re: Statistics Spinoff Thread: How much would you pay to play this "game of chance"

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If you flip heads on the first flip you win nothing yet. The pot has grown

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I am, at all times, guaranteed the $ in the pot. So once I flip heads, I have won that $.

Flipping tails doesn't win the $, it ends the game.

By playing, I'm guaranteed the $2 pot. To say my expected value on the first flip is .5 of $2 doesn't make sense.

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So what is the EV of the first flip?

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I think we're going in circles here. You can look at the EV of the first flip two ways.

1) EV is infinity since you have a 50% of winning nothing (assuming your rule of $0 if you flip tails to start) and a 50% chance of winning $4 or more - which can be expressed as a 25% chance of winning exactly $4, a 12.5% chance of winning exactly $8, a 6.25% chance of winning exactly $16... all the way to infinity. Those only equal $1 each, but they add up forever, so the sum is infinite. You have a 50% chance of winning $0 and a 50% chance of winning infinite dollars - the answer is still infinite

2) The value of winning the pot - flipping a tails on the first flip - is 50% times the pot of $0 due to your added rule. The value of that outcome is $0.

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This is the difference between a mathematical equation and gambling. Based on the rules of the game I get the pot. Whatever is in it, I have won.

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Sure, but gambling or mathematically, you don't get the pot until you flip a tails. It sounds contradictory, because you'd think you want to flip heads for as long as possible, but you don't win the pot until you flip a tails.

You have similar odds to win the Powerball as you do to flipping heads 27 times in a row in this game, but you don't win any money until you flip that tails on the 28th flip.