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The Martingale Betting System
Increases your chances of winning, but you lose more when you do lose
by Michael Bluejay, 2003-2011
The Martingale betting system increases your chances of winning in the short term. It's a fact. How can we say this when the most respected gambling math authority on the planet, the Wizard of Odds, says that "all betting systems are worthless"?
Simple: The Wizard's only criteria for the worth of a system is whether it beats the house edge in the long run. But the point of a betting system isn't to overcome the house edge in the long run, it's to make you more likely to win in the short run. Most of us play for a few hours while on vacation. For short gaming periods like this, a betting system can make it more likely that you'll finish your session a winner. Even the Wizard wouldn't dispute this.
Here's how the Martingale can make you more likely to win in the short term: You'll win most of your sessions, but your wins will be small. Then on the rarer times that you lose, your losses will be much greater. Like most things in life, it's a trade-off.
What is the Martingale?
The Martingale is one of the oldest betting systems around. Here's how it 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 the same bet for the next hand. But if you lose, you double your bet for the next hand. When you eventually have a winning hand after a series of losing hands, 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 win, so you bet $5 again. Then 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, and since you won $5 before your losing streak, now you're ahead a total of $10.
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 couldn't bet it anyway, since most casinos limit maximum bets to $500-1000 on a $5 table. And usually, the higher the maximum on a table, the higher the minimum, too.
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, but an hour is about right. 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, and how much money you have to gamble (your "bankroll"). Let's take a game of roulette, where you bet $5 on red, you play for an hour (30 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 $16. You'll lose the other 54% of the time, with an average loss of $28.
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%! But when we win our average win is only $66, and when we lose our average loss is $462. Bing! There's the tradeoff.
Remember that the Martingale works best in the short term. The longer you play, the more likely you are to lose, because the longer you play, the more likely you are to lose several bets in a row and then run out of money or run up against the table limit. In fact, if we use the example above with an eight-hour session, then our chances of winning with the Martingale are only 38%. (Our chances with flat-betting $5 every time are 22%.)
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 72%.
Increase your odds by playing a better game
The odds on a standard American roulette wheel are pretty bad in general -- the casino has about a 5.3% advantage over the player. You can increase your chances of winning by playing a game with a lower house edge instead, such as craps or European roulette. Craps is the preferred game, because it's much easier to find than European roulette.
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 European roulette. The extra money would allow you to survive a longer losing streak with those games.
Baccarat has a low house edge (1.06%) so it's a good choice for the Martingale, but only if you can get a slow game. Mini-Baccarat is played about five times faster than craps or roulette in terms of rounds per hour, and as you recall, the more you play, the more likely you are to lose. The whole point of the Martingale is to try to win in the short term. Of course, if you're playing online instead of in a casino, then all games are played about the same speed and it doesn't matter which game you play -- but you'll need to be extra careful that you don't play too long. How long is too long? See note at the beginning of the table at the end of this article.
European roulette wheels offer better odds than American roulette wheels. American wheels contain both a 0 and a 00, while European wheels have just the 0. The house edge on a European wheel is 2.7%. Some European-style game offer a "surrender" feature which means you lose only half your bet if the ball lands on 0, or an en prison feature which is complicated to explain but is effectively the same thing. Either feature lowers the house edge to about 1.35%. European wheels are hard to find in land casinos in the U.S., and where they are available they usually come with high table minimums. Online it's a lot easier. For example, Bodog has a single-zero European wheel (2.7% edge), but only in the download version (not in the Flash version).
Does it work
if you have a huge bankroll?
Methodology: Data derived from computer simulations of 100,000 to 1,000,000 sessions for each cell of data. Strategies: Baccarat=banker; Craps=pass line, no odds; Roulette=red or black. Rounds per hour per game: Baccarat=150 (typical for Mini-Baccarat), Craps & Roulette=30. Baccarat is eight decks. Session is over when all rounds have been completed or player lacks sufficient funds to double a bet as required. When table limits prevent the player from doubling the player makes the maximum bet allowed if s/he has funds to do so. Odds used in calculations from WizardOfOdds.com.
You can't use this system at just any table -- the table has to allow a bet spread at least $1-$200 or $5-1000. Casinos that offer this range abound in Vegas. By contrast, the betting range at many online casinos is too tight, but there are exceptions. Our preferred casino, Bodog, lets you spread from $1 to $500. And William Hill allows bets between $0.25 (!) to $5000. (They also meet my criteria for recommendation by having their payouts professionally audited, in this case by Price Waterhouse Coopers.)
"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. Starting your third hour later doesn't reset your odds.
Where you went wrong was tring 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. 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.