"Let's say on the one hand you guess a 50% getting it if the headbands don't matter. Then this situation has a chance of 0.5^10 of coming up, since each one was a coinflip anyway."

"But if you instead thought 60% with headbands and 40% without, then for the headbanded people it'd be 0.6^3*0.4^2, with the winners being 0.6s and the losers being 0.4s, and then for the non-headbanded people you'd have 0.6^3*0.4^2 too, for the opposite reasons. So that's a chance of 0.6^6*0.4^4. Then we can multiply everything by 10^10 to make the math easier, and the idea of 60/40 and 40/60 increased in likelihood vs pure 50/50, by, umm...

(6^6)*(4^4)/(5^10)

"Let's say on the one hand you guess a 50% getting it if the headbands don't matter. Then this situation has a chance of 0.5^10 of coming up, since each one was a coinflip anyway."

"But if you instead thought 60% with headbands and 40% without, then for the headbanded people it'd be 0.6^3*0.4^2, with the winners being 0.6s and the losers being 0.4s, and then for the non-headbanded people you'd have 0.6^3*0.4^2 too, for the opposite reasons. So that's a chance of 0.6^6*0.4^4. Then we can multiply everything by 10^10 to make the math easier, and the idea of 60/40 and 40/60 increased in likelihood vs pure 50/50, by, umm..."

"(6^6)*(4^4)/(5^10)"

"Let's say on the one hand you guess a 50% getting it if the headbands don't matter. Then this situation has a chance of 0.5^10 of coming up, since each one was a coinflip anyway."

"But if you instead thought 60% with headbands and 40% without, then for the headbanded people it'd be 0.6^3*0.4^2, with the winners being 0.6s and the losers being 0.4s, and then for the non-headbanded people you'd have 0.6^3*0.4^2 too, for the opposite reasons. So that's a chance of 0.6^6*0.4^4. Then we can multiply everything by 10^10 to make the math easier, and the idea of 60/40 and 40/60 increased in probability vs pure 50/50, by, umm..."

"(6^6)*(4^4)/(5^10)"

"Let's say on the one hand you guess a 50% getting it if the headbands don't matter. Then this situation has a chance of 0.5^10 of coming up, since each one was a coinspin anyway."

"But if you instead thought 60% with headbands and 40% without, then for the headbanded people it'd be 0.6^3*0.4^2, with the winners being 0.6s and the losers being 0.4s, and then for the non-headbanded people you'd have 0.6^3*0.4^2 too, for the opposite reasons. So that's a chance of 0.6^6*0.4^4. Then we can multiply everything by 10^10 to make the math easier, and the idea of 60/40 and 40/60 increased in probability vs pure 50/50, by, umm..."

"(6^6)*(4^4)/(5^10)"