How to win $1 million at a table game with a $10 bet

In an earlier article we looked at the odds of winning $1 million or more with the lottery or progressive slot machines. (see article)  In theory, you could get much better odds of winning $1 million by betting $10 on a table game (say red or black on roulette), doubling your bet every time you win, and winning 17 times in a row. Yeah, your chances of winning 17 times in a row aren't that great, but they're a lot better than winning a million dollars on a slot.  Your odds of hitting $1 million would be about 1 in 119,000 on a table game, but a whopping 1 in three million or so on a slot machine.

But there's a catch:  No casino on the planet will let you double up a table game bet to $500,000. The max bet on a table is usually limited to around $5000, and the highest limit I know of is $50,000, at Caesars Palace.  But it's still interesting to see how such a series bet could work, and it's certainly possible to double up to a nice jackpot of $1,000 or more, with way better odds than on a slot machine.  So let's take a look at how to do it.

How to do it

You remember that old story you heard as a kid about the person who wanted his salary to start at only $1 and then double every day?  The punchline was that in 30 days the salary would be over a billion dollars.  We're working with the same concept here.  If you start with a $10 bet and win 17 times in a row, you'll be betting $10, $20, $40, $80, $160, $320, $640, $1280, $2560, $5120, $10240, $20480, $40960, $81920,  $163,840,  $327,680,  and $655,360, and in you win that last bet, you'll wind up with $1,310,720.

So now we just need to pick a game to play.  We want a game with a low house edge, because that will give us the best chance of winning.  That rules out roulette, since its house edge is a whopping 5.26%.  A single-zero wheel is better a 2.7%, but that still twice what you'd get in a good game.  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 problem:  If we bet the farm on every hand, there's no money left for doubles and splits.  So let's put blackjack aside for now and come back to it.

Our next idea might be the banker bet in baccarat, with a low edge of only 1.06%.  But here again there's a problem:  In baccarat we have to pay a 5% commission on winning banker bets.  If we win 16 times in a row and lose the 17th, we'd be on the hook for $16,384 in commissions.  Ouch.  So to do the banker bet we'd have to squirrel away 5% of every win in order to pay the commissions.  That means our bets would grow slower, and so it would actually take 18 bets to get to get to $1 million, not 17.  That makes it twice as hard to reach our goal, so that bet is out.

Next up is the player bet in baccarat with an edge of 1.24%.  It has no problems, so this will work!  The chance of winning a single player bet is 49.317562%, so the chances of winning 17 in a row are 1 in 1 ÷ 49.317562%¹⁷, or 1 in 165,567.  That's about twenty times easier than with a slot machine.

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 ÷ 49.292929¹⁷, or 1 in 166,979.  That's nearly as good as with baccarat.

Tweaking it further

Did you notice that even though our goal was only a million dollars, after our 17th bet we're up $1.3 million?  We can use that to our advantage.  Instead of bet #17 being $655,360, we can bet only $500,000 to to win the $1 million.  That way if we lose, we'll have $155,360 left, and we can try to double that up to $1 million.  And here again, we'll always limit our final bet to $500k, so we don't overshoot our goal, and so we have some left over in case we lose.  That improves our chances to 1 in 125,926 for baccarat and 1 in 128,110 for craps.  (You can't easily calculate that, so I figured that through a computer simulation of five billion attempts to win the $1 million.  I estimated all the remaining figures in this article the same way.)

You might think we could improve our chances further by taking the "free odds" bet in craps, since it carries no house edge.  (See our 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.  Yes, 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 stopped screwing with odds and put as much on the pass line as necessary to hit the $1 million goal if we won the bet.)

Using a more realistic goal

Everything above is really academic because no casino will let you make bets that large.  But Caesars Palace allows bets up to $50k, which would allow us to win $100,000.  So what are the odds of winning this more realistic amount?  A whole lot better:

And we can improve our chances even further.  So far we've been talking about our chances if we start with only $10, which gives us just one attempt.  But if we started with $100 then we could try ten times.  If we started with $1000 we could try 100 times.  That greatly increases our chances of making our goal.  Let's see by how much:

[TABLE COMING EVENTUALLY]

If you'd like to get your hands dirty and calculate 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 are 1 in 40,000 and we try 100 times, our chances are 1 - (39,000 ÷ 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.

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!

Related articles:

• Betting Systems in general
• Martingale betting system
• Half-Bankroll betting system