Board Thread:General Discussion/@comment-26907577-20191002153041/@comment-26907577-20191129145917

Okay, let's say that with no curfews, we get 1 human per 1 Fall Time Unit. t+0 is when the villages are founded, with approximately their current populations.

t+1 FTU, 1 fall.

t+1.167, a second. (change since previous: 0.167)

1.4 (0.233), 1.75 (0.35), 2.333 (0.583), 3.5 (1.167), 7 (3.5).

All villages now have curfews in place. An indeterminate amount of time passes, and the Red Village gives up.

There is now a 0.167 FTU window where any fall will fulfill what is seen in-game. However, the expected time till a fall with the current restricted population is a whopping 3.5 FTU. The approximate probability for Frisk to fall in this time is 4.77%. But it's not over.

The second village relents (95.33% that Frisk hasn't already fallen by now.) Now, Frisk's odds are the same, but a second human from the second village are also. This window is 0.233 FTU long, so it's a 6.66% chance that either human falls here. (Total for Frisk: 0.0477+0.9533*0.0666 = 11.12%)

The third village. (86.68*95.33 = 82.63%) Once again, expected 3.5 for Frisk, but also 3.5 for two more humans. This window is 0.35 FTU long. 10% on any village. (Total for Frisk: 0.1112+0.8263*0.1 = 19.38%)

Fourth. (70*82.63 = 57.84%) 0.583 FTU. 16.66%. (Frisk: 0.1938+0.5784*0.1666 = 29.02%)

Fifth. (33.36*57.84 = 19.3%) The time is irrelevant at this point; probabilities add to greater than 100%. We expect a human to fall in this period. 20%.

Frisk's grand total is 0.2902+0.193*0.2 = 32.88%

Not bad.