very simplified likelihood problem, n+1 -> n

[RobinHankin]

in inst/very_simplified_likelihood.Rmd we have the focal competitor and n clones giving n+1 competitors. Maybe we should have n-1 clones, giving n competitors. This would make things easier?

[RobinHankin]

However this suggestion causes ugly equations. Currently we have:

"Placing after $r < n$ of the $n$ clones of strength $b$ finish:

$$\mathcal{L}(a)=\frac{b^ra}{(a+nb)(a+(n-1)b)(a+(n-2)b)\cdots(a+(n-r)b)}=\frac{B-1}{(B+n-1)(B+n-2)\cdots(B+n-r-1)}$$

where $B=1/b$ [also using the fact that $a+b=1$].

Making the change to $n-1$ clones of strength $b$ would give

$$\mathcal{L}(a)=\frac{b^ra}{(a+(n-1)b)(a+(n-2)b)(a+(n-3)b)\cdots(a+(n-r)b)}=\frac{B-1}{(B+n-2)(B+n-3)\cdots(B+n-r-2)}$$

which is a bit weird.