Like. I know they are different and that one is less likely. But could someone explain this in a way that I can explain it to my partner? I know it is true but cannot remember anything about why and how to explain my point.
In: 6
The expected value is the same, if you always get to play to the end:
A single 70% chance to win a dollar will, on average, net you 70 cents.
The 7% chances will, on average, net you 7 cents each, for a total of an average of 70 cents if it’s 10 completely separat attempts.
But with the single 70% chance, you can at most win $1. With the 10 chances, you could, theoretically, win $10. It’s unlikely, but possible. But there’s also a 48% chance that you’ll end up with nothing (the chance of getting nothing the first time is 93%, the chance of getting nothing the first and then second time is 93% * 93%, the chance of getting unlucky 10 times in a row is 93%^(10)).
However, if you stop the game once you win, for example because the other side only has one dollar, it’s a different game that’s much worse for you – there’s still a 48% chance of getting nothing, but no chance to get more than one dollar to make up for it.
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