> In essence I will be gambling that there will be more 20 in a row same side than 21 in a row same side, which might be probably true, I have to test it.
I think you're missing a subtlety here.
It's true that 20 in a row is twice as common as 21 in a row.
But 20 in a row is exactly as common as 21 or more in a row.
When you bet on that coin toss, you're not betting on 20 vs. 21. You're betting on 20 vs. 21+. So it's 50:50.
For every thousand times you reach 20, the bet that it ends at 20 wins about 500 times, and the bet that it goes above 20 wins about 250 + 125 + 62 + 31 + 16 + 8 + ... = 500 times.
I think you're missing a subtlety here.
It's true that 20 in a row is twice as common as 21 in a row.
But 20 in a row is exactly as common as 21 or more in a row.
When you bet on that coin toss, you're not betting on 20 vs. 21. You're betting on 20 vs. 21+. So it's 50:50.
For every thousand times you reach 20, the bet that it ends at 20 wins about 500 times, and the bet that it goes above 20 wins about 250 + 125 + 62 + 31 + 16 + 8 + ... = 500 times.