I don't know if anyone has made anything like this, so I apologize if this is something that has already been done.
I made this calculator in OpenOffice Calc. Across the top row, enter the per-board survival rates and starting level (5+). At the bottom, probabilities of reaching the KS are shown for the number of men in reserve.
Hopefully, others might find this interesting, if not useful.
Quick explanation of how it works:
The numbers below the headers represent all the possible combinations of 3 or less deaths a player can have before reaching the KS. To the right (Column E), is the probability of that particular combination occurring. At the bottom are sums of those probabilities.
The formula in Column E is the number of combinations multiplied by death rate raised to the number of deaths multiplied by survival rate raised to the number of survivals. Number of combinations is kinda tricky. If a player reaches the KS and died X times on barrel boards, he will have played 51+X barrel boards (L5+). The last board must have been survived, therefore the number of combinations is 51+X-1 choose X, i.e. choose X deaths to occur over 51+X-1 boards.
