Betting Systems - Gambler’s Fallacy

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.

My question concerns baccarat, is a 1,2,3,5,8,13,21,etc. progression a profitable method of play? I add the previous two bets and bet the sum on a loss and subtract one level of the progression on a win. Any two wins in a row and I go back to 1 unit. i always bet on banker. I've tried this online in several casinos (as well as your site's baccarat game, and it has worked great. Is it flawed?

Brantley from Waycross, Georgia

All betting systems are flawed. Progressive systems like yours usually do when but with occasional large losses. Over the long run, you will do no better nor worse than the flat bettor or user of any other system.

My question revolves around the system Norman Leigh used in the 60s to break the bank in Nice. His team used a reverse Labouchere system, which involves absorbing a number of small losses before hitting a big win (based on the idea that instead of canceling out wins they are added to the sequence and losses are crossed out ensuring that each game can only lose a fixed amount but can potentially win the table limit). Other than Norman's book (and books based on it) I have not seen any analysis of the system. The book states that this approach uses the house edge against them and that in the long run the player will come out ahead. Is this nonsense or is there something in this idea?


If, indeed, they won it was because of luck and not because it was a winning system. As I have said a thousand times before, any system based on a negative expectation game in the long run not only can't overcome the house edge, it can't even dent it.

Say, Wizard I was wondering about roulette. With the boss media software, you can spin the wheel without actually placing a bet. Isn't this in the player's favor? With some of the roulette betting systems I have seen, like the Martingale you double up when you lose and such. Can't you just watch the wheel without placing a bet and based on the previous spins place your bet. An example would be to spin the wheel 5 times before placing a bet. Suppose that all the numbers were odd. Wouldn't it make sense to begin playing the wheel by betting on even? I know this kinda buys in to the gambler's fallacy and the wheel doesn't care what the last spin was, but also the probability diminishes with each spin that an odd number will continue to come up. Am I on to something or just going over an old theory?

Craig from Detroit, USA

You're just rehashing the gambler's fallacy. If the ball landed in odd 100 times in a row on a fair wheel the odds that the next spin would be even are still the same as every spin, 47.37% on a double zero wheel. So it does not help that you can spin without betting. The ball does not have a memory.

This is a question regarding fixed odds betting. If you say that the odds are 4 to 1 on something happening, then is that equivalent to saying the probability is 1 in 4 i.e. 0.25? If you consistently bet on 4 to 1 shots would you simply break even over time? Therefore could you not beat fixed odds betting by doubling up after every loss since you would expect a winner every fourth bet?

Calvin from Long Beach, USA

If the odds against something are 4 to 1 then there are 4 chances it won't happen and one chance that it will. So, in this example, the probability would be 1/5. It doesn't matter what the probability is, if the events are independent then the past does not matter.

I am thinking of taking the following strategies to play mini baccarat. I only bet after either the Banker or Player has appeared four times in a roll. I double my money if I don't win the first time. However, if the second time I don't win, I stop betting for the time being until the next four continuous appearance coming again. Once I win, I also stop betting until the next 4 continuous appearance coming. Please evaluate my strategy. Thank you!

Mandy from Gold Coast, Australia

Waiting for streaks of four in a row is not going to help. The cards do not have a memory. Doubling after a loss is also not going to help. I would recommend betting on the banker every time. Skipping hands is fine, in fact not playing at all is the best possible strategy.

My co-worker D. insists that he has perfected a way to consistently win at Roulette. I’m not convinced. Is he just lucky or is there any system that works?

Tom from Merrit Island, USA

He is just lucky. As I have said thousands of times, no betting system can pass the test of time.

What do you think about the strategy of add 50% after second winnings in blackjack, ex, 2-2-5-7-11-15-22-33....

KYK from Hong Kong

As I have said many times, in the long run all betting systems are equally worthless.

Hi Wizard, I’m Andrés Varillas from Lima - Per?, South America, I begun to play just 6 years ago, and I loose 20 thousand dollars in this years, for me is too much, I’m really upset of this situation and I want your help, I offer you if you make me win I receive you here in Per? to take vacations, Per? is a beautiful country, and you enjoy Know it, in the Casino I play, there are many machines of IGT Co., like Catch a Wave, Cleopatra, The Monsters, Leopard, I really loose in 1 of 15 chances, I want to try back my money. Maybe you can give some secrets to win in these machines. I appreciate your help, and send you a big hug.

Andrés from Lima, Peru

Sorry to hear about your misfortune. However that is the fate that awaits most who overplay their bankroll, especially in slots. There is no way to beat any of these games. I would recommend you quit gambling completely.

Dear Sir, We are avid Keno players. It is our intuitive belief that if we play two or more keno machines using the same numbers that our chances for hitting those numbers are significantly increased. Can you enlighten us with some statistics to support our intuition? Thank you.

Gene & Rosie from Bayside, WI

Your overall expected return is the same regardless of how many games you play. Of course it is more likely to hit a number the more machines you play, but if they all miss you lose more money.

In your last column you said anybody could create a roulette system that showed a 6.5% profit over 7500 spins. Well, I’m anybody and am challenging you to give me one.


You got it! Actually the system boasted an advantage of 7.94%. I'll up that and go to 8.00%. So here is "Wizards 8.0% advantage system." Here is how to play it.

  1. This system can be played on any even money game, including roulette, but craps is strongly suggested due to the lower house edge.
  2. Player makes only even money bets. In roulette any even money bet will do and the player may change the bet at will (as always the past does not matter).
  3. Player must be comfortable with a betting range of 1 to 1000 units.
  4. The first bet is 1 unit.
  5. After each bet the player will determine 8.1% (the extra 0.1% is a margin of safety) of his total past wagers. If his net win is less than this figure he will bet the lesser of the difference and 1000 units. If his net win is more then he will bet one unit.
  6. Repeat until 7500 bets are made.

In roulette I did a computer simulation of this experiment 10,000 times and the player made his 8.0% 4236 times and failed 5764 times. So the first time with live play it would not be unlikely that the player would report a success story. In craps betting on the pass line using the same system resulted in 6648 wins and 3352 losses, for a success rate of 66.48%. Going back to roulette, if the spread is 1 to 10,000 units the numbers of wins was 8,036 and 1,964 losses. In all cases when the system doesn't hold up over 7,500 spins the loss is big, more than 8.0% on average.

Of course this system is just as worthless as every other. The point I hope I have made is that it is easy to easy to design a system that usually wins. However when you do lose you lose big. Over the long run the losses will be more than the wins and the player will have a lot less money in his pocket.

Dear Wizard, I know from reading your web site and from other sources that betting systems do not give you an advantage over the house. My question is do they decrease the house advantage? I have been playing the betting system outlined in Progression Blackjack by Donald Dahl for the last 8 years and it gives me the excitement of betting higher amounts then I normally would. I usually play the $10 tables and I often get up to $30 bets and on my last trip to Vegas I got up to the $100 level at Sam’s Town which really got my heart pumping not to mention a $600 profit that I left the table with. Thanks for your help.


No! Not only do betting systems not overcome the house edge but they can’t even put a dent in it. Nor can they increase the house edge. All they can do is affect volatility. Since it sounds like you like a volatile, exciting game than your system is fulfilling its purpose. Just don’t expect to win.

I was at Casino On Net. I was playing Roulette. I was making safe bets, only betting on the 1st 12(L), 2nd 12(M) & 3rd 12(H). I spun the wheel 5 times without betting, waiting for a pattern of one of the sets to not come up so I could bet on it, hoping this would shift probability of it landing in my favor. 5 spins later L didn’t show. I kept betting in L, I figured the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 OR 12 would land within 12 Spins so that I could at least recoup my money...but they didn’t. The table went 17 spins in a row without a LOW number & I went from $258 to $ was Bonus Money anyway. This is a 3 part question:

  1. Did my waiting for 5 spins without a low number popping actually increase the chances of probability for a L to show up?
  2. What are the odds that a Low number won’t show up 16 times in a row?
  3. What are the odds that a Low number won’t show up 17 times in a row?

Thank you, I also want to thank you for that Blackjack Guide, I turned $5.00 into $100.00 using your method.

Brad from Sydney, Nova Scotia

  1. No
  2. A single-zero wheel is used at Casino on Net. So the probability of going 16 times with a zero is (25/37)16 = 0.1887%.
  3. (25/37)17 = 0.1275%.