In two-player cribbage, when the pone is dealt a hand that includes a run and a 5+pair (e.g. 3,4,5,6,Q,Q) is it better to keep the run (3,4,5,6) or the 5+pair (_,5,Q,Q)?
It seems like there should be a statistically optimal play here.
In the specific example above, either choice leaves the pone 6 points, but the run has a chance of improving to a double run (12 out of the remaining 46 cards) and is improved by 24 other cards (2s, 7s, Ts, Js, Qs, Ks). The main downside of that play is it concedes a pair to the dealer. On the other hand, the 5+pair can improve through any 5, Q, or ten-value card. If the connecting 6 is kept, it can also improve through a 4 or 7. Overall, there are 24 cards that improve that hand. It also concedes a 3,4 to the dealer - which seems less likely to give the dealer points.
My intuition is to keep the run, but a mathematically sound analysis of expected value would be nice.
P.S. For the purposes of this question, we can ignore the exact position of the players, and assume it's somewhere mid game (as opposed to really close to the end where pegging considerations become more important).