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Written by J.P. Wicklein
I had a thought recently. If a person walked into a casino with the single goal of winning $5 I think the odds are overwhelmingly in their favor of walking away with the casino’s money. Fair warning: I may be wrong so, PLEASE DO NOT ATTEMPT THIS.
Imagine you walked up to the roulette wheel in a casino and bet $5 on black. The probability of you winning is 47.37%. For the sake of easy math let’s say it’s 50%. (It shouldn’t matter that I’m rounding up to 50%).
The first roll of the wheel lands on a red number. You lose $5. For the second roll of the wheel you double your bet on black to $10. If you win the second roll you’ll walk away with a net gain of $5. Let’s assume that you don’t win your second bet and double your wager every time you lose - until you eventually win. The table below spells out the scenario.
| Round | Bet | Outcome | Cumulative Odds of Losing |
| Round 1 | $ 5 | Lose $5 | 1/2 |
| Round 2 | $ 10 | Lose $10 | 1/4 |
| Round 3 | $ 20 | Lose $20 | 1/8 |
| Round 4 | $ 40 | Lose $40 | 1/16 |
| Round 5 | $ 80 | Lose $80 | 1/32 |
| Round 6 | $ 160 | Lose $160 | 1/64 |
| Round 7 | $ 320 | Lose $320 | 1/128 |
| Round 8 | $ 640 | Lose $640 | 1/256 |
| Round 9 | $ 1,280 | Lose $1,280 | 1/512 |
| Round 10 | $ 2,560 | Win $2,560 | 1/1028 |
Each roll of the roulette wheel your odds of winning remain 50% (in actuality 47.37%). The odds of you failing to win a single roll, however, decrease over time. As the table reveals, your odds of losing 10 rolls in a row are 1 in 1,028 (in actuality it’s a bit lower since we rounded up to 50%). Statistically speaking, you’ll eventually win one roll.
As the table shows, even though it took you 10 rolls of the wheel to win a single bet, you’ll still walk away up $5. Statistically, there’s a strong chance you’ll win long before your tenth roll. The catch is that you need to have enough money to double your wager each time you lose.
Now things get interesting
The odds of winning, or losing, remain the same no matter how much you wager. Let’s assume a person with an infinite supply of money walked into a casino and applied the same approach. Instead of attempting to win $5, though, they tried to walk away up $100,000.
| Round | Bet | Outcome | Cumulative Odds of Losing |
| Round 1 | $ 100,000 | Lose $100,000 | 1/2 |
| Round 2 | $ 200,000 | Lose $200,000 | 1/4 |
| Round 3 | $ 400,000 | Lose $400,000 | 1/8 |
| Round 4 | $ 800,000 | Lose $800,000 | 1/16 |
| Round 5 | $ 1,600,000 | Lose $1,600,000 | 1/32 |
| Round 6 | $ 3,200,000 | Lose $3,200,000 | 1/64 |
| Round 7 | $ 6,400,000 | Lose $6,400,000 | 1/128 |
| Round 8 | $ 12,800,000 | Lose $12,800,000 | 1/256 |
| Round 9 | $ 25,600,000 | Lose $25,600,000 | 1/512 |
| Round 10 | $ 51,200,000 | Win $51,200,000 | 1/1028 |
Although they’d need to bring a lot more money with them, their odds of walking away with $100,000 of the casino’s money are just as good.
Am I a genius or a fool?
The only way I could see a casino preventing this approach from working is if they implemented a maximum bet amount. Most casinos do just that. There may, however, be a few that do not.
I doubt I’ve uncovered a way to “break Vegas”. Then again, I can’t find a flaw in this approach. So, you tell me: Am I a genius or a fool? Add your comments below!
Photo by: Sid/Stephen
5 responses so far ↓
1 Financial Fellow // Aug 20, 2009 at 6:37 am
After I wrote this article I stumbled across the same method on the internet. Not surprisingly I’m not the first person to think of this approach.
The system I describe above is apparently known as the “Martingale System”. It has been around for a few hundred years. As I suspected, casinos institute table limits to defeat the system.
Again, though, I believe there are some casinos - presumably in Las Vegas - that don’t have limits. Why would they let someone use the Martingale system?
John
2 Don // Aug 20, 2009 at 10:23 pm
John,
Ah yes, the Martingale. Many moons ago, I was thinking the same thing. And yes, for the most part, casino table limits are there to ‘protect’ against this method of betting. I actually did witness someone attempt to do this playing BlackJack. He was trying to win $500…and he wound up losing over $10K before he stopped!
Casinos don’t exactly discourage this sort of betting pattern, because either the player will run out of money, or they’ll hit the limit.
In Las Vegas, most of the casinos have a ‘no max’ area. However, the player either has to be a ‘known whale’ to them, or be referred by a known whale, to even be admitted into the area. Not everyone can enter this area (and yes, I do speak from experience). If the player is one of their whales, the casino will let him win as much as he wants, because he’ll be back. They all come back. If he doesn’t, I can guarantee he will not be treated as well. This is how casinos can afford to literally give away everything else, as long as the player shows the action for it. Mathematically, the player will lose….eventually.
Regards,
Don
3 Stan Zbornak // Aug 21, 2009 at 10:52 am
Unfortunately, there are also 0 and 00 slots on the roulette wheel. 47.37% is how the house has the edge, versus your rounded up 50.0% probability.
4 Financial Fellow // Aug 22, 2009 at 3:19 pm
Don -
Thanks for the explanation on the “max bet” areas. That makes sense. They basically allow you to play if they know you bet big and have a habit of coming back. If they can’t confirm that they won’t let you play no limits in the first place.
Thanks for the great response!
John
5 Financial Fellow // Aug 22, 2009 at 3:21 pm
Stan -
When applying the Martingale System I describe above, 47.37% doesn’t really matter if you’re looking to only win a single roll. Thanks!
John
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