Galton and Watson voluntarily skipping some generations

A riddle on a form of a Galton-Watson process, starting from a single unit, where no one dies but rather, at each of 100 generations, Dog either opts for a Uniform number υ of additional units or increments a counter γ by this number υ, its goal being to optimise γ. The solution proposed by the Riddler does not establish his solution’s is the optimal strategy and considers anyway average gains. Solution that consists in always producing more units until the antepenultimate hour (ie incrementing only at the 99th and 100th generations),  I tried instead various logical (?) rules and compared outputs by bRute foRce, resulting in higher maxima (over numerous repeated calls) for the alternative principle

s<-function(p=.66){ 
   G=0;K=1 for(t in 1:9){ 
      i=sample(1:K,1) 
      K=K+i*(i>=K*p)
      G=G+i*(i<K*p)}
  return(c(G+sample(1:K,1),K))}