Expected Value: Cards

Calculate expected value for card scenarios

Expected Value in Poker

A♠

K♠

Q♠

J♠

10♠

In video poker, each hand has a payout. Let us calculate expected value for a simplified payout structure.

Hand	Payout	Probability	E(contribution)
Royal Flush	800×	0.000154%	0.0012
Straight Flush	50×	0.00139%	0.0007
Four of a Kind	25×	0.0240%	0.0060
Full House	9×	0.144%	0.0130
Flush	6×	0.197%	0.0118
Straight	4×	0.392%	0.0157
Three of a Kind	3×	2.11%	0.0634
Two Pair	2×	4.75%	0.0951
Jacks or Better	1×	21.5%	0.2150
Nothing	0×	54.5%	0

Sum of all E(contribution) values:

Expected Return per $1 Bet

E(Return) ≈ $0.995

House edge ≈ 0.5% with optimal strategy (9/6 Jacks or Better)

In live poker, EV decisions involve pot odds:

Positive EV! You should call.

In poker, expected value thinking is essential: