Penney-Ante Game

2 Player Games

a coin flip PATTERN 'race' game between 2 players and where the patterns have the same length.

Below spreadsheets answers the questions like "What is the probability of pattern B showing first before pattern A in a seires of fair (or biased) coin tosses?" or "What is the average length of a Penney-Ante game until one pattern wins?

below are spreadsheets for the 2, 3, 4 and 5-tuple pattern games.

Where the patterns are (in length) 2 vs. 3, 3 vs. 4 and 4 vs. 5, please see the uneven Penney-ante Game page at this site.

R code section at end of page in section 1r.

3-TUPLE PATTERNS

Included is a text file for all 56 - 2 player 3tuple game results. Distribution matrices and mean values for length of game, mean given a win for Player A and for Player B. updated: 3.7.2019. Text file loses formatting in Google Docs so the .txt file will be listed.

4-tuple patterns

5-tuple games

1r. R code for the mean number of games until a win and each player win probability.

Function is called: pWinsRace(c(1,1,1),c(0,0,0)) ;

meaning pWinsRace(c(player A pattern),c(player B pattern))

Example: c(1,1,1) could mean HHH (H = Heads) or SSS (Success,Success,Success)

c(0,0,0) could mean TTT (T = Tails) or FFF (Failure,Failure,Failure)

Penney-ante Game: 2 Players

calculates and prints mean number of games and win probabilities

Both player patterns MUST be the same Length and can NOT be the same pattern