We want to help the poor git...
Old Question
...with a bias to speed up things. We replace step 1
1. Draw ball, memorize color, throw it back.
with
1a-c. Draw ball, memorize color, throw it back. Repeat three times.
1d. Take majority color of the three colors in 1abc, use that color in step 2.
Everything else stays the same. Can you still find a closed form (for random values of closed :-) for the expectation value of steps until all colors are equal?
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asked Jun 12, 2017 at 8:44
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2$\begingroup$ It would be better to make this problem self-contained. This process is no longer a martingale. Do you have a closed form for the probability that you reach all black from $b$ black and $w$ white? Why do you expect there is a closed-form for the expected time until all colors are equal, and why is this process of interest? $\endgroup$– Douglas ZareCommented Jun 12, 2017 at 11:41
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$\begingroup$ The problem makes me think of this related paper : itc-conference.org/_Resources/Persistent/… $\endgroup$– N. GastCommented Jun 12, 2017 at 13:34
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