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**F**ollowing Le Monde puzzle #810, I tried to code an R program *(not reproduced here)* to optimise an awalé game but the recursion was too rich for R:

Error: evaluation nested too deeply: infinite recursion / options(expressions=)?

even with a very small number of holes and seeds in the awalé… Searching on the internet, it seems the computer simulation of a winning strategy for an awalé game still is an open problem! Here is a one-step R function that does not produce sure gains for the first player, far from it, as shown by the histogram below… I would need a less myopic strategy by iterating this function at least twice.

onemorestep=function(x,side){ # x current state of the awale, # side side of the awale (0 vs 1) M=length(x);N=as.integer(M/2) rewa=rep(0,M) newb=matrix(0,ncol=M,nrow=M) for (i in ((1:N)+N*side)){ if (x[i]>0){ y=x y[i]=0 for (t in 0:(x[i]-1)) y[1+(i+t)%%M]=y[1+(i+t)%%M]+1 last=1+(i+t)%%M if (side){ gain=(last<=N) }else{ gain=(last>N)} if (gain){# ending up on the right side rewa[i]=0 while (((last>0)&&(side))||((last>N)||(!side))) if ((y[last]==2)||(y[last]==3)){ rewa[i]=rewa[i]+y[last];y[last]=0 last=last-1 }else{ break()} } newb[i,]=y } } if (max(rewa)>0){ sol=order(-rewa)[1] }else{ sol=rang=((1:N)+N*side)[x[((1:N)+N*side)]>0] if (length(rang)>1) sol=sample(rang,1,prob=x[rang]^3)} return(list(reward=max(rewa),board=newb[sol,])) }

Filed under: Kids, pictures, R Tagged: awalé, infinite recursion, Le Monde, R

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