I'm at a roulette table. I only bet on red. When I lose I triple my bet, when I win I restart. Is this a roulette strategy?
Ok so here's the rules
- I just bet on red every time
- I start with 1 dollar
- every time I lose, I triple my previous bet
- every time I win I restart
I'm going to simulate 10 games
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Game 1 - Bet $1 Lose
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Game 2 - Bet $3 Lose
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Game 3 - Bet $9 Win $18
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Game 4 - Bet $1 Lose
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Game 5 - Bet $3 Lose
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Game 6 - Bet $9 Win $18
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Game 7 - Bet $1 Lose
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Game 8 - Bet $3 Lose
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Game 9 - Bet $9 Lose
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Game 10 - Bet $18 Win $36
In this simulation I'm losing at a rate of 70%. In reality the lose rate is closer to 52%. I put in $54 but I'm walking away with $72, basically leaving the building with $18.
Another example. Let's pretend I walk in with $100,000 to bet with. I lose my first 10 games and win the 11th.
- 1 lose
- 3 lose
- 9 lose
- 27 lose
- 81 lose
- 243 lose
- 729 lose
- 2187 lose
- 6561 lose
- 19683 lose
- 59049 win $118098
$88573 spent out of pocket, $118098 won
Walk out with roughly $29525.
I get most casinos won't let you be that high but it's a pretty extreme example anyway, the likelyhood of losing 10/11 games on 48% odds is really unlikely.
So help me out here, what am I missing?
Congratulations, you've invented the Martingale betting system and are well on your way to becoming an adept probability theorist
The short answer is that casinos account for this by changing the profit returns and the odds of making a profit at all so that catastrophic losses are much more likely
Betting limits.
Also, n^3 grows fast.
It's 3^n, not n^3. n^3 is actually way slower.