A Jenga tower usually collapses after about 30-35 pieces are drawn. Here's one way to simulate that.
A d6 dice pool. Every time you use a card you roll 1d6. If you roll a 1 you lose one die from the dice pool. On average it takes 6 rolls of a d6 to get a 1 so to simulate a jenga tower you want a dice pool of 5-6 six sided dice.
Here's a simpler method that only requires one six sided die.
Write down on a sheet of paper the number 5. Roll 1d6 each time you draw a card. If you roll a 1, reduce the number by 1. When you reach 0 it's the same as the jenga tower collapsing.
5 dice will give you 30 rolls on average before you reach 0. 6 dice will give you 36 rolls. You can increase the average number of rolls very easily by increasing the number you start with. Increase by 1 to increase the average number of rolls by 6.