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Ask the Wizard #12

As a first time gambler in Vegas, I've been told to play craps and Caribbean Stud. How much money should I prepare to take to a sitting of each to try to stay in the game long enough to see results?

Vinnie from Tulsa

If you play long enough, the only results you will see is that you will lose all your money. Don't bring to the table more money than you care to lose in that sitting.

Second, Caribbean Stud Poker has a house edge of 5.22%, so if you're trying to stay in the game as long as possible, I would avoid that one. The best table games are craps and blackjack, when played properly.

This is my second question to you, this time the subject is state lotteries. I'm sure you've heard of a group of "investors" which used to wait for a jackpot to reach a certain level, at which point they would purchase tickets with every combination of numbers possible. This would assure them a share of the prize. Assuming the cost of a ticket is $1, how high must the jackpot get for this to be a profitable venture?


A factor in the answer is the total number of tickets sold to other players. In the event more than one player hits the jackpot it will have to be shared. Let's call the number of possible combinations n, the total number of other tickets sold t, the rate of return on the small prizes r (in the case of the Big Game r=0.179612), and j be the jackpot size. For this to be a break-even venture j*n/(n+t) + r*n - n=0. This works out to j=(1-r)*(n+t).

In your blackjack strategy you surrender 16 against A,10,9. You say to split a pair of 8's against those cards. I have been told that a pair of 8's is a 16 and should be surrendered. What do you think?

Jim from Naples, Florida

Whoever told you to surrender two 8's gave you incorrect advice, assuming American late surrender. To illustrate why you should split 8's against a 10, check my blackjack appendix 9b. This shows expected return for any initial situation for any given play. The table shows that splitting 8's against a 10 in double deck has an expected return of -0.4706, if allowed to double after a split. In other words, you can expect to lose 47.06% of the initial bet on average.This is less than the 50% you would lose by surrendering. If not allowed to double after a split, then the rate of return is -0.4801, again more than -0.5 . Splitting 8's against a 9 or ace has an even greater return.

I was wondering... Knowing that online casinos shuffle after every hand, making card counting impossible, I have found that there are, indeed, a few advantages.

A) You do not have to tip,
B) You can go one-on-one against the dealer (no other players),
C) You can play more hands (again, due to the lack of other players) per hour than in a real casino, and
D) you can enjoy a large betting spread without suspicion.

Do these factors make the online game advantageous in any way? Has any test been run on these systems? So far, I've done nicely -- in fact, I've done better online than in any real casino. What do you think? Any input is appreciated. Thanks!


You have already pointed out some of the advantages of online blackjack, as opposed to a physical casino. Unless you are card counting, it is to your advantage that they shuffle after every hand. In the land casinos they will usually play until a specific point is reached in the deck, finish that hand, and then shuffle. This works to the player's disadvantage because more cards will be dealt when the shuffle point is reached in a deck rich in small cards than one rich in big cards. In other words, in a physical casinos the player will see slightly more small cards than large cards over the long run, which is bad for the player. However, much more important is the fact that you don't have to feel obligated to tip in an online casino. The faster play, one on one play, and the larger spreads do not help nor hurt the casual player. I attribute your better results in online casinos to any combination of luck, better rules, and not having to tip.

Would it be that in general the longer you play the more likely you are to lose, with the exception of games where the player can overcome the dealer advantage? Do you recommend a strategy to overcome this, such as initially making large bets as a percentage of deposit. If you come out ahead on larger bets, then you can reduce the size of your bets to try to stay in the game longer.

Chris from Andover

Yes, in a negative expectation game (as most are) the longer you play the more likely you are to lose. If you want to maximize your chances of a net win, at the cost of a possible very large loss, then the best strategy is to bet more after losing, thus trying to recoup past losses. The Martingale is an example of a very aggressive form of this strategy.