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Ask the Wizard #184

I would like to know the decisions per hour in particular for the poker games: Three Card Poker, Caribbean Stud, and Let It Ride. Thank you.

Giorgio I. from San Juan

Please see the following table. This table also shows the house edge assumed for player rating purposes. My source is an executive with a major Strip casino here in Vegas, who wishes to remain anonymous.

Hands per Hour and Average House Edge

Games Hands/Hour House Edge
Baccarat 72 1.2%
Blackjack 70 0.75%
Big Six 10 15.53%
Craps 48 1.58%
Car. Stud 50 1.46%
Let It Ride 52 2.4%
Mini-Baccarat 72 1.2%
Midi-Baccarat 72 1.2%
Pai Gow 30 1.65%
Pai Pow Poker 34 1.96%
Roulette 38 5.26%
Single 0 Roulette 35 2.59%
Casino War 65 2.87%
Spanish 21 75 2.2%
Sic Bo 45 8%
3 Way Action 70 2.2%

A test consists of 10 multiple choice questions, each with 5 possible answers, 1 of which is correct. To pass the test a student must get 60% or better on the test. If a student randomly guesses, what is the probability that the student will pass the test?

Kirk from Canton

The probability of exactly 6 correct is combin(10,6)×0.26×0.84 = 0.00550502.

The probability of exactly 7 correct is combin(10,7)×0.27×0.83 = 0.00078643.

The probability of exactly 8 correct is combin(10,8)×0.28×0.82 = 0.00007373.

The probability of exactly 9 correct is combin(10,9)×0.29×0.81 = 0.00000410.

The probability of exactly 10 correct is 0.210 = 0.00000010.

Adding the probabilities for 6 to 10 correct, the probability of at least six correct is 0.00636938.

If I show you a Roulette game with no zeros and all usual roulette rules apply, is it possible to win 100% of the time?

Jon P. from London

No.

I am curious about the current online gaming law. I won a free wagering account ($75) at an online sports book and have managed to turn it into nearly $200. I know that you are not an attorney, but is it ’legal’ to cash out and present the check at my bank? Or, when I present the check, will alarms sound and a net be dropped from the ceiling, capturing me? I fully plan on claiming my winnings, albeit small, on my Federal taxes. I always remember that the only thing Al Capone ever did time for was tax evasion! Thanks for your time and consideration wiz! Best of luck to you!

Rob from Pittsburgh

I’m not an attorney, so I’ll refrain from giving an opinion on the legality. For practical purposes checks from Internet casinos and sports books are sent from generic accounts, usually out of Canada. From looking at the checks you wouldn’t know whom they are from. I have never once heard of a bank not honoring such a check (unless it bounced), or anyone being prosecuted for attempting to cash a single check. So, my advice is go ahead and cash it. You should do so inside with a teller, because some banks don’t like foreign checks deposited in an ATM.

What is the probability of getting a straight flush (including the 4 royal) in Omaha poker? Thanks in advance.

Mickey F. from Gambrills, MD

I hope you’re happy, my computer spent five days cycling through all 464 billion possible hands in Omaha. Here are tables for both the high and low hand. For the benefit of other readers, in Omaha the player gets four cards to himself and five community cards. He must use exactly two of his own cards and three community cards to make the best high and low hands. For the low hand, straights and flushes do not count against the player, and aces are always low.

Omaha High Hand

Hand Combinations Probability
Royal Flush 42807600 0.000092
Straight Flush 368486160 0.000795
Four of a kind 2225270496 0.0048
Full House 29424798576 0.063475
Flush 31216782384 0.067341
Straight 52289648688 0.112799
Three of a kind 40712657408 0.087825
Two pair 170775844104 0.368398
Pair 122655542152 0.264593
All other 13851662832 0.029881
Total 463563500400 1

Omaha Low Hand

Hand Combinations Probability
5 high 7439717760 0.016049
6 high 25832342400 0.055726
7 high 51687563904 0.111501
8 high 76415359104 0.164843
9 high 90496557312 0.195219
10 high 87800751360 0.189404
J high 68526662400 0.147826
Q high 39834609408 0.085931
K high 13835276928 0.029845
Pair or higher 1694659824 0.003656
Total 463563500400 1

A long time ago, I asked you about progressives on slot machines where they decide to pull that slot. And I asked if the amount over the base minimum for the progressive is just kept or if it is redistributed to players in some other way. You weren't entirely sure. Well something interesting happened over Christmas. I follow jackpot amounts at the IGT website. The jackpot for $0.25 Wheel of Fortune jumped unexplainably from about 3-400,000 to over $5 Million literally overnight. At the same time, I noticed that they had pulled the Quartermania machines, which had a jackpot of over $2 Million at the time. There were some other brands that had disappeared as well. If you click on the link for the $0.25 Wheel of Fortune, you'll see that it shows the last win at over $5 Million at Caesars. So my question is, do you have the resources to figure out what happened here? Is it just a typo or error, or did they really roll other discontinued jackpots into this one? Thanks in advance.

Roger S. from Dallas, Texas

I agree with your hypothesis, that they pulled out the Quartermania machines and rolled the progressive jackpot into Wheel of Fortune. It can't be a coincidence.

I’m totally baffled! If in an 8-deck or continuous shuffle blackjack game there is no difference in the probabilities of a card appearing at any time, why have you posted Blackjack Appendix #18? If the probabilities say hit on 16 vs. 7 or higher, how can the probabilities change if you have 5 or 6 cards as opposed to 2 cards? 16 is 16 no matter how you construct it, right? I see the change if the deck is shrinking or in a game like Spanish 21 where there is a bonus for 21 with 5 or more cards, but why in an 8-deck game or continuous shuffle?

Ernie from Toledo

The reason the strategy changes, according to the number of cards in your hand, as shown in appendix 18, is that every card that leaves the deck changes the probabilities of every card left to be played. A good example is the single-deck basic strategy says to surrender 7,7 against a 10; but for any other 14 you should hit. The reason you should surrender is half the sevens have already been removed from the deck. You need another seven to make 21, the only hand that will beat a dealer 20. So the shortage of sevens lowers the expected value of hitting to under half a bet, making surrender the better play.

In an eight-deck shoe there are 416 cards. That may seem like a lot, but 16 against a 10 is such a borderline hand that removal of just one card can making standing a better play. The rule is that for eight or fewer decks if your 16 is composed of three or more cards, and the dealer has a 10, then you should stand. In a two-card 16 the average points per card is 8, with a 3-card 16 the average is 5.33. With more small cards out of the deck in the 3-card hand the remaining deck becomes more large card rich, making hitting more dangerous, swaying the odds in favor of standing.

What is the maximum amount of money you can win on a college football wager in a Vegas casino without having to provide your personal information to the casino when you cash out your ticket? I’d like to know the amount I can win (per wager) and still have them pay me cash with no questions asked.

Harold from Monterey Park, CA

$10,000. A cash transaction of more than $10,000, whether in sports or not, will necessitate a CTR (cash transaction report). You may also ask to be paid in chips, although the same CTR would be generated if and when you cashed them in.