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Ask the Wizard #92

How does the casino practice of calling established come bet odds "off" during the "come out" roll affect the house advantage, how is that computed, and how is the house advantage affected by leaving the odds on come bets turned on during come out rolls?


Good question. For those who don’t understand the question, unless otherwise requested, odds on come out bets are not active on come out rolls. So if the player rolls a seven on a come out roll any come bets will lose and odds on come bets will be returned. Likewise if the player’s point on the come bet is rolled on the come out roll the come bet will win but the odds will push. The answer depends on how we define the house edge. If we define it as expected loss to total bets made then turning the odds off would not matter. This is because the player is still betting the odds and it still counts as a bet even if it is returned as a push. However if you define the house edge as expected loss to bets resolved then turning the odds off on a come out roll does indeed increase the house edge. I wrote a computer simulation to determine this effect. Assuming the player takes fives times odds then turning the odds off on come out rolls increases the ratio of losses to total bets resolved from 0.326% to 0.377%, or an increase of 0.051%. So if you want to maximize your return on bets resolved then leave those come odds turned on.

Could you provide some details about the mechanics of "buying in", for example, at a crap table? Do dealers take cash only? If so, and I wish to make a substantial buy-in, does this mean I must arrive at the casino carrying nothing but cash (a risky action in LV)? What about travelers’ checks? Can I make advance arrangements for credit with the casino Cashier’s Office? If so, how does that work exactly? Get specific, please.


I remember my first trip to a casino I didn’t know how to actually get chips to play with and purchased them at the cage and walked them to the blackjack table. The proper way to buy in at the table is simply to lay your cash on the table and at the appropriate time the dealer will exchange the cash for chips. However if you wish to play for amounts too uncomfortable or unsafe to carry in cash you can wire funds to the casino in advance. Then all you have to do when you get there is ask the pit boss for chips and he will have you sign something, stating you are buying chips against your cash account. To get off topic a bit I think it is time the United States Treasury should start making $500 bills, making it easier to carry large amount of money. A 500 Euro note already exists, which is worth $598 U.S. dollars at the time of this writing.

I have encountered an unusual kind of bonus at Aqua Online casinos. If you deposit $100 they will lend you $200. However if you have any money left when you cash out they will deduct the $200 your borrowed. What is your advice on how to maximize the value of this bonus?


My advice is to try to achieve a very large win or go bust trying. The greater your winning goal is, up to a point, the greater your expected return. Personally I would try to get to about $2000. It is paradoxical but the only way to realize the value of the bonus is to lose everything. So you want a high probability of ruin. Hopefully that won’t happen and you will have a very nice windfall.

Playing deuces wild if I hold three deuces what is my probability of getting four deuces on the draw? What if I hold two deuces?


If you hold three deuces there are 46 ways you can get the other deuce and another card. There are combin(47,2)=1081 to choose two cards out of 47 left in the deck. So the probability of getting four deuces on the draw with three held is 46/1081 = 4.26% = 1 in 23.5. If you hold two deuces there are 45 ways to get two more deuces plus another card. There are combin(47,3)=16215 ways to choose 3 cards out of 47. So the probability of getting four deuces on the draw after holding two is 45/16215 = 0.28% = 1 in 360.33.

At a single deck game what is the probability all three players and the dealer get a blackjack the first round after a shuffle?


Following are the probabilities:

Player 1 0.048265
Player 2 0.036735
Player 3 0.024823
Dealer 0.012560

The product is 1 in 1,808,986.

Mr. Wizard, you’re site is great. I think you may be the only honest expert on the internet. My question is this. I know how odds are calculated in craps but I cannot shake the feeling that once a player gets up multiple bets, either through placing them or betting the pass line and making successive come bets, that the odds shift dramatically into the houses favor. It only takes one seven to wipe out all the bets at one time. In order to win, you must hit each number and after it is hit, a seven would wipe out the remaining numbers.


Thank you for the kind words. I still say that the house edge is not dependent on the number of come bets you make. Yes, it is depressing to establish one come point after another and then lose everything on a seven. However there are other times when the shooter takes ages before rolling a seven and you win lots of come bets along the way.

If playing Basic Strategy significantly helps the player not lose as much to the casinos, why do some casinos freely give BS cards out and allow players to consult BS cards while playing? I have seen this in Shreveport, Vicksburg and Black Hawk, CO. Friends have told me that they have done this in Vegas too.


I have played blackjack at casinos all over the United States and have never seen a basic strategy card in blackjack given out for free. However most casino gift shops sell them and they are indeed allowed at the tables. I think the casinos aren’t crazy about the cards the alternative of prohibiting them would be even worse. It would cause a lot of bad player relations to try to enforce a no strategy card rule. Furthermore, where would they draw the line? What if the player wrote the basic strategy on his hand, could the casino prevent a player from looking at his own hand?

Can you explain how the Internet casinos (Random Computers) determine their percentage of money returned. For example: If you are playing basic strategy in black jack you should lose approximately 2.5 to 3 percent over time. Is that based strictly on the hands you are playing at the time; or the number of people online playing at the time; or over a specific number of hands played at that casino by everyone over a period of time etc. The reason I am asking is - can heavy hitters that may be winning in other games affect the cards you are receiving in order for the casino to win its percentage or profit.


When a casino says they pay back 98% for example in blackjack it is generally a historical statistic, looking at the last month or so. They should state somewhere the time period on which it is based. The 98% is the ratio of money returned to money bet is 98%. This generally includes money bet on doubles and splits in the denominator. So if a casino had all basic strategy players their return percentage would likely be less than the house edge, which is based on the initial bet only. Heavy hitters can definitely skew the percentages. That is why sometimes a casino will pay over 100%, because a high roller got lucky and won more than all the other players lost.