Risk of ruin calculation
This just comes down to a risk of ruin calculation. As a member of the MIT blackjack team, I think I can safely say that being outrolled by your opponent does not matter. The key to the situation is being able to risk an amount of your bankroll that you choose on each event.
Yes, it's true that if you sit down with your whole bankroll and play the parrot heads up, you are going to lose. However, even the non-mathematically inclined easily recognize that this is not smart bankroll management.
In a typical game, you have almost complete control over the amount of money you have at risk at any given moment. It's a straight-forward math problem to figure out your edge over the parrot, and then choose to sit with the ideal amount of money given the probability of ruin you wish to take. With proper bankroll management, you can make it essentially a lock that you will bust the well-funded parrot. You simply sit down with less money every time you lose, while taking some off the table whenever you double through.
good luck.
Eric
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