Ask the Wizard #76
John from Milwaukee, USA
The probability of hitting x royals in an n-play machine when drawing to a 4-card royal is combin(n,x) * (1/47)x * (46/47)n-x. For an explanation of the combin(n,x) function visit my section on probabilities in poker. In the case of 3-play the probabilities are as follows:
0 royals: 0.937519
1 royal: 0.061143
2 royals: 0.001329
3 royals: 0.000010
Larry from Silverdale, Washington
There are combin(52,3) = 22100 ways to arrange 3 cards out of 52. So the probability of any given hand matching the last one exactly is 1 in 22100.
Andrés from Lima, Peru
Sorry to hear about your misfortune. However that is the fate that awaits most who overplay their bankroll, especially in slots. There is no way to beat any of these games. I would recommend you quit gambling completely.
Bayne Steele from Petaluma, California
This pay table has a house edge of 13.07%, the lowest I have heard of for Let it Ride. Still a sucker bet though.
Jan from Ontario, Canada
There are two software programs that can produce near optimal strategies for almost any video poker game. One if Video Poker Strategy Master by Tom Ski and the other is Frugal Video Poker by Jean Scott. Winpoker 7.0 promises to offer this feature as well but as of this writing it is not out yet. I don’t like to give away too many video poker strategies for free because other experts have to make a living selling video poker software or strategy cards.
I just had an eye-opening experience at Casino Windsor. No where do they publish their percent payback on slots. However, that aside, I was going to play quarter (my comfort level) video poker. I was really taken aback when I put up the paytable. They were 5/4 machines. I am talking Jacks or better was only 5 coins on a full house and 4 coins on a flush. I looked at about 20 machines and only found one that paid any better and that was a 6/4 machine.
As I stated, I am not a mathematician but I think that payback percentage must be in the very low 70s. Needless to say I didn’t play video poker there because I know that the longer I would have played the greater the loss I could have expected with the house taking approximately $30.00 from every $100.00 put through the machine. That is not a gamble with some expectation of winning, it is a sure loss for players. On the Detroit side of the river, MGM Grand has their machines at 7/5. Not really great but a whole lot better than 5/4.
Could you please tell me the exact percentage payback on the 5/4 and 7/5 machines. Since none of the area casinos post their average payback on slots I am (and this is dangerous) assuming that their reel slots payback the same percentages. Best regards.
Mort from Walled Lake, Michigan
Actually with perfect play the 5/4 pay table return 92.78%. Still one of the worst pay tables I have ever heard of. Have you tried the Greektown casino in Detroit? I don't know what games they have but I do know they have had security remove several winning video poker players from the building, including a old lady who hit a royal on a machine with a 97% pay table. They must have something good enough to warrant throwing winners out for.
Richard from Saint Joseph, USA
There are combin(52,7)=133,784,560 ways to arrange 7 cards out of 52. The number of 7-card sets including a four of a kind is 13*combin(48,3) = 224,848. The 13 is the number of ranks for the 4 of a kind and the combin(48,3) is the number of ways you can choose 3 cards out of the 48 left. So the probability is 224,848/133,784,560 = 0.0017, or 1 in 595.
Gordon from Niagara Falls
Thanks for the kind words on my Travel Channel appearance. For those of you who missed it the show was titled Sucker Bets. The dealer was right. In general bets are turned off on a come out roll in which a seven would cause the player to lose. I guess they don’t want some players to sour the mood of the table by rooting against a 7 on the come out roll. Since a 7 would cause the odds on the don’t pass to win they are left on.
Eric from Ephrata, Pennsylvania
I maintain that even with an infinite bankroll, betting limits, and time the Martingale still would not beat a negative expectation game like roulette. My reason is that as these elements approach infinity the expected value of the Martingale on roulette is still -5.26%.
Still, mathematicians I respect have disagreed with me. The debate tends to get very abstract and absurd, hinging on the nature of infinity, which is a man-made construct to begin with. There is nothing known in our universe that is infinite. If forced, I think it is a ridiculous question.