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Ask the Wizard #19

I've always thought that the major flaw,(but certainly not the only one),in the Martingale system was that the return was simply too small to justify the risk. My question is, would a tripling of the bet which would yield a profit per win of approx. 50% of the winning hand justify the system. In other words, would a bankroll of 1093 units playing through 7 betting levels produce an overall profit exceeding its loss, or is it doomed to eventual failure the same as the standard Martingale?

Jack from Desoto, Texas

Every betting system based on a negative-expectation game like craps is doomed to eventual failure. By tripling your bets, you will have bigger single wins, but you will reach your bankroll limit faster and have more losses. It all averages out to the house edge in the long run.

Do you believe that "wishful thinking" on behalf of the players can affect the outcome of a game. Note that I'm not concerned with the SIZE of the effect, just your philosophical opinion. Also, do you think that the manner in which a player tosses the dice in craps can cause a bias (good or bad) in the outcome. As always, your site is AWESOME.

Ted F. from Perth Amboy, New Jersey

Thanks for the kind words. No, I don't think that wishful thinking helps in the casino, all other things being equal.

The question on the dice influence is a hotly debated topic. Personally, I'm very skeptical. As I review this reply in 2013 I still have yet to see convincing evidence anybody can influence enough to have an advantage.

Your newsletter gives the casino advantage on Spanish 21 as 0.34% if the dealer doesn’t hit soft 17. How effective is card counting in further reducing this house advantage and giving the advantage to the player?

Rod from Newburgh, Indiana

Good question. Yes, this house edge is definitely low enough to consider card counting. Since most card counters don’t even consider Spanish 21 I think the field is ripe to exploit the game and to do so with a great deal of impunity. However counting may not be as effective in Spanish 21 as regular blackjack. A small card rich deck will benefit the player in more multiple card 21’s. To the best of my knowledge nobody has developed index numbers for Spanish 21 but somebody should. Maybe I will.

Are you confident of your figures on the online software? In particular, do you really have a .53% advantage over the house just with good basic strategy? I’ve never seen anyone give figures of a player advantage before for any rules with only basic strategy.

Jack Z. from Olympia, Washington

I’m confident with that figure. It was determined using a random simulation program of mine. I speculate the creators of the software made a mistake and only intended to offer late surrender on tens and aces, as was the case with the preceding version. I called one online casino that uses Unified Gaming and they were not even aware the new software allowed for early surrender on aces. I give the house edge figures as a service to my visitors. (Update Jan 22, 2005: Unified Gaming changed the rules of their game years ago to remove the player advantage)

Hello Mike. Two questions about Caribbean Stud Poker. It has a big house advantage. Can this advantage be reduced by seeing one other player's cards? This happens often, especially if you are playing with a spouse or friend, even though the casino says you not supposed to do it. The second question is about draw Caribbean stud. The dealer has to qualify with a pair of 8's or higher. You (and the dealer) can draw 3 or more cards. This game is offered in only a few locations. Are the odds any better (especially if the dealer tries to draw to straights and flushes)?

Rod from Newburgh, USA

To answer your first question, yes, the house advantage can be reduced by sneaking peaks at other cards. For example if you have an ace/king hand it should make you more inclined to raise if you see another player matching the dealer’s up card. In the book Finding the Edge Peter Griffin and John M. Gwynn Jr. address the question of player collusion in Caribbean stud poker. Assuming perfect knowledge of all other cards, and having perfect knowledge of how this information affects the odds, their paper states the player would have a 2.3% edge in a seven-player game. In a six-player game, the house would have an edge of 0.4%.

Your analysis of various side bets like Streak, Pair Square and others was very interesting. Do you know how these new games get invented and established? Do the casinos employ guys like you to compute the probabilities? If so, are the games copyrighted in some way?

Bob P. from Lake Charles, Louisiana

I could talk about this all day. Part of my income is derived from analyzing games such as these. The gaming authorities require such analysis before a game can be licensed to play. Usually, these games are invented by an individual. Here in Nevada, after the game owner receives a license, then it must go through a 30-day trial period. If the trial period went well, then the owner can then apply for a permanent license. The entire process is very slow and it is difficult to get a casino to be the guinea pig for the trial period. Casinos are actually quite risk averse in their business decisions. Yes, the game owner will usually seek a copyright to protect others from stealing the idea.

You can find much more information about the business of marketing casino table games at my Gaming Math site.