True, but it's probably not a good idea to tell your girlfriend that.

Interesting. I am assuming you would. Can you briefly explain your reasoning?

Unless you really, really need 100 million, no reasoning will make that a good bet. The expected value is 10 million, and since that's what you're putting at stake, you have nothing to gain. Whereas the utility value of a guaranteed 10 million, assuming you're not very rich already, is huge. It's more than an average lifetime of hard work.

If determination could increase your chance, then you may be better going for $100 million. Otherwise take $10m.