Interesting gambling paradox I learned of some time ago.
A guy offers the following. He flips a coin as many times as required until he first flips a tail. If he flips T on first try you get $2. HT he pays you $4. HHT, $8; HHHT, $16; HHHHT $32, etc.
How much should you be willing to pay to play this game?
Answer - the EV of this game is infinite, as you have 1/2 chance at $2 payout, 1/4 chance of $4 payout, etc. and each of these pieces is worth $1 of EV, so if you add them all up you get 1 + 1 + 1 + ... Thus, you could argue that you should be willing to pay any amount to play this game. It's a paradox because you can easily see that you probably wouldn't wanna pay $1M to play a round, not to mention that it's impossible to have arbitrarily high payouts (there is a practical limit to how much money you can actually win - all the money in the world is the limit, and even that isn't really worth the nominal value if you were to actually hold it all.
YODL
npub162…atdhy
2026-05-29 16:01:31 UTC
Author Public Key
npub162zpxufpw8pnuytaf0gfxzkqtvk9rvcwkvppa7x57y3n7qkfpg4shatdhyPublished at
2026-05-29 16:01:31 UTCEvent JSON
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"content": "Interesting gambling paradox I learned of some time ago.\n\nA guy offers the following. He flips a coin as many times as required until he first flips a tail. If he flips T on first try you get $2. HT he pays you $4. HHT, $8; HHHT, $16; HHHHT $32, etc.\n\nHow much should you be willing to pay to play this game?\n\n\nAnswer - the EV of this game is infinite, as you have 1/2 chance at $2 payout, 1/4 chance of $4 payout, etc. and each of these pieces is worth $1 of EV, so if you add them all up you get 1 + 1 + 1 + ... Thus, you could argue that you should be willing to pay any amount to play this game. It's a paradox because you can easily see that you probably wouldn't wanna pay $1M to play a round, not to mention that it's impossible to have arbitrarily high payouts (there is a practical limit to how much money you can actually win - all the money in the world is the limit, and even that isn't really worth the nominal value if you were to actually hold it all.",
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