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Ask the Wizard #10

In blackjack, do you improve your chances by playing two hands at once for x each, versus 1 hand at a time for 2x? If the odds are better, how much better?

Jim from Atlanta

The simple answer is no, it neither helps you nor hurts you. However, you will have less bankroll variance by betting two hands of x as opposed to one of 2x. Card counters are an exception to the simple no, they may play multiple hands to draw more cards out of a deck rich in good cards, thus improving their odds.

We have been playing online for about two years, and have been quite lucky, but recently, I got bit by the "cash advance" fee on one of my credit cards. I noticed you mentioned that on your online gambling page, and wondered if you had had any success disputing the charge? I tried with mine, and they said anytime money goes to a casino, it's considered a cash advance. This is the first time in all the time we've been playing online, and on a new credit card. Is there a good argument to use with the bank, they just brushed me off? It was Bank of America, incidentally, so watch out for them. Thanks for your time.

Vpwhiz from Long Beach, California

As you read on my page, this has happened to me a few times. When it happened to me, the banks and the casinos each blamed each other for deeming the transaction as a cash advance. Since that time I have found that many credit cards now tell you up front that casino chip purchases are considered a cash advance. This seems to be the situation with your card so I'd say that you are stuck with the fee. If you read the fine print of the Yahoo or Ebay credit card agreements they say this directly. To quote from the Ebay Visa terms and conditions, "Transaction Fee for purchase of wire transfers, money orders, betting or casino chips or similar items, purchase of foreign currency and travelers checks from other than a bank; and use of convenience checks 2% of the transaction amount, with a minimum of $5."

Now, I use a debit card for most of my online casino purchases and never have to worry about cash advance fees. The reversals seem to happen faster as well with a debit card. However, I still use the Next Visa and MBNA Mastercard for my big Golden Palace purchases and they have never charged me a cash advance fee.

Love your site, I have a math degree and I am a blackjack counter who has made numerous trips to Vegas and I want to start to use my math skills to play poker. I have watched poker from a distance in Vegas and would appreciate any advice/explanations of the rules of poker. Can I gain an advantage similar to counting in blackjack?

Kal from Chicago

First, let me say that I'm not an expert on poker. It is no big secret that Texas Hold 'Em is the most popular form. In this game there are five community cards and only two down cards per player so a person good at calculating probabilities has more to go on. However, even the best math genius may make a bad poker player if he can't read the other players or the other players can easily read him (both of which I think are true in my case).

Recently, at a casino I occasionally visit, they had a "teaser" for Baccarat that reduced the commission to 4% during certain periods of the day. I know this would have some effect on the 1.06% house edge on a banker bet, but is it enough to create a +EV for the banker bet? How much would it drop the house edge with a 4% commission on banker bets?

Michael from Sand Springs, Oklahoma

The probability that the banker will win is 45.843%, player 44.615%, and tie 9.543%. So the return of the banker bet with a 4% commission is .45845*.96 - .44615 = -.00606 . So the house still has a thin 0.6% edge.

First of all, I'd like to say I really like your site. It's hard to find a casino site that actually gives good information. Secondly, I'd like to ask a question. I'm from Europe, so I play blackjack with the European hole card rule. It's a multiple-deck game. The dealer deals out the first card to all of the players and one to himself. After that, he gives all the players their second card and none for himself. The players can make decisions after that. After all the players are done, the dealer gets his second card and after that he can make his "decisions". I was wondering what basic strategy I should use for this game. Should I use the Microgaming strategy? The rules of the Microgaming casinos are a bit different though."


For the benefit of others, let me explain that in European blackjack the dealer does not check if he has a blackjack until all players have finished playing their hands. If the dealer does have a blackjack and a player doubled or split, then the player will lose his entire bet. In the United States, the player can lose no more than the original bet if the dealer has blackjack. As you pointed out, online casinos that use Microgaming software follow the European rule. However, Microgaming casinos also play a single-deck game and let you draw to split aces which is unlike the European rules. To make a long story short, please see my European basic strategy.

Let me begin by saying that of all the gambling related sites, the Wizard of Odds is by far the best. My question has to do with a betting strategy for craps. My question has to do with what some people have termed variance. As you state in your Ten commandments, the house has an edge in the long term, but there are short term fluctuations.

A casino I played at had the 3,4,5 odds system where you were allowed 3x on the 4 and 10, 4x on the 5 and 9 and 5 x on the 6 and 8. I feel that with this "system" of placing odds, you reduce the fluctuations (with respect to standard 5x odds on all numbers) in your bankroll, and change the distribution of net gain/loss per session, i.e. you would produce a sharper peak located slightly more to the loss side than with 5x odds. Is this so, and could you put some numbers to it?


That is known as 3-4-5X odds, and is now pretty common. The following table shows all the possible outcomes, for the pass and odds combined, with full odds.

Return Table with 3-4-5X Odds

Event Pays Probability Return
Pass line win 1 0.222222 0.222222
Pass line loss -1 0.111111 -0.111111
Point of 4 or 10 & win 7 0.055556 0.388889
Point of 4 or 10 & lose -4 0.111111 -0.444444
Point of 5 or 9 & win 7 0.088889 0.622222
Point of 5 or 9 & lose -5 0.133333 -0.666667
Point of 6 or 8 & win 7 0.126263 0.883838
Point of 6 or 8 & lose -6 0.151515 -0.909091
Total 1.000000 -0.014141

The standard deviation per pass line bet is 4.915632.