I have the following problem.
In blackjack, you have 20, and dealers top card is 10. The remaining cards (including dealer's second card) are A and 10. Your bet is $100. Solve the game (find the value of the game and an optimal strategy).
I was thinking that the optimal strategy here is to say, not to draw a card, since its only 50/50 that the dealer will get the 10 needed to take my money. Both our odds are only 50% so shouldnt it not matter which we choose?
You should always draw a card.
If dealer has a $10$, you draw an ace and win.
If dealer has an ace, then he already has $21$, so he beats you if you stay (since $21$ beats $20$), and he beats you if you draw (since you will bust).
If you stay, your expectation is negative since you either tie or lose, each with probability $\frac{1}{2}$.
If you draw, your expectation is zero, since you either win or lose, each with probability $\frac{1}{2}$.
Thus, drawing is optimal.