I can give you higher odds, but I will have to ask for a longer string of same side. Say like 20 in a row.

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.

Edit: in reply to your edit, I will do this "virtual" bet and update this comment with the result. I will try to tweak it to be in my favor, if there is no way to do so, then I guess the gamble fallacy is a real fallacy.

PS: not an actual bet, just tinkering stuff (betting is haram).