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Sep 8 at 3:09 vote accept user19904
Sep 7 at 23:22 comment added Henry If they were looking at the results of the same die, the probability of Peter's pattern coming before Paula's is the same as the probability of Paula's coming before Peter's so each $\frac12$ (first throw until you get a $1$, then if you immediately throw as $1$ or $2$ then stop with your winner, and otherwise start again). But that race is not the question, which is instead about expectations of numbers of throws.
Sep 7 at 16:29 comment added whuber For more on this problem (or very closely related version of it) please see stats.stackexchange.com/questions/12174 and stats.stackexchange.com/questions/544811.
Sep 6 at 23:34 answer added Dave2e timeline score: 3
Sep 6 at 23:20 comment added jginestet Peter and Paula are not using the same die; each has their own. So Paula can not use Peter's result..
Sep 6 at 22:49 history asked user19904 CC BY-SA 4.0