(mean(replicate(1e4,any(diff(cumsum(rbinom(100,1,0.5)),5)==5))))
[1] 0.8089
>
> (mean(replicate(1e4,with(rle(rbinom(100,1,0.5)), max(lengths[which(values=
<rle(rbinom(100,1,0.5)), max(lengths[which(values== 1)])>=5))))
[1] 0.8117
>