Ask The Wizard #152

Watching "Deal or no Deal". I realize the "offer" from the banker is just the remaining values of the cases divided by the number of cases [give or take rounding]. Is there ANY strategy to this game at all, or is "the deal" always just an OK thing to take? Does it depend on how many cases you have to open or anything?

Darren from Elk Grove, CA

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.

Love the site!!! Amazing! Now, according to your BJ House Edge Calculator with 6-deck, dealer stands on soft 17, double on any first two cards, late surrender, and resplit to four hands the house edge is 0.334%. Can you tell me why a similar calculator at a reputable source (QFit) gives a house edge under the same rules of 0.325%, or 0.009% lower?

Daryn from Santa Monica

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.

My wife and father in law went to Las Vegas a couple of months ago and she asked where the Keno games are (sot the Keno slot machines) and was told that most hotels didn’t have keno any more. Is that true? And if so do you know why Mr. Wizard?

Bill from Malibu

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.

What are casinos’ policies on old chips? Let’s say you had a 20-year old chip worth $100, will they exchange it for a new chip? Will they give you more because of appreciation? Also, are chips from casinos which no longer exist usable anywhere? Thank you.

Paul from Glendale

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.

Hi. I just stumbled onto your site, and I think it's a fabulous site for blackjack info. I have a question, though. Can you explain how is there a positive expectation when you follow basic strategy and have a total of ten against a dealer 10 or ace showing (no dealer blackjack). Your table shows a positive expectation for both these scenarios, but I can't understand how. I would think under this scenario the player and dealer follow the same strategy, that is to hit until 17 or better or bust. The soft 17 is eliminated for the player under this scenario so I can't understand where the positive expectation comes from.


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.

On my recent visit in Vegas I saw two dealers independent from each others (one at The Orleans, one at Circus-Circus) suggest to double on 4-4 vs. 6 instead of split. I was the BJ guy of our group and so my friends started to ask me about that. All I could say was: no, splitting is the right decision. (Of course provided that double after split is allowed.) Can I find out the probabilities of these alternatives or can you tell me? kind regards


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)

Firstly, thanks for a great and informative website. I have a quick question about Fortune Bonus Pai Gow. I realize that the fortune bonus bet is a sucker bet as it only pays off less than 20% of the time, however I like to play it anyways, just in case I hit a big hand. At the Trump Casino in Gary, Indiana (near Chicago) the fortune bonus pays out the regular bonuses for a 3 of a kind or better, but also pays 1 to 1 for 3-pair. Statistically speaking, how will this increase your chances of winning on the bonus? What percentage of the time will a player have 3-pair in their hand? Thanks again,


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% .

My boyfriend and I have been dating for three years. Since we started dating on halloween, he said I was no longer allowed to have friends because the only person I needed in the world was him. This rule has only become more strict and now i am no longer allowed to say hi to our roommate, to his friends while at work, or even answer his phone. Since our last anniversary, we’ve done nothing but fight and our relationship seems to be failing. He’s been talking about bringing other people into the relationship and his ex girlfriend has been calling "just to check up on him". She started out of the blue moon, they haven’t spoken in several year. Now, she’s been calling him three times a week for an hour or two at a time. Im not sure if they are planning to get back together or just being friends. I find this to be a double standard. Either way, our relationship is failing and I see it ending soon. I want to know if I should work with him to see whats happening and how to control it, end the relationship or if I should wait for him to approach me.

Jamie from Seattle

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.

I am currently playing your Ties Win BJ at Harrods. I really love it. Great game. My question is about a promo Harrods is having at the moment where if I win five hands/bets in a row I win back the lowest bet in that sequence. As I flat-bet I will win back one of my bets, effectively. Should I have chosen another game to play for this promo? Roulette is excluded but all other games at Harrods are permitted. Thanks,

Mick from Port Kembla

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.