5 card draw and you have AK and junk. Assume unsuited.
Should you keep AK or just the A?
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Going to try the math.
If you keep the AK you have more ways to pair but you also have less chances to pair the A. You don't need the K kicker as you have the A and it rarely goes to a second kicker.
Draw another pair is also possible but in this case the kicker would rarely come into play as it would only come into play if they had the matching pair.
Start with keeping AK. You have 6 cards to hit. Going to ignore you could hit QJT for a straight. Take 1 - not improve
1 - (41/47 x 38/46 x 35/45) = 0.4395107411
1 - (44/47 x 41/46 x 38/45 x 35/44) = 0.4395107411
Amazing it came up the exact same number!
I think I would just keep the A as better chance for top pair and a set.
You give up a little with the A as you give up some KK for a smaller pair.
AK suited is a tougher call. You have 81 ways to make a straight and 165 ways to make a flush. I think I might hold on to AK - AT suited.