Backwards martingale convergence theorem
Let's imagine you're playing a game with coins. You flip a coin and if it lands on heads, I give you one dollar. If it lands on tails, you give me one dollar. This is a type of betting game and we call it a martingale.
Now, let's say you start with one dollar and you're allowed to play this game as many times as you want. You can choose to stop playing at any time, but you can also continue playing for as long as you want.
Normally in a martingale, you would increase your bets after each loss, but in a backward martingale, you do the opposite. Instead of increasing your bets after each loss, you decrease them. So if you lose, you bet less money on the next round.
The backward martingale convergence theorem says that in this type of betting game, if you keep playing for long enough, you will eventually reach a point where you can't decrease your bets anymore. At this point, you will have won all of your losses back and you will have a profit.
The theorem is based on some very complicated math, but the idea is that if you keep betting less and less money after each loss, you will eventually reach a point where you either win your money back or you run out of money. And if you have enough money to keep playing, you will eventually reach a point where you can't bet any less because you're already betting zero, and at this point, you will either break even or make a profit.
So the backwards martingale convergence theorem is a way of saying that if you keep playing a betting game where you decrease your bets after each loss, you will eventually reach a point where you can't decrease your bets anymore and you will either break even or make a profit.
Now, let's say you start with one dollar and you're allowed to play this game as many times as you want. You can choose to stop playing at any time, but you can also continue playing for as long as you want.
Normally in a martingale, you would increase your bets after each loss, but in a backward martingale, you do the opposite. Instead of increasing your bets after each loss, you decrease them. So if you lose, you bet less money on the next round.
The backward martingale convergence theorem says that in this type of betting game, if you keep playing for long enough, you will eventually reach a point where you can't decrease your bets anymore. At this point, you will have won all of your losses back and you will have a profit.
The theorem is based on some very complicated math, but the idea is that if you keep betting less and less money after each loss, you will eventually reach a point where you either win your money back or you run out of money. And if you have enough money to keep playing, you will eventually reach a point where you can't bet any less because you're already betting zero, and at this point, you will either break even or make a profit.
So the backwards martingale convergence theorem is a way of saying that if you keep playing a betting game where you decrease your bets after each loss, you will eventually reach a point where you can't decrease your bets anymore and you will either break even or make a profit.