When kids get bored, they make up games. One of the easiest games to play is of course the "Finger Game." You know, the one where you tap the opponent hand to increase the number of fingers he or she has to hold up? And if one of the hands reaches more than 4, than the hand is out.
Assuming no splits (Tapping your own hands to redistribute the number), I found out player two can always win. A few minutes of boredom made me draw up a simple tree of each move each player can do. I assumed the following: having two hands out is better than one (meaning that the player will strike out a hand as soon as possible) and no stupid moves to the depth of one (translation: not commiting suicide by seeing only one move ahead).
So by the second move, the hands will look like 1 1 - 2 1 (1 on left hand and right hand for P1 and 2 on left hand and 1 on right hand for P2). If player two strikes P1 with the 2 hand, P2 will lose as P1 can easily get out one hand of the opponent.
Now, if player two strikes with the one hand, then no matter what P1 does, he or she will lose. If P1 makes it a 2 1 - 2 2, P2 can win it by striking the one (try it out yourself if you don't believe me). Or if P1 makes it a 2 1 - 4 1 or a 2 1 - 3 2 game, both results in P1 getting into too huge a hole (down by a whole hand) to be able to climb out of the hole.
I should really write a computer program to simulate the whole fingers with split...
-runiteking1
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5 months ago
Lol I noticed this too when I play (way to spill the secret! :P :D )! That's why the finger game isn't fun unless 1) the other person has never played before, 2) uneven splits are allowed, 3) you throw in some variety (read: not playing to win).
ReplyDelete--Wii