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When playing a game where you are the underdog, betting systems have no affect on the eventual outcome of the game, you lose. Betting systems do affect the expected duration of the game. The probability of increasing a bank to a specified level is also affected.

Progressive Betting

Most popular betting systems are either of the type up as you win or up as you lose. Depending on the method of determining the next bet in the sequence, most systems can be categorized as being multiplicative, additive, or linear. None of these systems work!

Martingale

This is one of the most widely used betting systems. The betting strategy, multiplicative in nature, requires you to double your bet after each loss until you win, then you start over.

For example, suppose the game is roulette. You bet one dollar and lose, bet two dollars and lose, bet four dollars and lose, bet eight dollars and win. The total won is one dollar (the loss was 1+2+4=7). With this betting system there is a high probability of winning a small amount (1 dollar) and a small probability of losing a great amount.

The chance of the roulette ball not landing on red is 20/38. The chance of not landing on red twice in a row is (20/38) x (20/38) = 100/361. The chance of not landing on red three times in a row is (100/361) x (20/38) = 1000/6859. The chance that you have to make the fourth bet of sixteen dollars is just under 1/7.

To avoid going very far with the Martingale bettor, casinos have betting limits. A routine betting limit at roulette is usually $2500. How many losses would you have to incur before the limit prevented you from doubling again? If the ball failed to land on red for eleven times the next bet would call for a wager the size of $2048. If that bet lost the next bet would put you over the limit.

Were the limit to be raised to $10,000, only two more failures to land on red and your over the limit once again. The chance of not landing on red for twelve times in a row is .000451. This will happen about 4.5 times in 10,000 plays. Using this betting system, an increase (double) as you lose system, will cause you to win, on average, one dollar, 9,995.5 times out of 10,000, and lose $4095 x 4.5 times, or $18427.5.

The final result after 10,000 separate plays of betting and doubling until either you win a dollar or reach the betting limit of $2500 (twelve losses) and start over again at one dollar, is most likely to be a loss of $8432.

DAlembert

This is a simple linear system named after the eighteenth century theorist Jean le Rond dAlembert. He wrongly reasoned that if a fair coin landed on heads for a long run, that tails was more probable. In the system bearing his name, you raise your bet by a fixed amount if you lose and lower it by a fixed amount, if you win. It could look like this in practice: bet 1, lose and bet 2, win and bet 1, lose and bet 2, lose and bet 3, lose again, bet 4, win, bet 3, ad infinitum. The final result is the same: you lose.

Labouchere

Also known as the cancellation system, the Labouchere system is additive in nature. A sequence of numbers, say 1,2,3,4, is chosen. The first bet is the total of the two numbers on the end, or 5 units in this example. If the bet is lost, the lost bet now becomes the last number of the new sequence,1,2,3,4,5.

The next bet is now the sum of the new first and last numbers. In the above example, 6. If the bet is won, the first and last numbers in the sequence are canceled, in this case with the sequence 1, 2,3,4, the 1 and 4 are canceled, and, the next bet is the sum of the two non-canceled numbers, 2 and 3. If you win, you proceed to the inside numbers until they are all canceled out. Again, a loser, but an insidious one.

Anti-Martingale

This system requires that you double your bets after a win instead of a loss, just the reverse of the Martingale above. There is a high probability of a small loss and a small probability of a huge win. When you lose a bet you have wiped out your wins plus one unit.

Anti-DAlembert

This system adds or subtracts a fixed sum depending on whether the previous bet was a winner or loser. It adds the sum for a winner and subtracts the sum for a loser.

Anti-Labouchere

The opposite of the Labouchere system above, adding a term to the sequence after a win and canceling the last two terms of a sequence after a loss.

The kinds of systems that can be invented are limited only by the imagination, with the same result, none of them work. Nothing is going to turn them into winning systems.

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