Martingale System Betting
© Robert Crowne & Assoc., March 29, 2012

A Martingale system is a money management system that increases the amount wagered after a loss.  The classic Martingale System involves doubling your bet after every loss.

The Martingale System was originally developed for even-money propositions in roulette -- black/white or odd/even.  The attraction of the Martingale System is that it guarantees you must win over the long term.  If you keep doubling your bet, in the long term a 50% proposition will have 50% wins for both sides of the bet, and thus, in the long term the bettor will eventually get an equal number of wins and losses.  When one doubles, every win makes up for all the prior losses and gives you a profit of one minimum bet.

The problem with the Martingale System is that, in mathematics, the long term is defined as infinite.  Red is only guaranteed to win 50% of the time in an infinite number of spins.  Thus, to be guaranteed you will win, you must have an infinite bankroll.  Not even The Donald has an infinite bankroll.  Even if you are like the U.S. Government, and you can keep printing an infinite supply of your own money, the casinos are way ahead of you.  They put maximum bet limits on the tables to stop the very rich from continuing to double.

If, for example, the minimum bet is \$5 and the table maximum is \$1000, as it is in many casinos, you will bump into the table maximum after just 8 losses in a row.  If the table maximum is \$3000 you will be stopped after 10 losses.  The probability of an even money proposition losing 8 times in a row is 255-1, and 10 times in a row is 1023 -1.  That means you will hit the table maximum and be unable to make up your losses once in every 256 Martingale Series at a table with a \$1000 maximum, or once in every 1024 Martingale series if the table maximum is \$3000.

Some bettors may go a long time before they have that inevitable losing series.  But there is no guarantee it won't happen to you on the first try.  When you are blocked by a \$3000 maximum at a \$5 table, your total loss will be \$2555.  That's tough to ever get back winning just \$5 on every winning series.

Next, we'll examine Martingale Betting with other casino games and with sports and race betting to see if the advantages and disadvantages change.

Martingale Betting on Other Casino Games

Some people have tried to use the Martingale System at blackjack or craps.  In those games, however, the Martingale System prevents the bettor from using the most advantageous game strategies.

In blackjack, two of the greatest player advantages lie in doubling and splitting.   If you are sitting at a \$5 table and have lost the prior 7 bets in a row, your bet is \$640.  To double or split, you must put up an additional  \$640 out of your pocket.  If you lose, you will need to add the extra \$640 loss to the normal double bet of \$1280 for a total bet of \$1920 on the next hand. Then, what if you get another doubling or splitting situation, or you are able to split again after the first split, or double after a split?  If your hand requires a split, then a resplit, and then two doubles you could end up with \$9600 out on the table.  A loss on the hand would be much higher than the table maximum, and your unrecoverable loss would be much higher than otherwise expected.

At craps, one of the biggest player advantages is to make no-house-edge odds bets with each pass or don't pass bet.  If, for example, 3x odds are permitted, the odds bet would be three times the bet on the board.  Thus, if the table minimum is \$5, your pass line bet after the come-out roll would be \$20.  If you lose, the next bet on the line must be \$25 instead of just \$10 at the roulette wheel, and with odds that becomes a total of \$100.  Lose again, and your next bet with odds will be \$500.  Lose three in a row, and you will need to stop if the casino has a standard \$1000 maximum bet at a \$5 table.  Even if the casino has a \$3000 limit, you will be required to stop after only the 4th loss in a row, and you will be down over \$3700.   Anyone who has ever played craps knows that winning or losing four rolls in a row is a frequent occurrence.

Martingale Sports Betting

The Martingale System cannot be used in points-line sports betting because the 11-10 odds you must lay will very quickly exceed the amount you can win at the end of the winning series of bets.  For example, if you start by betting \$5, and keep doubling your bet after each loss, after four losses your cumulative loss will be \$75 and your next bet will be \$80.  At 11-10 odds, the win on an \$80 flat bet is only \$73.  Obviously, the \$73 win will not make up for your prior \$75 of losses, and that situation only gets worse the higher your bet goes before you win.

The same problem that exists with points-line sports betting prevents the Martingale System from being usable in any situation in which you must lay more than even money on the bet.  Martingale can be used, however, in any situation in which the bettor is getting even or plus odds on the money line.

Betting money-line underdogs in sports actually provides several advantages over using the Martingale System with roulette.

1. The potential profit for a winning series when betting money-line underdogs increases with the bet size. When betting at even money, your potential profit on any win is only one starting bet.  To illustrate, if you play +120 underdogs, and you have lost 4 in a row, your 5th bet would be \$80.  At roulette if the 5th bet wins, your profit after subtracting the \$75 of prior losses will only be \$5.  If you are betting +120 underdogs, the profit if you win the 5th bet will be \$80 x 1.20 = \$96 minus the \$75 you lost on the prior bets, leaving you with a net profit of \$11.  The plus odds situation makes the Martingale System a bit more attractive by increasing the potential profit.

2. The maximum bet limit is much higher, thereby greatly increasing the number of losses than can be endured before the Martingale System crashes.  Every bookmaker has a maximum bet, but you can bet the same team at many different bookmakers.  When using the Martingale System for betting money-line sports, the limit is one's own bankroll.  Still, there is no guarantee you won't run out of money or available bookmakers before you get a winning underdog and a profitable series.

3. Sporting events can be successfully handicapped, thereby giving you a positive expectation along with the positive odds.

Martingale Pari-mutuel Betting

Pari-mutuel betting is a form of betting in which the amount of the final pay out the bettor receives is determined by the amount of money bet on each proposition in the wagering pool to the entire pool.  Pari-mutuel betting is the form of betting used at racetracks and Jai Alai.  The horse with the race upon which the most money is bet has the lowest odds and therefore the lowest payout, and the horse with the least amount of money bet has the highest odds and payout.

As when betting underdogs in sports, the Martingale system used at the race track, when betting Jai Alai, or when the odds are positive in other multi-bet pari-mutuel situations provides a few extra advantages over using the Martingale with casino games.  There is, however, a counterbalancing disadvantage.

1. Because of the comparatively high positive odds, there is the potential for a huge profit at the end of a winning Martingale series.  Let's assume you decide to bet the second favorite in each race starting with a \$2 bet.  If you lose 6 races in a row, doubling after each loss your next bet will be \$128, and your cumulative prior losses will total \$126.  If the odds on the second favorite are, hypothetically, 4-1 for your \$128 bet, a win will provide a profit of \$512, minus the prior \$126 of loss for a net profit of \$386.  Compare that to the potential \$2 net profit at roulette.

2. Pari-mutuel betting theoretically has no maximum bet, although there is a natural limit, which is the main disadvantage.

3. As with other types of sporting events, those bet with a pari-mutuel system can be successfully handicapped, but see the "Disadvantages" section below.

1. The biggest disadvantage to using the Martingale System when pari-mutuel betting is that as your bet increases you will be decreasing your own odds and payout.  It would not be unusual for the second favorite in our example above to fail to win for one entire day of 12 races.  When that happens, your next bet the following day must be \$4096.  That size bet can cause your second favorite to become the favorite in most races on most days at most tracks.  Lose two more races, and at many tracks, and in some lesser-bet races at the largest tracks, your system bet of \$16,000 will cause your horse to be odds on.  As we discussed, when the odds are negative, the Martingale System guarantees losses.  Thus, the number of bets you can lose when pari-mutuel betting is naturally limited by the nature of pari-mutuel betting.

2. The larger number of possible winners in most pari-mutuel situations decreases the frequency at which you can expect to win, even if you handicap.  The potential for longer losing streaks becomes a prohibitively negative factor when combined with the natural bet limit in pari-mutuel wagering.

Conclusion

The casinos are littered with bettors who were ruined by increasing their bets after a loss.  The Martingale System is so dangerous that the stories about breaking the bank at Monte Carlo involved a team that pooled their money and forced the Casino to play the Martingale System at a time when Monte Carlo used to have no limit except the money in the table bank. The team, the story goes, simply reversed the Martingale System and doubled up on wins instead of losses at the roulette wheel until they finally hit a streak of wins large enough to break the bank.  Of course, an equally large string of losses would have cost the team a great deal of money, but not close to as much as they stood to win, and not close to the amount that a double after losses would have cost

Realistically, the only area in which using the Martingale System of Money Management should ever be considered at all is when betting money-line underdogs in sports.  You should not, however, even attempt to use the Martingale System betting underdogs without a 6-figure bankroll and unless you can handicap the sport well.  You must also be sure that you have enough places to bet to be able to place a single bet equaling 50% of your starting bankroll.

Starting with a \$5 flat bet, a \$160,000 bankroll will last through only 16 losses.  A +120 underdog has a 55% chance of losing.  The odds against losing 16 in a row with a 55% chance of losing are 14285-1.  Sound like it can't happen?  I am a 58% handicapper and I've had a 19-0 winning run, and several 16-0 winning runs.  If a 58% probability of winning can create 19 wins in a row, then a 55% chance of losing can create 16 losses in a row during your betting lifetime.

If you are not lucky enough to avoid that 0-16 losing run for your entire betting life, then, when it comes you will have a \$160,000 catastrophe.  Betting at odds of +120, your long-term expected average win per successful series of bets will be just \$8.   That means you will need to have 20,000 winning series just to break even from a single losing series.  But the odds say you will lose another \$160,000 before you get to 14,285 winning series.  You see the problem.

If, by handicapping, you can increase your probability of winning each +120 underdog to 55% in favor of winning, you will not run out of money until you have 18 losses in a row, and your probability of getting to 20,000 winning series before a losing series increases to 21-1 in your favor.

Remember, however, that even in the most favorable situation, the Martingale System will only guarantee that you win if you have a no-limit infinite bankroll with which to bet, and someone to bet with who has a no-limit, infinite ability to pay you when you win.  Otherwise, it may take a very long time, or even several lifetimes, but the Martingale System guarantees that eventually you will lose it all, and nothing says it won't happen long before you accumulate enough wins to equal a replacement bankroll.  Disaster could could strike on the very first try.

Unless repeatedly risking \$160,000 to win an average of \$8 is your idea of a great time and easy road to riches, the best advice is: AVOID ANY SYSTEM THAT INCREASES YOUR BET SIZE BASED ON PRIOR LOSSES.