I like to think about this slightly differently: at first, you bet based on no information, and you know you’re probably wrong. In advance of the host helping out, though, you have no way to put money on your initial bet being wrong. (It’s like playing roulette — the casino is not going to give you even odds betting on two dozens, which would have almost 2/3 chance of being right.)

After the host helpfully takes a door out of play, though, you can bet that you were wrong, and the payout doesn’t change. You already knew you were probably wrong, and now you can bet on this. Of course it’s a good deal. A player can probably avoid the cognitive dissonance by thinking of their initial bet as being their best guess at finding a door that doesn’t have a car behind it.