I'm late to the party, but here's a simple, non-Jenga mechanic that I've been playing with:
- Write down the numbers 1 through 6 in two lists with a bar in between them (1 2 3 4 5 6 | 1 2 3 4 5 6).
- Every time the game tells you to pull from the tower, roll a d6.
- If the number that comes up has not been crossed out from the left list, cross it out and continue with the game.
- When all of the numbers on the left list have been crossed out, start crossing out numbers on the right list.
- When all of the numbers in both lists have been crossed out, the tower falls/alien breaks into the derelict/barbarians enter the library/etc.
The distribution (is that the right word?) for a 10,000 run trial looks like
with 90% getting to the 19th pull, and 50% getting to the 27th pull.