# The Martingale Betting System

The Pros & Cons

Last update: May 2021

The Martingale betting system increases your chances of winning in the short term.  The catch is that when you do lose, you lose big.  For example, starting with \$1000 and a starting bet of \$5, you've got about an 80% chance of turning a profit after one hour at craps or roulette, with an average win of about \$100.  Nice!  However, if you lose, the average loss is around \$500.  Ouch.

So, like most things in life, the Martingale is a tradeoff.  You trade an excellent chance of winning for a punishing loss if you do lose.  That's a pro and a con.

Many other gambling writers dismiss the Martingale out of hand.  For example, the Wizard of Odds famously says that "all betting systems are equally worthless".  But that's true only if your criteria is really narrow, like whether the system reduces the house edge (which is the Wizard's criteria).  To me, that's like saying that bicycles are worthless because they don't go as fast as airplanes.  Millions of bicycle-riders would beg to differ.  The Martingale won't reduce the house edge, sure, but it can provide entertainment and it gives you an excellent chance of winning in the short term—which makes it far from "worthless".  Risky?  Absolutely.  Worthless?  No.

## What is the Martingale Betting System?

Here's how the Martingale works:  You make your standard bet, say \$5, on an even-money bet, such as red in roulette or the Pass Line in craps.  Every time you win you make that same bet for the next round.  If you lose, you double your bet for the next round, and keep doubling until you win.  When you eventually have a winning round after a series of losing rounds, your net win will be \$5.  In fact, every time you win a bet, you'll be up another \$5, regardless of past losses.

Here's an example:  You bet \$5.  You lose, so you bet \$10.  You lose again, so you bet \$20.  You lose again, so you bet \$40.  You lose again, so you bet \$80.  Man, it's not your night!  Then you win.  Your net win on that series was \$5.  You're now ahead \$5.

If you could always double your bet when you lose you'd be guaranteed to always come out ahead.  But in real life you can't always double your bet.  First of all, you'll run out of money at some point and be unable to double your bet.  If you start with \$5 and lose thirteen bets in a row (it happens), you'll have to cough up \$40,960 for your next bet.  Ouch.

Bet even if you had that much money, you might not be able to bet it anyway, because casinos limit how much you can bet.  It wouldn't be a problem in Vegas, where you can bet up to \$1 million in the ultra-exclusive high limit rooms at the tonier casinos.  (These are not the normal high limit rooms adjacent to the main casino floor, they're on another floor entirely, and most folks will never see them.)  In most other parts of the country and the world, you'd have a hard time betting more than \$5000 at once.

So that's the risk of the Martingale: If you lose enough times in a row, you'll go broke and not have enough money to make the next bet, or you'll bump up against the table limit.  So while the Martingale can work in the short term, the longer you play, the more likely you are to have a long losing streak during which you couldn't double your bets high enough.  How short is short enough?  Well, the shorter the better.  An hour in a live casino gives you about an 80% chance of coming out ahead in craps or roulette.  You can certainly play for longer, but the longer you play, the more likely you are to lose.

## An example: Increase your odds of winning from 46% to 82%

So now that we know how the system works, exactly how much does it increase our chances of winning?  The answer depends on many factors: which game you play, the amount of your initial bet, how much money you have to gamble (your "bankroll"), and how long you play.  Let's take a game of craps, where you bet \$5 on the pass line, you play for an hour (43 spins), and you have \$1000 total to play with.  Betting \$5 every time (no Martingale), you'll win only about 46% of the time, with an average win of \$25.  You'll lose the other 54% of the time, with an average loss of \$27.

Now let's use the same setup except we'll use the Martingale, and double our bet after every loss.  All of a sudden our chances of winning our one-hour session shoot up to 82%!  And when we win our average win is \$100 (much better than the \$25 from flat-betting), but when we lose our average loss is a whopping \$528.  Bing!  There's the tradeoff.

But the longer you use the Martingale, the more likely you are to lose several bets in a row and then run out of money.  In fact, if we use the example above with an eight-hour session, then our chances of coming out ahead with the Martingale are only 37%.  (Our chances with flat-betting \$5 every time are 41%.)

Another thing that decreases your chances of winning is having a smaller bankroll. You have to have enough money to double up your bets when you hit a long losing streak.  In our one-hour example above, we had an 82% chance of winning if we brought \$1000 to the table.  But if we bring only \$500 to the table, our chances drop to 69%.

## Craps is the best bet

The best game for the Martingale is craps, betting either the Pass line or Don't Pass.  Other games aren't so hot.

Roulette carries a higher house edge than roulette, even most single-zero versions.  Single-zero with the half-back rule has a house edge as low as craps, but besides being a rare game, the table minimums are almost certainly higher than for craps.

Blackjack offers good odds with proper strategy, but to use the Martingale with blackjack you need a bankroll that's four times as large as normal.  That's because you might need to split hands or double down, and will need extra money to do so.  If you had this much extra money and wanted to use the Martingale, you could use it to much better effect with craps or single-zero roulette.  The extra money would allow you to survive a longer losing streak with those games.

Baccarat has a low house edge but it's generally played much faster than craps or roulette, so that increases your chances of losing.  The more rounds you play, the greater the chance of busting out.  That also means you should beware of playing for real money online, because online games are played way faster than at brick-and-mortar casinos.

## Does it work if you have a huge bankroll?

We know that the problem with the Martingale is that once you've lost several times in a row, you have to make really huge bets.  Well, what if you can afford to make those really huge bets?  How would the Martingale fare under those circumstances?  I decided to test it.

We'll assume our gambler is willing to lose up to \$100k.  That would mean he could start with \$5 and place 14 bets in a row, with the final bet being \$40,960, for a total loss of \$81,915 if bet #14 lost.  Caesars Palace accepts bets up to \$50k, so this would work there.  With these betting limits, how long could our gambler play "safely"?  I decided that "safely" would mean that he'd have a 95% chance of coming out ahead and only a 5% chance of losing the \$82k.  Under those circumstances, he could play the Pass Line bet in craps for a mere 30 hours before he dipped below a 95% chance of coming out ahead.  Wow!

So even with a huge \$100k bankroll, you can't use the Martingale very long without a significant risk of tapping out completely.

## Should you use the Martingale?

Should you use the Martingale?  That's for you to decide, but here are some guidelines.

The Martingale may be for you if:

• In exchange for increasing your chances of winning, you're willing to lose a larger amount than normal if you do lose.
• You have at least a \$200 bankroll if you're making \$1 bets, or a \$1000 bankroll if you're making \$5 bets.
• You're going to play for no more than a an hour or two.
• You're willing to accept the catastrophic risk of losing your whole bankroll.

The Martingale is NOT for you if:

• You only skimmed this article and you think the Martingale will make you a guaranteed winner.
• You don't have at least \$200 for \$1 bets or \$1000 for \$5 bets.
• You're planning on playing for more than a couple hours, especially if you plan on playing American roulette, a fast game of Baccarat, or anything online.

## Chances with the Martingale under various conditions

The figures for hours of play are based on land casinos. Play on the Internet is much faster.  To have the chances of winning listed in the table below for Internet play, play a certain number of rounds rather than a certain number of hours.  See the Methodology below the tables for how many hours of which game equals how many rounds of play.

 Martingale: 1 hour of play Chances of Winning \$1 bet, \$200 bankroll, \$200 table limit \$5 bet, \$1000 bankroll, \$1000 table limit Avg. Win Avg. Loss Avg. Win Avg. Loss Craps (pass line) 82% \$20 \$105 \$100 \$528 Roulette (0) w/Surrender 79% \$25 \$105 \$126 \$528 Roulette (0), red 78% \$23 \$106 \$116 \$532 Roulette (00), red 75% \$22 \$107 \$113 \$536 Baccarat (player) 68% \$43 \$105 \$217 \$527
 Martingale: 8 hours of play Chances of Winning \$1 bet, \$200 bankroll, \$200 table limit \$5 bet, \$1000 bankroll, \$1000 table limit Avg. Win Avg. Loss Avg. Win Avg. Loss Craps, no odds 37% \$169 \$120 \$848 \$600 Roulette (0) w/Surrender 31% \$213 \$114 \$1066 \$569 Roulette (0), red 29% \$195 \$117 \$976 \$586 Roulette (00), red 24% \$190 \$117 \$952 \$589 Baccarat (player) 20% \$345 \$110 \$1727 \$554

Methodology:  Data derived from computer simulations of 1,000,000 sessions for each cell of data.  A "session" is either 1 hour for the top table and 8 hours for the bottom, but ends early if we run out of money.  When table limits prevent doubling the bet, we make the maximum bet allowed.  Rounds per hour per game: Baccarat/Blackjack =90, Craps = 43, Roulette=50. Odds used in calculations from WizardOfOdds.com.

## Want to try it on a table?

The best way to try out the Martingale is to play the fake-money games at Bovada online, because then you're not out anything if you lose.  You can certainly bet with real money, but remember the very real chance of the catastrophic loss!

Note that for this to work, the table has to allow a bet spread of at least \$1-\$200 or \$5-1000.  Lots of online casinos don't, but Bovada does.  In brick-and-mortar casinos, \$5 to \$1000 is pretty common.

Without actually placing the bets, you can use my Martingale tester which plays a bunch of times automatically and tells you how you did.

## Making sense of the time factor

A reader writes:  "Okay, I understand that the longer I play, the more likely I am to lose.  Here's what I don't understand:  I want to play for three hours total.   Let's say I play for two hours and win.  For the third hour, I could either keep playing at my current session, for a three-hour session, or I could quit my current session and play the last hour at some other time.  The odds of winning are lower for a three-hour session than for a one-hour session, so I'm thinking I should stop my session after the first two hours, and then play the third hour separately at some other time.  That way I reset my odds, because my odds will be in a one-hour session and not in a three-hour session.  But that doesn't make sense, because it shouldn't matter when I play that third hour, should it?"  —Oliver S., Denmark

You're right, after you played two hours and won, it doesn't matter when you play your third hour.  You can play it at the end of the first two-hour session, or the next day, or the next year.  It doesn't matter, the odds will be the same.

Where you went wrong was trying to compare a three-hour session to a one-hour session.  Instead you should have compared a one-hour session to a one-hour session.  That's because after you play for two hours, that two hours is finished, so you don't include it when figuring future odds.

This is just another version of the Gambler's Fallacy.  For example, the odds of flipping five heads in a row on a coin are very small.  But if you've already flipped four heads, the odds of getting heads on the next flip are 50/50.  After you've flipped four heads, you're not looking at the odds of flipping five heads in a row, you're looking at the odds of flipping just one more heads.  Likewise, after you've played for two hours and won, and want to play another hour, you're looking at the chances of winning after just one hour, not three.

You're not the first person who's been tripped up by this concept.  Years ago I remember telling an old girlfriend how it seemed safer to fly after a big crash, since another crash so soon after the first was unlikely.  She tried to explain to me that the first crash had no bearing on the odds of a future crash, to no avail.  In hindsight, I'm lucky she didn't dump me right then.  Anyway, I get it now, so now I'm sharing.  See my Gambler's Fallacy article for more.

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