Re: Card Sharks
To prove my game show nerdiness....
In the actual game show, you also get bonus money every time you move up to the next row and also get the opportunity to replace the card that is moved up. That is, if your first row of cards is T4JJ3, the 3 gets moved up to the next row and you get a bonus added to your bankroll (a set amount, not a percentage). Then on the 2nd row, I think there are only 3 cards, at which point you move the 3rd card up and get another bonus. Then the final row there is just two cards (the card moved up is one of them so there is only one betting round).
How does the addition of the bonuses along the way affect the ideal strategy? It certainly affects the EV of the final bet of each row. For example, if you have only $100 left on the final bet of the lowest row and the bonus is $500 for moving up, betting $100 can't be ideal as, when you lose it all, you won't get the $500 bonus you'd be guaranteed so long as you had money left over.
Is the optimal EV strategy on the final wager of each row to bet everything you have but $1?
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