A while back, I posed a question regarding a closed form expression for the number of weeks (similarly, number of cards) needed until the Ace of Spades is drawn in a game of "Catch (Chase) the Ace!".

The game is quite popular and at times causes quite a frenzy.

My post is here: Average time to win "Catch (Chase) the Ace!"

The distribution turns out to be a discrete uniform, and I verify this initially through simulation.

Some time later, @whuber brought up an interesting extension within the comments to a response by @Glen_b which reads in part:

"...Although it is evident that 26.5 represents the expected number of plays needed to win, it doesn't directly reflect the accumulated jackpot (whose increments apparently are considered independent random variables themselves)"

Since I had also mentioned in the post my general interest in the statistical properties of the game, it seems that examining the dynamics of the progressive jackpot is only fitting and would prove some interesting discussion.



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