Society & Culture & Entertainment Games

Poker Mathematics - Part 3 - Calculating EV (The Basics)

Expected Value (EV) describes the average amount of chips/($) won or lost by that strategy (any actions or series of actions).
The normal goal is to always choose the strategy with the highest EV.
EV requires 3 elements:
  1. How often you win the money in the pot
  2. How often you win your opponent(s) bet(s)
  3. How often you lose your bet(s)
* This is YOUR EQUITY (note: Hot/Cold equity only refers to 'everyone all-in' scenarios) The standard formula is: EV = ($ won from pot) + ($ won from bets) - ($ lost from bets) Example: A $10 bet made by you $20 pot Opponent folds 40% Opponent calls 50%..
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you expect to win 70% and lose 30% Opponent raises 10% x $50..
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you expect to win 35% and lose 65% ($ won from pot) Calculate how often the pot will be won (win %) and the value of the win % (win $) Pot win % = 0.
40 + (0.
50*0.
70) + (0.
10*0.
35) = 0.
785 or 78.
5% Pot win $ = $20 x 0.
785 = $15.
70 Therefore ($ won from pot) is $15.
70 ($ won from bets) Identify how often, on average, you WIN the pot when the opponent(s) put various amounts of money into the pot ($ x % chance of call or raise x % equity for each event): Opponent Calls = $10 x 50% x 70% = $3.
50 Opponent Raises = $50 x 10% x 35% = $1.
75 Therefore ($ won from bets) is $5.
25 ($3.
50 + $1.
75) ($ lost from bets) Identify how often, on average, you LOSE the pot when the opponent(s) put various amounts of money into the pot ($ x % chance of call or raise x % NO equity for each event): Opponent Calls = $10 x 50% x 30% = $1.
50 Opponent Raises = $50 x 10% x 65% = $3.
25 Therefore ($ lost from bets) is $4.
75 ($1.
50 + $3.
25) (Total EV $ Value) Add the results together: EV = $15.
70 + $5.
25 - $4.
75 = $16.
20 No Folding If the EV strategy comparison does not involve anyone folding, ignore ($ won from pot) and the formula becomes: EV = $ won from bets - $ lost from bets Shortcut A shortcut for ($ lost from bets) is to subtract the ($ won from bets) value from the total value of the bet you are going to make.
If we use the figures in the example above: $10 - $5.
25 = $4.
75

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