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Ask the Wizard #139

At the showboat in Atlantic City there’s a new bet on the layout where the big 6/8 was. I’m wondering what the odds were on this one roll bet. 6-7-8 pay even money, hard 6/8 pay double. Thanks.

B.L. from NYC

The following table shows the house edge is 5.56%.

Low Bet

Total Combinations Probability Pays Return
Hard 6,8 2 0.055556 2 0.111111
Soft 6,8 8 0.222222 1 0.222222
7 6 0.166667 1 0.166667
All other 20 0.555556 -1 -0.555556
Total 36 1 -0.055556

What is the best strategy in one of those booths with the money that blows around while you have to collect as much as possible in a limited amount of time?


I asked this question to Randy Hill of Fun Industries Inc.. He said you should hold your arms straight out, palms down, and let the money blow up against the bottom of your hands and arms. When enough has accumulated you stuff it through the slot.

What’s your opinion on backing advantage players off of 6 to 5 blackjack? Would you still let them play? Every advantage player that I’ve met says he won’t play 6 to 5 because he gives up too much.


Even 6 to 5 blackjack can be beaten if the penetration is close to 100% and a huge bet spread is used. Sometimes counters will play such games because they can get away with much more. The decision must be made on a case by case basis.

When playing video slots and there is the option to stop one or more wheels or to stop all of them, does that change the outcome of the spin or would the results have been the same if you did not use the touch screen? Great site. Keep up the good work!

Kevin from Fallon

Thank you for the kind words. I passed along your question to an industry insider. Here is his reply.

Manually stopping video reels early has no impact on the outcome. If it did, this would make it a true physical skill game, which is not legal in any US class 3 gaming jurisdiction that I know of. In fact, in some states, physical slot games which can award cash or prizes are allowed only if they offer a true physical stop mechanism which turns the device into a physical skill game.

when i got with my new boyfriend i knew he had a baby on the way but he told me that him and the mother were done. the baby was born and he has been a part of her life but i was on yahoo messagner and the babies mother thought i was her babies father i was on as him. but she wrote me and was like i enjoyed the other night it was wonderful, it just so happens that me and him wasnt together that night. When i asked him about it he got mad and told me to believe whoever i wanted to. so i guess my question is who should i believe?

Cassandra from Cincinnati

I believe the baby’s mother. My advice is to get out of this mess and take some remedial English classes.

I have a friend (ex-girlfriend) who is in a bad relationship. Her husband, married and stayed with because of two unexpected children and a third on the way (all while on birth control), treats her awful, emotionally abuses and manipulates her, and does little in the ways of either housework or regular work. She has almost filed for divorce a couple times, but has stopped herself because she did not know if she would be able to support her children alone. She makes a decent amount of money as the sole breadwinner, so I’m starting to wonder if this is a copout answer (though he doesn’t work, he does provide free daycare services). She also never wants to be the bad guy, especially in her children’s eyes, and she thinks being with her husband is less damaging to them than being without. Let’s say she wins the lottery or somehow comes upon a large sum of money. Do you think she would really leave him?

Wayne from Chicago, Illinois

First, I think you should stay out of it. She seems to be looking at this as the better of two bad choices for her and her children, which is the best way to look at it. Without knowing the situation better I can’t make any predictions but I would let them work it out while you go on with your life.

I would love to see more detail on your "NFL picks" numerical model. Hey, if you start utilizing this to actually make bets, wouldn’t this be defined as a "betting system"?

Ed from Indianapolis

Some of them I like more than others. My model creates what it estimates to be a fair spread in every game and I list the ones that have a disparity of more than a chosen number of points. Personally I bet more on the ones with the larger disparities. However until I have proven my picks are any good I think it would be pretentious to post degrees of confidence.

Suppose we roll three fair six-sided dice. What’s the conditional probability that the first dice shows 4, given that the sum of the three numbers showing is 12?

Shikha from North Ryde

The probability of A given B is the probability of A and B divided by the probability of B. In this case the probability of rolling a 4 on the first die and then a total of 8 on the other two is (1/6)*(5/36) = 5/216. The probability of rolling any total of 12 with 3 dice is 25/216, as shown in my sic bo section. So the answer is (5/216)/(25/216) = 5/25 = 20%.

Concerning your answer about the Italian lottery (see Sep 11, 2005 column), you showed that the probability of 53 not being picked in two years is 1 in 1,707,460. You should have followed up with the probability that any one (or more) of the 90 numbers would be missed during the same two-year period; I think that’s what the person asking really wanted to know. Also, you could have explained (once again) why 53 is no more likely to be picked in the next lottery than any other number, despite the unlikely past situation.


The probability that any number would not be hit in a two-year period could be closely approximated as 90*(1/ 1,707,460) = 1 in 18,972. The actual probability would be slightly less than that because I double counted two numbers being missed, which is very negligible. Of course the past down not matter in the lottery and every drawing has the same probability of picking the 53.

With regards to your NFL picks, are they all weighted the same, that is to say, are any of the picks stronger than others according to your model?

Craig from Calabash, North Carolina

Some of them I like more than others. My model creates what it estimates to be a fair spread in every game and I list the ones that have a disparity of more than a chosen number of points. Personally I bet more on the ones with the larger disparities. However until I have proven my picks are any good I think it would be pretentious to post degrees of confidence.

Whenever my boyfriend of 16 months has a bad day, he gets really cranky and he takes it out by being short and kind of rude to me. I don’t think it’s personal, but how do I get him to stop being mean to me just cause he’s having a bad day?

Caitlin from Elmhurst

I would just turn around and leave the room when he does that. If he follows you then leave the house until he has cooled off. If that doesn’t work I would throw that fish back in the sea. There is an endless supply of nice guys out there who would treat you like a queen who women usually ignore in favor of guys like yours.

I am new to Texas Hold’em and my first book on the subject was Play Poker Like the Pros by Phil Hellmuth. After comparing his ’Top Ten’ Hold’em hands with yours, I have noticed major differences. For example, he has 7-7 as the tenth best and you rank this hand far down the list. There are other major discrepancies. I trust your analyses of various casino games and I wonder how your lists could be so different. Thank you.

Scott from Ruston

Poker is a hard game to advise on because the behavior of other players is unknown. My model assumes all players stay in until the end of the hand, for the sake of simplicity. While I respect Phil’s opinion Get the Edge at Low-Limit Texas Hold’em by Bill Burton lists hands in three groups, and 7-7 is the lowest of pairs to play only in middle or late position. He says 6-6 should only be played in late position. In other words he doesn’t seem to think highly of 7-7 either.

On a full pay deuces wild machine how does a progressive jackpot affect the percent payback. For example on a full pay non-progressive machine the pay out for a Royal Flush no deuces is 4000 coins. This machine has a 100.76 pay out. How is the pay out percentage affected if the Royal Pays 4400 coins?


Assuming no strategy changes for every extra 100 coins in the jackpot the return goes up by 0.044%. So the return with a 4400 coin jackpot would be 100.762% + 4*0.044% = 100.939%.

How long would it take me to lose $10,000 with $5 flat bets playing 6-deck Vegas strip blackjack?

Rachel from La Paz

The expected loss per hand would be $5*0.0062 = 3.1 cents, assuming you play proper basic strategy, and that the dealer hits a soft 17, which is usually the case in $5 games. Assuming you lost exactly that amount per hand it would take 322,580 hands. However the actual number would be a little less because of bankroll volatility and you can’t play after you go broke. To make an educated guess I would say about 300,000 hands. At 60 hands per hour this would be 5000 hours, or two and a half years of full-time play.