Expected Value: Thinking in the Long Run

Every lesson so far has quietly relied on one idea: some decisions make money over time and some lose money over time, whatever happens in a single hand. That idea is called expected value, or EV. It’s the single most important concept in poker strategy. Once you think in EV, bad beats stop feeling like proof that you played badly, and lucky wins stop fooling you into repeating mistakes.

Key takeaways

• EV is the average result of a decision if you could repeat it many times.
• EV of a call = (your equity × final pot) − the amount you call.
• Folding is the zero point: every other option is compared with it.
• Money already in the pot belongs to the pot, not to you — ignore what you've invested.
• Judge decisions by their EV, not by the result of one hand.

What is expected value?

Expected value is the average amount a decision wins or loses if you made it again and again in the same situation.

A simple example: a friend offers you a bet on a coin flip. Heads, you win 12; tails, you lose 10.

EV = (0.5 × +12) + (0.5 × −10) = 6 − 5 = +1

You’ll lose half the flips, but on average you make +1 per flip. Take this bet as often as you can. That’s exactly how winning poker works: make lots of small +EV decisions, and the results follow over time.

EV of a call

When you’re deciding whether to call a bet, the formula is:

EV(call) = (equity × final pot) − amount to call

where the final pot includes everything: the pot before the bet, your opponent’s bet and your call.

Example. On the river the pot is 100 and your opponent bets 50. You think you win 30% of the time.

EV(call) = 0.30 × 200 − 50 = 60 − 50 = +10

Calling makes money. With 20% equity it would be 0.20 × 200 − 50 = −10, and folding would be better. The break-even point is exactly the required equity from Pot Odds and Outs: 50 ÷ 200 = 25%.

EV of an all-in

Before the flop, you have Q♥ Q♠ and your opponent shows A♦ K♣. You each have 100bb and everything goes in. (We’ll ignore the blinds.)

QQ AK

Queens win about 57% against ace-king. The final pot is 200bb, and you put in 100bb:

EV = 0.57 × 200 − 100 = +14bb

You’ll lose this all-in 43% of the time — often painfully — but every time you take it, you gain about 14bb on average. That’s why a great player can lose a big pot and still be happy with the decision.

Folding is zero

When you fold, you neither win nor lose any more money from that point. That makes folding the natural baseline: every call or raise is either better than zero (+EV) or worse (−EV).

This leads to one of the most important lessons in poker:

Money in the pot isn’t yours

Suppose you raised preflop, bet the flop and bet the turn. Now your opponent makes a big raise on the river and you’re almost sure you’re beaten. It’s tempting to call because you’ve “already put so much in”.

But those chips belong to the pot. The only question is: from here, does calling win more on average than folding? If your equity is below the price you’re being offered, folding is correct — no matter how much you’ve invested. Economists call the mistake the sunk cost fallacy. Poker players call it “pot-committed thinking”, and it costs beginners a fortune.

(The size of the pot does matter — it changes the price you’re getting. What doesn’t matter is who put the money there.)

Results vs decisions

Because poker has luck in the short term, a good decision can lose and a bad one can win. Players who judge themselves on results fall into two traps:

• After a bad beat, they stop making a good play that “never works”.
• After a lucky win, they repeat a bad play because “it worked last time”.

Instead, ask: given what I knew, was the decision +EV? That’s the only thing you control. The results come from making good decisions over thousands of hands — which is also why variance is a whole lesson later in this course.

Quick check

The pot is 60 and your opponent bets 30 on the river. You estimate you win 40% of the time. What is the EV of calling?

−6+6+18+30

Check answer

Final pot = 60 + 30 + 30 = 120. EV = 0.40 × 120 − 30 = 48 − 30 = +6.

Quick check

You've put 80bb into a pot and now face a river all-in. You're sure you're beaten. What should you do?

Call — you're pot-committedFold — the money you've put in doesn't change what calling is worth nowCall if the pot is bigRaise

Check answer

If you're beaten, calling loses more money. Previous bets are sunk: judge the call only on the price and your equity now.

You’ve finished Level 2

You can now choose hands, use position, calculate pot odds, open and 3-bet sensibly, read board texture and think in EV. Take the Level 2 quiz to earn your badge, practise in the trainers, and then start Level 3 by learning to think about your opponent’s whole range: Thinking in Ranges.