Ask the Wizard #98

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.

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.

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.

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.

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.

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.