WORD5 #603 3/6* (Hard Mode) ⬛⬛⬛⬛🟧 ⬛🟧⬛⬛⬛ 🟪🟪🟪🟪🟪

WORD5

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.

WORD5 #602 X/6* (Hard Mode) ⬛⬛🟧⬛⬛ ⬛⬛⬛🟪🟪 ⬛⬛⬛🟪🟪 🟧⬛⬛🟪🟪 ⬛🟪⬛🟪🟪 ⬛🟪⬛🟪🟪

WORD5

Since waking today, I've had the song from Star is Born ("tell me something, boy...") stuck on my head on loop. Hoping sending this note will break the curse