Ask The Wizard #152

As my December 26, 2005 column shows the banker offer is usually much less than the average of the remaining cases. However, hypothetically, if it always were, then every strategy would have the same expected value. The player would be indifferent at every offer.

Thanks for the compliments. There are several assumptions going into the calculation that may cause the small difference. For example are the cards shuffled after every hand or is a cut card used? Does the player use total dependent basic strategy or composition dependent basic strategy? Is rule interaction factored in, or is the calculator simply adding up the effect of each rule? My figures are based on a random simulation using total dependent basic strategy, both of which work against the player, which may be the reason I come in a little higher. It also may be due to an insufficient sample size in the random simulation. Despite all these factors I think the difference is still negligible: just one bet per 11,000 hands played.

I disagree. I can’t think of a single major Strip casino without a keno lounge. In general the only casinos without keno are the locals casinos in the suburbs of Vegas, because most of us locals know that keno is a sucker game.

P.S. A reader later wrote in to correct me, stating that the New York New York casino in Las Vegas removed their keno lounge.

Sometimes in the Las Vegas Review Journal there is an announcement in the classifieds that a casino is discontinuing the use of a style of chip with a deadline to redeem them. After that time the casino would not be obligated to honor the chip. However there is a teeming market for casino chips, especially expired ones. I don’t know much about it except there are shows here in Vegas for the collectors and the Vegas museum in the Tropicana has lots of old chips for sale.

Thanks for the kind words. Let's assume six decks (it doesn't matter whether the dealer hits or stands on soft 17). My blackjack appendix 9 shows the expected value of 6+4 against an ace to be +0.081336, and 6+4 against a 10 to be +0.026796. The reason the expected values are positive is my expected value tables assume the dealer already has peeked for a blackjack and has confirmed that he doesn't have one. Meanwhile, the player can still draw an ace for a 21. In other words the player can make 21 on his next card and the dealer can not by assumption. If I had such a table under the European no-peek rule, then the expected values would indeed be negative.

I’ve said this before but as much as I respect dealers as a group they give out a lot of bad advice and misinformation. Splitting fours against a five or six is a frequent play where both players and dealers incorrectly rebuke splitting. Sometimes you hear people say falsely that you should never split "anything that starts with F", in other words fours, fives, and faces. That is true about fives and faces but the player should indeed split fours against a five or six if double after split is allowed. Otherwise the player should hit, except in single deck he should double if allowed. My blackjack appendix 9 shows in a six-deck game where the dealer hits a soft 17 the following expected values of 4,4 against a 6.

Stand: -0.114085
Hit: + 0.113365
Double: + 0.092929
Split: +0.207228 (double after split allowed)
Split: + 0.056954 (double after split not allowed)

You're welcome. Here is the number of ways to make a three pair:

No joker: combin(13,3)*10*combin(4,2)³*4 = 2,471,040
Joker used in a pair of aces: combin(12,2)*10*4²*combin(4,2)² = 380,160
Joker used as singleton: combin(13,3)*combin(4,2)³ = 61,776

The total number of possible combinations is combin(53,7) = 154,143,080. So the probability of a three pair is (2,471,040+380,160+61,776)/154,143,080 = 0.0189. So, changing a three pair from a loss to a 1 to 1 push would reduce the house edge by 1.89% .

What a waste of three years! You should have walked the moment he started setting down rules about who you could be friends with. Cut this insecure jerk lose immediately. My pity will go to his ex-girlfriend, assuming they get back together.

Thanks for playing it. Yes, Ties Win Blackjack was a good choice for this promotion. The probability of a full win is 43.314%, a half win is 8.75%, and a loss is 47.936%. So the probability of any win is 52.064%. The probability of five consecutive wins is 0.52064⁵ = 3.825%. Flat betting this results in an extra 3.825% of return for the player. The house edge normally is 0.247%, so the player advantage under this promotion would be 3.5785%. However I find no mention of this promotion on the casino web site and given my usual 2-3 week delay to answer e-mail it is probably over.