Swings, sessions and bankroll
What a normal hour looks like, and how much to bring.
A 2.19% edge is tiny next to the swings. In one hand you can win 6 antes or lose 6, and rarely win hundreds (a royal flush pays 500 to 1 on the Blind). The standard deviation of one hand is about 4.94 antes. Over an hour of 30 hands it's about 27 antes, while the expected loss is only 0.66 antes. In the short run, luck is about 40 times bigger than the edge.
Here's what an hour looks like with the basic card (≈ 1 million simulated hours of 30 hands, results in antes):
| Worst 10% of hours | Bottom quarter | Middle (median) | Top quarter | Best 10% |
|---|---|---|---|---|
| −29.5 or worse | −16 or worse | −1.5 | +13.5 or better | +27.5 or better |
About 52% of hours are losing hours, and 48% are winning ones.
How much to bring. "Busting" here means dropping below 6 antes, when you can no longer cover a full 4x hand. Chances of busting (≈ simulated, basic card, 30 hands an hour):
| Bankroll | Bust within 1 hour | Bust within 3 hours |
|---|---|---|
| 20 antes ($200 at $10) | 48% | 70% |
| 30 antes | 25% | 52% |
| 40 antes | 11% | 37% |
| 60 antes | 1.1% | 16% |
| 80 antes | 0.05% | 5.5% |
| 100 antes ($1,000 at $10) | ≈ 0% | 1.4% |
A good rule of thumb: 60 antes for an hour, 100 antes for an evening. If that's more than you want to risk, play a smaller Ante. Halving the Ante halves the cost and the swings.
Session rules that help:
- Set the bankroll before you sit down, and treat it as spent.
- Pick a time limit. The expected cost grows with every hand.
- A win goal ("stop if I'm up 30 antes") doesn't change your EV, but it lets good nights end as good nights.
Show the math: Where the swing figures come from
The standard deviation per hand under perfect play is exact: √24.3967 ≈ 4.94 antes (basic card: 4.94 too). An hour of 30 independent hands has SD ≈ 4.94 × √30 ≈ 27.1 antes.
The percentiles and bust rates are simulated (30 million hands for the hour table, 200,000 sessions per bankroll), so they're approximate. Real results are lumpy: about a third of the variance comes from rare Blind bonuses such as royal flushes.
Quiz
What's the standard deviation of one hand of UTH, in antes?
- About 0.5
- About 2
- About 5
- About 27
Show the answer
C: About 5. About 4.94 antes per hand; about 27 per 30-hand hour.
Quiz
You play an hour at $10 with the basic card. Which result is most typical?
- Exactly −$6.55
- Somewhere between about −$300 and +$280
- Always a small loss
- Always a small win
Show the answer
B: Somewhere between about −$300 and +$280. The expected loss is $6.55, but 80% of hours land between about −30 and +28 antes.
Quiz
Which bankroll gives about a 1-in-100 chance of busting within an hour at a $10 Ante?
- $200
- $400
- $600
- $100
Show the answer
C: $600. 60 antes: about 1.1% within an hour (simulated).