Proposition bet

[Guernica4000]

Player “A” propositions Player “B” to a bet.

The rules are that Player “A” will go all-in for one unit ($100) in the dark. Player “B” looks at his two cards and decides if he wants to call or fold. If he calls the best Poker hand wins after the river.
If player “B” loses he must pay player “A” 2 to 1 or $200 and another hand is played.


Please keep in mind that player “A” all-in is always for $100 regardless of the hands he has won or lost.
We are making the assumption that player “B” is a good player with a good understanding of poker.
There are no blinds or antes.


My question is:
Who is getting the better of this bet and what would be the minimum number of hands that would have to be played in order to remove or at least reduce the “luck” factor.