For a while now my percentage win for foodlewordle.io has been at 96%. A few weeks ago I wondered how many more games I needed to play to get to 97%. I discussed this with a pal at golf and he reckoned it wouldn’t be long. I sat down and worked through the algebra. We were both surprised by the result.
Here’s the calculation based on the results in the screenshot. The assumption is that I’m going to get the answer right each time I play the game in the future. Since I already know the answers, this is pretty likely.
Played = 550
Win = 144 + 31 + 118 + 130 + 74 + 32 = 529
Win % = ( 529 / 550 ) = 96.18 recurring - which rounds down to 96%
Formula for 97% is
( win + n ) / ( played + n ) = 97 / 100
( win + n ) * 100 = 97 * ( played + n )
( 529 + n ) * 100 = 97 * ( 550 + n )
52900 + 100n = 53350 + 97n
100n - 97n = 53350 - 52900
3n = 450
n = 150
check
529 + 150 = 679
550 + 150 = 700
679 / 700 = 0.97
Therefore in order to reach 97% I’m going to have to play foodlewordle.io another 150 times, approximately 5 months.
It might be sooner if 96.5% rounds up to 97%.