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gwern comments on Explicit and tacit rationality - Less Wrong
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Khoth suggests modeling it as starting with an endowment of $60k and considering the sum of the 3 equally probable outcomes plus or minus the difference between the original price and the closing price, in which case the optimal number of coins to hold seems to be 300:
Of course, your specific payoffs and probabilities imply that one should be buying bitcoins since in 1/3 of the outcomes the price is unchanged, in 1/3 one loses 90% of the invested money, and in the remaining 1/3, one instead gains 1000% of the invested money...
I've fiddled around a bit, and ISTM that so long as the probability distribution of the logarithm of the eventual value of bitcoins is symmetric around the current value (and your utility function is logarithm), you should buy or sell so that half of your current net worth is in dollars and half is in bitcoins.