House edge, element of risk and cost per hour
Three honest numbers for the same game, and the one that pays your bills.
You'll see three different numbers quoted for UTH's house edge. They all describe the same game; they just divide the same expected loss by different things.
| Name | Divides the expected loss by | Perfect play |
|---|---|---|
| House edge per Ante | your Ante | 2.185% |
| Edge per initial wager | your Ante + Blind | 1.092% |
| Element of risk | everything you put in action, raises included (4.15 antes on average) | 0.526% |
The 2.185% and 0.526% figures are computed exactly by the app and agree with the Wizard of Odds analysis; the Treasury Brisbane gaming guide quotes about 2.18% and 0.53%.
The app uses per Ante as its headline number, because it turns straight into money. Your expected cost per hand is 2.185% of your Ante, whatever happens with the raises. Element of risk is the fairer way to compare UTH with a game like blackjack, where most of the money you bet is the money you start with. In UTH you add a raise on most hands, so per dollar in action the edge is a quarter as big.
Cost per hour is what actually leaves your pocket:
cost per hour = hands per hour × Ante × edge per Ante
At the app's default of 30 hands an hour:
| Ante | Perfect play | Basic card (lesson 16) |
|---|---|---|
| $5 | $3.28 / hour | $3.57 / hour |
| $10 | $6.55 / hour | $7.14 / hour |
| $25 | $16.39 / hour | $17.86 / hour |
Real tables run anywhere from about 20 to 40 hands an hour, depending on how many players there are and how fast the dealer is. Change it in Settings → Hands per hour, and every per-hour figure on the EV sheet, in Drill and in auto-play scales with it.
Show the math: Exact definitions
Expected loss per hand (perfect) L = 50643648973/2317817502000 antes.
- Per Ante: L / 1 ≈ 2.1850%.
- Per initial wager: L / 2 ≈ 1.0925%.
- Element of risk: L / E[total wagered], with E[total wagered] = 2 + 4·P(4x) + 2·P(2x) + 1·P(1x) = 29163830173/7023689400 ≈ 4.1522 antes, so EoR = 50643648973/9624063957090 ≈ 0.5262%.
A folded hand counts as 2 antes wagered.
Quiz
Which number is the expected cost per hand as a share of your Ante, under perfect play?
- 0.53%
- 1.09%
- 2.19%
- 4.15%
Show the answer
C: 2.19%. 2.185% of the Ante. 0.53% is per dollar in action, and 4.15 is the average antes in action per hand.
Quiz
$10 Ante, 30 hands an hour, perfect play. Expected cost per hour?
- About $0.66
- About $1.60
- About $6.55
- About $12.45
Show the answer
C: About $6.55. 30 × $10 × 2.185% ≈ $6.55.
Quiz
Why is the element of risk smaller than the house edge per Ante?
- It ignores losing hands
- It divides by all the money in action, raises included
- It only counts the Blind
- It assumes you never fold
Show the answer
B: It divides by all the money in action, raises included. Same expected loss, divided by about 4.15 antes instead of 1.