How to win a million dollars at a table game with a $5 bet
Last update: October 2018
The idea is simple: Start with a $5 bet, and double it every time you win, 18 times in a row. The odds of doing that are about 1 in 300,000. Don't laugh: the odds of hitting a slot jackpot are are often 1 in two million or more, and the top prize is usually pretty far from a million dollars. So, if you want a huge jackpot, you're much more likely to get it on a table game than on a slot machine.
You might think that you can't actually make a $500,000 bet in order to win a million, because of table limits. But while it's true that the typical high limit rooms have max bets of $10,000 to $50,000, the ultra-exclusive high limit rooms let you bet up to a million. The Wizard confirmed for me that the Venetian took up to $1 million when he worked there.
You remember that old story you heard as a kid about the person who wanted his salary to start at only a penny a day and then double every day? The punchline was that in 30 days the salary would be over a 10 million dollars. We're working with the same concept here. If you start with a $5 bet and win 18 times in a row, you'll be betting $5, $10, $20, $40, $80, $160, $320, $640, $1280, $2560, $5120, $10240, $20480, $40960, $81920, $163840, $327,680, and $500,000. The last one isn't doubled because we don't want to overshoot our goal. More on this later.
So now we just need to pick a game to play. We want a
game with a high chance of winning an even-money bet. That
rules out roulette, which gives us only a 47.37% chance of winning
each bet. A single-zero wheel is better, at 48.6%, but still
too high. If you're in Europe where they have the en
prison rule, then the edge is a respectable 1.39%, and
roulette is a decent choice. If you're in Europe and are
trying this with roulette, you can use the numbers below for craps
without free odds, since the house edge for both games is similar.
But let's say we're not in Europe and so roulette is out. An obvious choice for a low-edge good would be blackjack, which carries an edge as low as 0.20%. But blackjack comes with a couple of problems: If we bet the farm on every hand, there's no money left for doubles and splits. Also, the odds of winning a single blackjack hand is only 1 in 42.43%, which is worse than roulette. (source) So that one's out. (The reason blackjack has a lower house edge than roulette even though the chances of winning are worse, is that with blackjack you often win more than your bet, with naturals, doubles, and splits.)
Our next idea might be the banker bet in baccarat, with a low edge of only 1.06%. And it'll work, though it's not so simple: In baccarat we have to pay a 5% commission on winning banker bets, so if we win 17 times in a row and lose the 18th, we'll be on the hook for thousands of dollars in commissions. Ouch! So to do the banker bet we'll have to squirrel away 5% of every win in order to pay the commissions. That means our bets would grow slower, and that means that it'll take 19 wins instead of 18. That's gonna be the deal-breaker here. The odds of making our $1 million are 1 ÷ 50.68%19 = 1 in 405,236. We can do better than this.
Next up is the player bet in baccarat with an edge of 1.24%. There's no commission to worry about, so it's simpler, but the odds are worse. The chance of winning a single player bet is 49.317562%, so the chances of winning 18 in a row are 1 in 1 ÷ 49.317562%18, or 1 in 335,715. This is as good as we're gonna get.
The house edge on the pass line in craps is almost as low, 1.41%. Yes, the Don't Pass is just a hair lower, but if you wanted the best odds you would have chosen baccarat. If you're playing craps it's because craps is more fun for you, and if that's the case you're almost certainly going to bet the pass line like everyone else. In that case your chances are 1 in 1 ÷ 49.29292918, or 1 in 338,748. Player in baccarat is still our best choice.
The 18th bet
Our goal is only $1 million, but after our 17th bet we'll have more than $500,000, so if we let our winnings ride and we win, we'll overshoot our goal. Specifically, after bet #17 we have $655,360. So, instead, on the last bet we'll bet only $500,000.
Now, those of you who are really sharp might point out that we didn't really win the whole $1,000,000, because we started with $5, so we really won only $999,995. To that I say, nobody likes a pedant. If it really bothers you, just bet $500,005 on bet #18.
Milking the 18th bet #1: roulette to the rescue
We've got $655,360 going in to the last round and need to win only $344,670 to hit our million-dollar goal. So we don't need an even-money bet, we can bet on something that pays less than even money, and in return get a better chance of winning. What we do is to use our $655,360 to bet on 23 individual numbers in single-zero roulette ($28,493 on each number). That gives us a 62% chance of winning our last bet, which is a lot better than the 49% chance of winning the baccarat player bet. That reduces our overall odds to 1 in 266,347. If we win, we'll wind up with $1,025,748.
Milking the 18th bet #2: a second chance
A different way of milking the 18th bet is to bet normally, in baccarat . At the beginning of bet #18, we have $655,360, of which we're betting $500,000 (or $500,005 for pedants). If we lose, we'll have $155,360 left over. So at that point we could simply start over again, but this time with a $155,360 initial bet rather than a $5 bet. And let me tell ya, it's a lot easier to get to $1 million from $155,360 than from $5.
Further, every time we're making our last bet, we'll bet only enough to hit $1,000,000, so we'll have some left over to try again if we lose.
This improves our odds a bit over the roulette option above. From the computer simulation I programmed to run 20 billion attempts, our chances of success are now about 1 in 260,000.
The odds bet in craps doesn't work
You might think we could improve our chances further by taking the "free odds" bet in craps, since it carries no house edge. (See my how to play craps for an explanation of this bet.) I thought the same thing, but a computer simulation proved otherwise. The problem is that we have to bet only a fraction of our bankroll on the come-out roll so we have money left over to put on the odds, and if we win the come-out with a 7 or 11 then our effort is kind of wasted since our bet was so small. Incidentally, I did find that betting 1/4th of the bankroll on the come-out (and not being able to put the max down on points of 5, 6, 8, and 9) yielded better chances of success then betting 1/5th or 1/6th of the bank on the come-out roll.
(My sims used 3-4-5 odds. Casino Royale offers 100x odds, but
they limit the payout on an odds bet to just $2500, so that won't
work for us. Caesars, which allows the highest bets in Vegas,
offers 3-4-5 odds, so that's what I used. But when we got close to
the goal, I had the sim stop screwing with odds and put as much on
the pass line as necessary to hit the $100k goal if we won the bet.)
Getting more playing time
Instead of betting the farm on every round, we could bet only half or 1/4 of our bankroll. This doesn't improve our odds (in fact it makes them worse), but it does let us play longer. After all, when you bet everything on every round, as soon as you lose a round, it's all over. Betting just a fraction of your bankroll each time lets you last longer, even though it makes it a little harder to reach our goal.
How to calculate the chances of winning repeated attempts
If you'd like to get your hands dirty and calculate some of this yourself, the chances of winning an event over multiple attempts is:
1 - (ways to lose ÷ (ways to lose+1) ) ^ number of attempts
So if our chances for 1 try at something are 1 in 40,000 and we try 100 times, our chances are 1 - (39,999 ÷ 40,000)100 ≈ 0.25%. To turn that into "1 in x" style, we divide the result into 1. So 1 ÷ 0.25% is 400, or 1 in 400.
This formula is useful for other gambling problems. For example, if the odds of hitting the jackpot on one spin on certain old-style electromechanical slot machine are 1 in 262,144, and you play the machine for 262,144 spins, you've got only a 63% chance of hitting the jackpot. Probably not what you expected!
Odds of winning consecutive bets
No article about winning lots of bets in a row would be complete
without a table showing your odds of winning several bets in a row
in various games, so here you go!
of winning multiple bets in a row (1 in X)
are rounded. Probabilitiy of winning a single round
is: Roulette 00: 18/38. Roulette 0: 18/37.
Baccarat banker: 50.682438%. Baccarat player: 49.317562%. Craps: 244/495.
Blackjack is n/a due to doubles, splits, and naturals.
* The bankroll column will be less than shown when the play is Baccarat Banker,
because of the 5% commission that must be paid on winning hands.