A standard $52$-card deck:
Player $1$ (is dealt first, only $2$ players in the "deal"), he looks at his cards, goes all in. He has a straight with high-card $H_1$.
Player $2$ (is dealt second), he doesn't look at his cards, and matches the all in.
$(1)$ What is the straight-up probability Player 1 will win the hand, with no other information. How is that probability adjusted based on the value of his high-card? Say $H_1 = 7$ versus $H_1 =$ Jack.
$(2)$ What is the straight-up probability Player 2 draws a straight, GIVEN Player 1 has already drawn a straight? What is the probability of having the same high card $(H_2 == H_1)?$ $(H_2 < H_1)?$ $(H_2 > H_1)?$ What is the probability of $(H_2 > H_1)$ by exactly one number: e.g, $H_1 = 7, H_2 = 8.$
This actually happened to me. I was the "lucky" player, Player $1$ was very much nonplussed.