Edge per bet vs edge per roll, and the cost of an hour
Chapter 4: The math that matters · Lesson 14 of 21 · 6 min read
Why a one-roll bet that "only" costs 5.56% is far more expensive per hour than a Pass Line bet.
So far, every house edge has been per bet resolved: what you lose on average each time a bet finally wins or loses. But bets take different amounts of time. A Field bet is over in one roll. A Pass bet lasts about 3.4 rolls on average. A Place 4 waits until a 4 or a 7 shows, about 4 rolls.
If you leave a bet up all session, what you actually pay depends on how many decisions it has. That's the per-roll edge: the average loss per roll, per dollar on the table. Wizard of Odds and John Grochowski both publish this per-roll comparison.
| Bet | Edge per bet | Edge per roll |
|---|---|---|
| Pass / Come | 1.41% | 0.42% |
| Don't Pass / Don't Come | 1.36% | 0.40% |
| Odds (either side) | 0% | 0% |
| Place 6/8 | 1.52% | 0.46% |
| Buy 4/10 or Lay 4/10 | 1.67% | 0.42% |
| Place 5/9 | 4.00% | 1.11% |
| Place 4/10 | 6.67% | 1.67% |
| Hardways (any) | 9.09–11.11% | 2.78% |
| Big 6/8 | 9.09% | 2.78% |
| Field | 5.56% | 5.56% |
| Any 7 | 16.67% | 16.67% |
Two surprises. Place 6/8 is nearly as cheap per roll as the Pass Line. And every one-roll bet keeps its full edge per roll, so a Field bet costs more than 13 times as much per roll as a Pass bet of the same size.
The cost of an hour. A typical table runs about 100 rolls an hour: a quiet one more, a crowded one fewer. You can change the pace in Settings, and every per-hour figure in the simulator scales with it. Expected cost ≈ bet × per-roll edge × rolls the bet is working:
| Your play (about 100 rolls/hour) | Expected cost per hour |
|---|---|
| $10 Pass Line, every round | $4.19 |
| $10 Pass Line + max odds | $4.19, the same: odds cost nothing |
| $10 Don't Pass + 6× lay odds | $4.04 |
| $6 Place 6 + $6 Place 8 (off on come-outs) | $3.91 |
| $5 Field, every roll | $27.78 |
| $1 Any 7, every roll | $16.67 |
| $4 Horn, every roll | $50.00 |
Don't Pass with full lay odds is only $0.15 an hour cheaper than Pass with full odds ($4.19 vs $4.04). A $5 Field bettor pays almost 7× what a $10 Pass Line bettor pays, while betting half as much.
Show the math: Per-roll edge and hourly cost
Average rolls per Pass decision: 1 + Σ P(point) × 1/P(point or 7 per roll) = 557/165 ≈ 3.376. Per-roll edge = 1.414% ÷ 3.376 = 0.419%. Place 6: it resolves on any 6 or 7, 11/36 of rolls. Per-roll edge = (1/66) × (11/36) = 0.463%. Place 4: (1/15) × (9/36) = 1.667%. Hard 8: (1/11) × (11/36) = 1/36 = 2.778%; Hard 4: (1/9) × (9/36) = 1/36 too. Share of rolls that are in the point phase: 1 − 165/557 = 392/557 ≈ 70.4%. Bets that are off on come-outs only work on those rolls. $10 Pass, 100 rolls: 100/3.376 ≈ 29.6 decisions × $10 × 1.414% = $4.19. Place 6 + 8: $12 × 0.463% × 70.4 = $3.91. Field: $5 × 5.556% × 100 = $27.78. Don't Pass: $10 × 0.404% × 100 = $4.04; the gap to Pass is $4.19 − $4.04 = $0.15.
Pass vs Field, one hour
Interactive practice table. Try this in the app (free, play money).
Per roll in action, which bet has the lower edge?
- Pass Line (0.42%)
- Place 6 (0.46%)
- Field (5.56%)
- Hard 6 (2.78%)
Show answer
A: Pass Line (0.42%). Pass is the cheapest per roll, with Place 6 very close behind. One-roll bets and hardways are far more expensive.
Roughly what does $10 Pass + max odds cost per 100 rolls?
- $0
- $4
- $14
- $40
Show answer
B: $4. About $4.19, exactly what $10 Pass alone costs. Odds add swings, not cost.
Why does the Field cost so much per hour?
- It has the highest edge on the table
- It's decided on every roll, so its 5.56% edge is paid every roll
- Dealers charge a fee
- It loses on 7
Show answer
B: It's decided on every roll, so its 5.56% edge is paid every roll. One-roll bets pay their full edge each roll; multi-roll bets spread it over several.