Answer
Dan should randomize his strategy as follows:
Probability of picking one coin = 77/548.
Probability of picking one coin = 107/548.
Probability of picking one coin = 117/548.
Probability of picking one coin = 122/548.
Probability of picking one coin = 125/548.
With this strategy, Dan can expect to win 3.640510949 coins every turn, regardless of how many coins Sam picks.
A solution can be found in my Math Problems site, problem 230.
A related question, which led to this one, can be found in my forum at Wizard of Vegas.