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Ask the Wizard #36

I recently started gambling online and like your site more than any other gambling site I've found. Somewhere I remember you wrote that every online casino you'd seen shuffled the decks after every game. By game to you mean hand? Also, if they shuffle after every hand, doesn't this minimize the benefit of card counting? Is there any significant benefit to card counting in that case?

Greg from Brighton, Massachusetts

Most online casinos shuffle after every hand. However, the six-deck game at Unified Gaming casinos shuffles at a random point in the deck. I have heard of other casinos that also penetrate more than one hand into a shoe, but I don't recall which ones. If the cards are shuffled after every hand there is no use in card counting, other than applying my composition dependent basic strategy exceptions.

I just wanted to know if there is an online casino which has single-deck blackjack and in which the cards are not shuffled after every hand.

Hugo from Santiago, Chile

I don't think so, I have never seen any.

First of all, I really enjoy your site. I thought I had the ultimate system until I did the math that your site provided me. My question is this, the casino is stationary, the gambler is mobile. If everyone went to the casino and promptly left after winning just one unit would there be any casinos? What I mean by one unit, lets say playing blackjack is a five-dollar chip, I show up with $50 and leave after winning $5. Is there a ratio that I should use if this is the strategy I want to play ($50 to $5 = 10%)? And most importantly can this work?

Peter from Vancouver, Canada

The casinos would still win. Most players would indeed walk away with their one unit but some would lose their entire stake, whatever it may be. If you consider only even money games with a probability of winning of p then the probability of winning 1 unit before losing x units is (((1-p)/p)x- 1) / (((1-p)/p)x+1 - 1). In the case of double-zero roulette, with a bankroll of ten units, the probability of winning one unit is 85.4268%. For every one of these players the casino will profit 10*(1-0.854268)- 0.854268 = 0.603056 units.

Also, changing casinos after a one-win doesn't make any difference in the odds compared to staying at the same casino and table.

Which is a better game for the player Spanish 21 or just regular blackjack in Atlantic City.

Michael from Philadelphia, USA

Spanish 21! Under Atlantic City rules blackjack has a house edge of 0.43% and Spanish 21 of .40%.

Do you have any idea what the "record" is for the most sevens thrown with a pair of fair dice in craps is? I had someone tell me it was 84, but the odds against that many sevens in a row being thrown is so long I'm skeptical. It seems it's more possible that 84 consecutive passes have come out, but even that's a million to one shot (figuratively--literally, it's much worse). I tried to look on the Web but have no idea where I would find something like that.


Since this question was submitted, a player held the dice for 154 rolls on May 23, 2009 in Atlantic City. The probability of this is 1 in 5,590,264,072. For the probability for any number of throws from 1 to 200, please see my craps survival tables. For how to solve the problem yourself, see my site, problem 204.

In craps, could one gain an advantage over the house by making both a Pass and Don't Pass bet (one unit each) and then playing the Don't Pass odds? Although the occasional 12 would steal one unit here and there, it seems that the seven would have an advantage over the point. At triple odds one could take 3x on the 4&10, 2x on the 5&9 and 1x on the 6&8.

Jon from Danville, New Hampshire

No combination of bets can give the player an advantage. In your example you would lose one unit for every 12 on the come out roll. You don't make up for it laying the odds. While you usually win laying the odds, you have to risk more. In the end, laying the odds has zero house edge.

I am interested in finding out some specific information on the odds of rolling dice. If you have 6 dice and roll them all at once, the odds of rolling all ones are 1 in 46,656. My question is what are the odds of rolling one to five ones. I am really interested in finding out the formula that should be used to calculate this type of problem.


The probability of rolling x ones out of y dice is combin(y,x)*(1/6)x*(5/6)y-x. See my section on probabilities in poker for an explanation of the combin(x,y) function. For example the probability of rolling 4 ones is combin(6,4)*(1/6)4*(5/6)2 = 0.803755%.

Number of Ones in Six Dice

Ones Probability
0 0.3348980
1 0.4018776
2 0.2009388
3 0.0535837
4 0.0080376
5 0.0006430
6 0.0000214
Total 1.0000000

I have been a dealer now for 10 years, and trying to get out of it. I can not count how many times I have heard people say, "Always assume there is a 10 in the hole". You and I know this cannot be correct all the time. I understand why they say it, but, what are the odds that it really is a ten, and when the dealer has an Ace up, and checks in the card reader for a blackjack, does not have one, you know definitely it is not a ten. What should you assume it is then?

Larry from Redwing, Minnesota

I don't like that expression either. At best it is a memory device to help people remember to hit a stiff hand if the dealer has a 7 to 10 showing. There is no simple rule of thumb that works in all situations.

I'm looking for on-line slots that are nickels and dimes to play.

Travis from Los Angeles, USA

Cryptologic casinos have one-cent minimums on their slots. Real Time Gaming casinos have a five-cent minimum. Most other places are 25 cents.

Michael, thanks for your advice. I have two questions regarding the Odyssey machines that are very popular at Vegas casinos. I like to play their Top Hat blackjack. My first question is how much of a dealer edge do I lose from only getting paid dollar for dollar in winning a blackjack versus receiving the standard 1 1/2 times my bet? Also this machine has a double or nothing feature that seems to give the person a 50/50 chance of winning. Is it worthwhile to use this feature?

Dave from Los Angeles, California

If you win only even money on a blackjack, then that increases the house edge by 2.3%. I recommend the double or nothing feature because it is a zero house edge bet. However, only double up on amounts you're comfortable with losing.