for nerds / expected value
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Expected value

8 steps · read as text
outcomes
win +$100 · 25%lose −$20 · 75%
math
0.25 × $100 − 0.75 × $20 = +$10fold always earns $0
100 hands
running total
after 0 hands: +$0per hand —
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You can pay $20 to play for a $100 pot. You’ll win about one time in four.

the rule

EV = sum of (chance × result) over every outcome

0.25 × 100 − 0.75 × 20 = +10

Work out the EV of each option. Choose the highest.

connection

Set EV to zero and solve for the win rate: you get cost ÷ (pot + cost). That’s pot odds again.

20 ÷ (100 + 20) = 16.7%

next
01Pot odds & equity03Combinatorics→Practice: pot odds
sources & further reading
The Mathematics of PokerBill Chen, Jerrod Ankenman · 2006 · book
The Theory of PokerDavid Sklansky · 1987 · book
Thinking in BetsAnnie Duke · 2018 · book