# bean bag win

[This article was first published on

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

**R – Xi'an's Og**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

**A** quick riddle from The Riddler, where a multiple step game sees a probability of a 3 point increase of .4 and a probability of a 1 point increase of .3 with a first strategy (A), versus a probability of a 3 point increase of .4 and a probability of a 1 point increase of .3 with a second strategy (B), and a sure miss third strategy (C). The goal is to optimise the probability of hitting exactly 3 points after 4 steps.

The optimal strategy is to follow A while the score is zero, C when the score is 3, and B otherwise. The corresponding winning probability is 0.8548, as checked by the following code

win=function(n=1,s=0){ if(n==4)return((s==3)+.4*(!s)+.8*(s==2)) else{return(max(c( .4*win(n+1,s+3)+.3*win(n+1,s+1)+.3*win(n+1,s), .1*win(n+1,s+3)+.8*win(n+1,s+1)+.1*win(n+1,s), win(n+1,s))))}}

To

**leave a comment**for the author, please follow the link and comment on their blog:**R – Xi'an's Og**.R-bloggers.com offers

**daily e-mail updates**about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.