Quote from: o_e_l_e_o on February 01, 2020, 11:38:06 AM

0.505¹⁰ is 0.0010787..., or 0.11%. So at a payout of 2x, you have a 0.11% chance of losing 10 times in a row. That becomes 0.004% for 15 losses in a row, and 0.0001% for 20 losses in a row.

To add what o_e_l_e_o said, 0.11% is probability of losing 10 times in a row when you are going to play only 10 times.

As the chance of losing 10 times in a row is that low, some people think that they can use martingale strategy and get rich.
Here is how martingale strategy decreases the chance of winning.
Assume that you have 1 BTC. The chance of doubling your balance with one wager is 49.5%
Some people think that they can wager 1 mBTC instead of 1 BTC, use martingale strategy and double their balance easily.
In this case for doubling the balance you must win 1000 times and you can lose up to 10 times in a row. As o_e_l_e_o said, the chance of losing 10 times in a row is only 0.0010787. But the chance of not happening this 1000 times is (1-0.0010787)¹⁰⁰⁰ = 0.34 = 34%

So, the chance of losing 10 times in a row depends on the total games you are going to play too.

For example, if you want to continue to gamble until you win 10,000 times, chance of losing 10 times in a row at least one time is 1- (1-0.0010787)¹⁰⁰⁰⁰ = 99.99%