Well, he's suggesting maximizing the expected value, which is a little different. For example, a situation where you have a 10% chance of making $10M and a 90% chance of making zero has an expected value of $1M, but its expected value in log10 space is 0.7 = only about $5, while a 100% chance of making $100K has an expected value of $100K, but in log10 space = 5 = $100K.
I still quibble about the use of log for this purpose (and even if you do, what base?), but I see his point. A non-linear utility function penalizes low-chance but high-value outcomes.
The most general (correct) form of this statement is "use the expectimax algorithm". Yeah, it's a bit weird that he's prescribing log as the mapping from dollars to utility.
If log is the correct mapping for you, it actually doesn't matter what base you use. It just comes out as a constant factor on the expected utility.
I still quibble about the use of log for this purpose (and even if you do, what base?), but I see his point. A non-linear utility function penalizes low-chance but high-value outcomes.