Thanks for the ideas.

You reminded me that I wanted to do some more analysis. While you are interested in infinity, I am still obsessed with ending the game in the minimum number of spins (7).

In another sample of 1 million games, 1509 ended in 7 spins. Of those games, there were 421 unique sequences of 7 spins. Some sequences only occurred once (38 out of 421). Other sequences occurred multiple times, up to a maximum of 10 times.

These 2 sequences occurred 10 times each:
    4->3->6->5->6->5->5
    1->4->4->5->5->4->4
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