Let’s consider a scenario where we skip the doubling. So, we have a long line of people, people play one at a time, 50% chance they win a prize, 50% they are eliminated, game ends after first elimination.
It’s quite clear that in expectation, more than 50% of people who played lose the game even though it’s a fair coin (we have a 50% chance of 100% of players losing). This will be explained momentarily.
Imagine the players as a team who score 1 point when they win and lose 1 point when eliminated, with the ability to stop at any time, but who have adopted this stopping strategy.
This strategy of stopping means you come out behind with 50% chance, even with 25% chance and ahead with 25% chance.
If we now look at the percent of wins vs. losses, we can see that we expect more losses than wins on average (though the calculation is more complicated).
The point is that you should only expect an average of half the coin flips to be heads when you adopt some kind of uniform stopping rule, such as always stopping after N rounds. Otherwise, you can pick a stopping rule that makes these kinds of trade-offs.
So you are more likely to lose than win. However, it allows you to maintain uncapped potential profit, whilst your losses are capped at 1.
We can note consider snake eyes from a team perspective. It’s similar, but more extreme. This time your team almost guaranteed to lose one point, though there is an infinitesimal chance that you score infinite points.
This sounds like free money from the perspective of the house, but it’s not, it’s just a martingale.
Let’s consider a scenario where we skip the doubling. So, we have a long line of people, people play one at a time, 50% chance they win a prize, 50% they are eliminated, game ends after first elimination.
It’s quite clear that in expectation, more than 50% of people who played lose the game even though it’s a fair coin (we have a 50% chance of 100% of players losing). This will be explained momentarily.
Imagine the players as a team who score 1 point when they win and lose 1 point when eliminated, with the ability to stop at any time, but who have adopted this stopping strategy.
This strategy of stopping means you come out behind with 50% chance, even with 25% chance and ahead with 25% chance.
If we now look at the percent of wins vs. losses, we can see that we expect more losses than wins on average (though the calculation is more complicated).
The point is that you should only expect an average of half the coin flips to be heads when you adopt some kind of uniform stopping rule, such as always stopping after N rounds. Otherwise, you can pick a stopping rule that makes these kinds of trade-offs.
So you are more likely to lose than win. However, it allows you to maintain uncapped potential profit, whilst your losses are capped at 1.
We can note consider snake eyes from a team perspective. It’s similar, but more extreme. This time your team almost guaranteed to lose one point, though there is an infinitesimal chance that you score infinite points.
This sounds like free money from the perspective of the house, but it’s not, it’s just a martingale.