Another relevant figure is EY's estimate that the bill was Nick's, and vice versa. We do not yet have enough data to solve the problem. If EY said that he also had a 20% probability that the bill was Nick's and Nick had a 15% probability that the bill was EY's, they should split it 50/50.

Also, if Nick had said it was 1% chance it was his and EY had said it was 3% it was his (they had both checked their wallets earlier, say), would it make sense to split it 3:1 in favor of EY, or anything close to that? I figure that in that case the probability that it was already in the cab and they should split it 50/50 as a windfall begins to dominate. Such a notion does not seem to have entered any of the above calculations.