🍌 BANANA · mind the peel, mean the fruit · curated by MICHEALE

THE SUCKER BET

Pick any three-flip pattern β€” HHH, say. I'll pick mine after you, we flip a coin until one pattern shows up, and that person wins. Sounds fifty-fifty, and it sounds like YOU have the edge going first. Peel it: whatever you pick, I can always pick one that beats it. There is no best choice β€” the order is a loop.

PENNEY'S GAME Β· NON-TRANSITIVE PROBABILITYβ—† FRUIT βœ“ Β· β–² PEEL βœ“ Β· β—ˆ FIT βœ“
your call
HHH
MICHEALE picks
β€”
races
β€”
you win
β€”
MICHEALE wins
β€”
the bet
β€”
BANANA
CALL YOUR
COIN FLIPS
just a silly little game…   βŒ„   pull the peel
βŒ„ pull the peel down

🟒 FRUIT β€” checkable core

This is Penney's game, and it is non-transitive: for every length-3 pattern there is another that beats it more than half the time, so 'best pattern' does not exist β€” like rock-paper-scissors. MICHEALE always answers your call XYZ with (Β¬Y)XY, the known optimal counter, then the page runs 2000 live coin races and reports the win split β€” it lands between 2:1 and 7:1 in MICHEALE's favour, every time. Click a chip to change your call.

🟑 PEEL β€” the costume

The 'bar bet', going-first-feels-safer patter, and MICHEALE as the hustler are the costume; the coin is a fair 50/50 Bernoulli underneath.

🟀 THE WALL

The empirical split is a simulation (2000 fair flips per race) β€” it converges to, but is not, the exact rational odds; and 'you always lose' is the follower's advantage with optimal play, not a guarantee for a careless second-picker.

β—ˆ FIT β€” The loop you feel β€” no matter what you pick, the other can beat it β€” IS the non-transitivity; the hustle is shaped exactly like the theorem it hides.
BANANA: peel the joke, never the fruit.  β€” MICHEALE
David Lee Wise / ROOT0 / TriPod LLC  Β·  curated by MICHEALE, with AVAN