Strategy for Pai Gow Poker", he presents an analysis of when to keep any two pairs together. Have you done a similar analysis? If not, do you think his analysis gives the optimal plays?

Mike from New York, USA

Yes, I have done a similar analysis. It can be found in my pai gow poker appendix 2. There are some important difference between my strategy and his. Wong’s is much more detailed, considering the highest two singletons, while mine considers only the single highest. Wong also differentiates between whether the player is banking or not. Finally Wong’s book is based on the California game with no 5% commission, unlike my strategy. I do trust Wong’s work and don’t disagree with his table.

What is the probability of getting two identical straight flushes (in both ranks and suit) two hands in a row in Three Card Poker?

Ralph from Harpster

The probability of getting a straight flush on the first hand is 4*12/combin(52,3) = 48/22100 =~ 0.0022. The probability that the next hand will be exactly the same is 1/22100. So the answer is (48/22100)*(1/22100) = 48/488410000, on 1 in 10,175,208. This is a 1.37 more likely than hitting a 6/49 lottery, which has a probability of 1 in 13983816.

What are the odds of making a royal flush in Texas hold-em on the river?

John from Trinity, Texas

For those readers who don’t know, the river is the fifth and last community card in Texas hold-em. The player must make the best poker hand between his own two cards and the five community cards. So you’re asking what is the probability that a player will form a royal flush in seven cards, and that the seventh card dealt will be part of the royal. The probability of forming a 5-card royal flush out of 7 cards, before considering card, is 4*combin(47,2)/combin(52,7) = 4324/133784560, or 1 in 30940. The probability that the seventh card will be part of the royal flush is 5/7. So the final probability is 21620/936491920, or 1 in 43316.

What is the probability that out of 600 bingo cards at least one will get a coverall within 54 calls?


The probability that any given card will have a coverall with 54 calls is combin(51,30)/combin(75,54) = 114456658306760/2103535234151140000 =~ 1 in 18738. The probability of 600 cards not winning are (1-1/18738)^600 =~ 96.79%. So the probability that at least one of the 600 players will hit is are 3.21%.

My question is a very basic one. Are the odds for slots and the payoff tables for games like Caribbean Poker, Three Card Poker and Let It Ride typically lowered on board the cruise ships from major cruise lines?

Paul from Novi, Michigan

I’m not sure. The only cruise I ever took was from Florida to the Bahamas and it only lasted about eight hours. This was before I ever started this web site so I didn’t pay close attention to the rules. However I do recall that the blackjack rules were stingy, and that I lost a lot! Other things I have read corroborate that cruise ships casinos are tight. After all, where else can you play? However the games you mention already have rather high house edges so perhaps there is no need to alter the rules. I also know that Caribbean Stud Poker has a more generous paytable in Europe and Africa, so maybe they use that one.