EV and the house edge, in plain English
What a decision is worth on average, and what the game costs.
Any single hand is luck. But every decision has an expected value: the average amount it wins or loses, over all the ways the remaining cards could fall. EV is how we compare decisions fairly, without being fooled by how one hand happened to turn out.
In UTH it's easiest to measure EV in Ante units. "+1.172 antes" means that on average this decision wins 1.172 times your Ante over the whole hand (Ante, Blind and Play together). At a $10 Ante that's +$11.72. At $25 it's +$29.30. The ranking of the choices doesn't change with your bet size.
Two examples from the first decision of a hand:
| Hand | Bet 4x | Check | Best |
|---|---|---|---|
| ace-king offsuit | +1.172 antes (+$11.72 at $10) | +0.569 antes | Bet 4x, by 0.60 antes |
| seven-deuce offsuit | −2.118 antes | −0.883 antes | Check, by 1.23 antes |
Notice that checking 7-2 still has a negative EV. Some hands lose money however you play them. You paid your Ante and Blind before you saw your cards. Good play is about losing as little as possible with bad hands and winning as much as possible with good ones.
The house edge. Average the EV of perfect play over every possible hand and you get the price of the game: −0.02185 antes per hand, a house edge of 2.185% of the Ante. At a $10 Ante that's an expected cost of about 22¢ a hand. No strategy does better. Every decision this course teaches is part of reaching that 2.19%.
Here's what decisions are worth. If you never raised early and always bet 1x at the river, never folding, you'd lose 40.7% of your Ante per hand. That's almost twenty times more. The Ante and the Blind are built to lose if you just ride them to showdown. Your raises with strong hands, and your folds with hopeless ones, win nearly all of it back.
Show the math: Where the 40.7% comes from
If you always bet 1x at the river, the Play bet is a pure coin flip. You win and lose equally often (47.97% each), so its EV is exactly 0. Look at the other two bets:
- Ante: it's paid only when the dealer qualifies, but it is lost whenever a qualifying dealer beats you. It wins 33.73% and loses 45.21% of the time: EV = −1330653811/11589087510 ≈ −0.1148 antes.
- Blind: it pays only on a straight or better, but it loses every hand you lose: EV ≈ −0.2922 antes.
Total: −6432686411/15803301150 ≈ −0.4070 antes per hand.
Under perfect play the EV is −50643648973/2317817502000 ≈ −0.021850 antes. These are exact enumerations over every deal.
Quiz
Your Ante is $20. An option shows +0.50 antes. What is its EV in dollars?
- +$0.50
- +$5
- +$10
- +$20
Show the answer
C: +$10. 0.50 × $20 = $10. Ante units scale with your bet.
Quiz
What is the house edge of UTH under perfect play?
- About 0.5% of the Ante
- About 2.19% of the Ante
- About 5% of the Ante
- Zero with perfect play
Show the answer
B: About 2.19% of the Ante. 2.185% of the Ante per hand. Nothing beats it, and Trips is extra.
Quiz
You played a hand perfectly and lost $60. Was it a bad decision?
- Yes, you lost
- Not necessarily: EV is about the average, not one result
- Yes, you should have folded
- Only if the dealer qualified
Show the answer
B: Not necessarily: EV is about the average, not one result. Good decisions lose sometimes. EV measures the average over all the ways the cards could fall.