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Ask the Wizard #98

You say the house edge on the pass line bet in craps is 1.414%. Is there any coincidence that this number is the square root of 2?

"Anonymous" .

Just a coincidence I assure you. The exact house edge in craps is 7/495, which by definition must be a rational number. In fact I would argue the house edge in all casino games must be a rational number because there are a limited number of possible outcomes in all games, resulting in a house edge of a perfect fraction. 2 is not a perfect square thus the square root of 2 must be irrational by definition. Therefore the two numbers can not be equal. To be specific the house edge on a $100 pass line bet would be $1.41414141... The square root of 2 is 1.4142135623731...

The Hollywood casino in Tunica started offering a FREE progressive side bet on two $5 tables. The rules are six decks and dealer hits a soft 17, all other rules are standard. They swear there are no rule changes to the game (Dealer hits, DAS, 4 splits, 6 decks). Suited sevens of diamonds gets the progressive, which starts at $1,000. All other triple sevens pay $50. So how high would the progressive need to be to get to breakeven?

"Anonymous" .

The probability of three seven of diamonds is combin(6,3)/combin(312,3) = 0.00000398937. The probability of three unsuited sevens is (combin(24,3)-combin(6,3))/combin(312,3) = 0.000399735. According to my blackjack calculator the house edge is 0.6233%. The expected loss on a $5 bet would be 3.12 cents. Just the value of the $50 for three unsuited sevens is $50*0.000399735=2.00 cents. To make up the other 1.12 cents the meter would need to reach $2802.

I read about someone winning 1.3 million at an Online Casino in Caribbean Stud and not being paid because they used robot play. What is robot play, how does it win, and why is it illegal?

"Anonymous" .

First, the game was Caribbean 21, not Caribbean Stud. The casino this money was won from alleges that the player used robot play, which is against their terms and conditions. If this is true (the player denies it) then it is within their rights to forfeit the winnings. Robot play is a program that can read the cards on the screen and can play against the casino by itself, by simulated mouse moves and clicks, or keyboard actions. Some casinos don’t allow it because they have some games with a theoretical return slightly over 100%. Robot play could ensure nice expected hourly profits for the person using it, but not enough to bother actually playing. A good example is Boss Media’s single deck blackjack game with a player advantage of 0.11%. Some casinos with no positive expectation game allow robot play and others do not. I do not know why those with no positive expectation games prohibit robot play. Some skeptics claim they retain the right to avoid paying big winners, simply by alleging robot play. In this situation the casino has released a taped confession in which the player offers to sell the robot. However the player says it was taken out of context. It is a long story, for more details follow this link to Casinomeister’s forum on this topic.

If there is no house advantage in the double up feature in video poker, why do the casinos offer it?

"Anonymous" .

Just to attract customers who like it. It definitely lowers hands per hour, and thus profits, but if they get extra players it may be worth it.

How does an online poker sites protect its customers from collaboration?

"Anonymous" .

I’m not sure, but they swear that they have tests for this. They wouldn’t want to explain exactly what they test for, lest the collaborators take countermeasures. However an easy sign would be when 2 or more players always play at the same time.

Mr. Wizard, great site. You are the one true expert on the internet. Because the odds in dice are based on the probability of winning as compared with the payout, I question whether it makes sense to take odds on bets that have a low a probability of winning. For example, the odds on the 4 and 10 are 2 to 1. Is it really a good bet to back up the pass line when the 4 or 10 shows. If someone offered a payout of 10,000 to 1, with the odds of winning 5000 to 1 (and you could only make one bet), it would appear to be a good bet, but the chances of winning are so slim that in reality it is probably a suckers bet. Is there any validity to what I am saying?

"Anonymous" .

Thanks for the compliments. As you know I strictly look at the expected value of a bet. However, if taken to an extreme it doesn’t make sense at some point. If you made the proposition to me in your example I would only bet about $200 on it, although it has a 100% player advantage. The reason is if I won I would win $2,000,000 and I don’t really need more than that. However in craps a 2 to 1 win is not going to change my lifestyle if I win. 2 to 1 in craps is not a big long shot so I say get aggressive on the odds. If you’re uncomfortable with bets that have a low probability of winning you might take up betting the don’t pass and laying odds.

I was playing jacks or better on your site. I had the following: 2(spades),5(clubs),J(clubs),10(diamonds),7(clubs). The optimal play is keeping the Jack only and your program stated the expected value was 2.3662715, but I calculated it myself and got 2.3662714. Which one of us has the rounding error?

"Anonymous" .

Leave it to a couple math geeks to argue over the eighth decimal place. I checked the exact combinations of each hand and you are right. The exact value is 5*(84412/178365), or 2.36627140974967 to 15 decimal places. Whatever you are using obviously carries floating point arithmetic to more decimal places than the internal Java calculator.