Expected Value (EV)
Every decision in poker has an average value — how much money it wins or loses when repeated over thousands of trials. This is its Expected Value, or EV:
Example: Pot is 100, opponent bets 50. You call 50 and win 35% of the time. When you win, you gain 150 (pot + opponent bet). When you lose, you lose your 50 call.
You lose nearly two out of three hands, yet making this call nets an average profit of +20 chips every time. Move the sliders in the simulator below to watch short-term luck converge to EV.
Implied Odds
Pot odds only account for chips currently in the middle. But if your draw hits, opponents will frequently call future bets — and those anticipated future chips can turn an otherwise unprofitable call into a +EV play. These are implied odds.
Flop: Pot is 20 bb, opponent bets 5 bb. You hold a gutshot to the nuts (4 outs). Immediate pot odds dictate: 5 / 30 = 16.7% required equity, but one-street hitting probability is only 4 / 47 ≈ 8.5%.
However, opponent has a set with 200 bb in their stack and will pay off on the turn. Solving for required future payoff: $0.085 \times (25 + X) = 0.915 \times 5 \implies X \approx 29\text{ bb}$. If you can extract 29 bb on future streets from a 200 bb stack, calling the flop is +EV.
Implied odds are maximized when: stacks are deep, your draw is disguised, and your opponent has a strong second-best hand.
Reverse Implied Odds
The flip side of implied odds is danger. Sometimes hitting your card wins a modest pot, but losing costs your entire stack: you hit the second-best hand.
- Low flushes on boards where opponents hold higher flushes.
- Pairs with weak kickers against dominating kickers.
- The dummy (low) end of straights.
These draws have reverse implied odds. This explains why dominated holdings like K♠ 7♦ are massive money-losers for beginners.
Minimum Defense Frequency (MDF)
Now view the math from the defender's perspective. An opponent bets 100 into a 100 pot. If they bluff with any two cards, they risk 100 to win 100: their bluff profits automatically if you fold more than 50% of the time.
To prevent pure bluffs from generating automatic profit, you must defend a baseline proportion of your range called the Minimum Defense Frequency (MDF):
- Against 1/2 pot bet: MDF = 67%
- Against full pot bet: MDF = 50%
- Against 1/3 pot bet: MDF = 75%