The Expected Value

In the short and medium term, the luck factor influences the results. It is interesting to minimize the luck factor whenever possible. The Expected Value (EV) reduces it.

  • For all pots without showdown, luck is not measurable. The hand's EV equals the hand's net gain.
  • For all pots with showdown before the river, the players' private cards are known, therefore their odds of winning. One considers that the hand stops and that the pot is split according to each player's odds of winning.

Example :

  • Player 1 owns As Qs and 6 $ at the hand's beginning 
  • Player2 owns Ks Kd and 5,25 $ at the hand's beginning
  • The board is Ts 8s 2d
  • Player1 is all-in and player 2 calls
  • The pot is 10 $. The rake is 0,50 $
  • Player1 has 44,1 % chance of winning, one considers he wins 4,41 $
  • Player2 has 55,9 % chance of winning, one considers he wins 5,59 $
  • In the end player 2 wins the hand :
    • Net of player 1 is -5,25 $ (0 $ won for 5,25 invested)
    • Net EV of player1 is -0,84 euro (4,41 $ in theory won for 5,25 invested)
    • Net of player2 is 4,75 (10 $ won for 5,25 invested)
    • Net EV of player2 is +0,34 euro (5,59 $ in theory won for 5,25 invested)

A session's net EV is the sum of its hands' net Ev.

The difference between EV and net Ev is called Diff. Ev, and reflects luck and bad luck.