Penney-Ante Game uneven Patterns
2 Player Games
This page displays spreadsheets for a 2 player game with uneven lengths of patterns.
Specifically, 2 vs. 3, 2 vs. 4, 3 vs. 4, 3 vs. 5 and 4 vs. 5
R code in last section on this page 1r.
2 vs. 3 (Length 2 in a race against a Length 3). As seen in sheet, there are only two 3-tuple patterns (player B highlighted in green) that has greater than a 50% chance of winning a race against a 2-tuple pattern.
2 vs. 4 (Length 2 in a race against a Length 4).
There are 0 winning games for a 4-tuple finishing 1st against a 2-tuple pattern. (p=H=1/2) sheet showing winning probabilities coming soon.
3 vs. 4 (Length 3 in a race against a Length 4). As seen in sheet, there are only four 4-tuple patterns (player B highlighted in green) that has greater than a 50% chance of winning a race against a 3-tuple pattern.
3 vs. 5 (Length 3 in a race against a Length 5).
There are 0 winning games for a 5-tuple finishing 1st against a 3-tuple pattern. (p=H=1/2) sheet showing winning probabilities coming soon.
4 vs. 5 (Length 4 in a race against a Length 5). As seen in sheet, there are only fourteen 5-tuple patterns (player B highlighted in green) that has greater than a 50% chance of winning a race against a 4-tuple pattern.
1r. R code for calculating the mean length of a game (PAG) and the 2 player win probabilities.
playerA pattern MUST be shorter than playerB pattern
#pWinsRace2(c(1,1,0),c(1,1,1,1),.55)
by default the probability for (1) = 1/2
call function as: pWinsRace2(c(player A pattern),c(player B pattern),)