How common are long streaks, really
“I waited all night for an eight-banker run.” Most of the rarity in that sentence comes from a miscounted denominator.
The answer first
A shoe holds about 74 decided hands (60,000 simulated shoes with full drawing rules: 82 hands per shoe, 9.5% of them ties). Across those 74 hands, the chance of seeing at least one run of length k:
| Run length | At least once per shoe | Roughly |
|---|---|---|
| 4 | 99.8% | every shoe |
| 5 | 92.6% | almost every shoe |
| 6 | 69.9% | every 1.4 shoes |
| 7 | 43.4% | every 2.3 shoes |
| 8 | 24.0% | every 4.2 shoes |
| 9 | 12.5% | every 8 shoes |
| 10 | 6.3% | every 16 shoes |
| 11 | 3.2% | every 32 shoes |
| 12 | 1.6% | every 64 shoes |
At 60–70 hands an hour, a run of eight turns up about every five hours. It is not an event worth recording.
Why intuition misses by so much
Intuition computes this: eight Bankers in a row is 0.5068⁸ ≈ 0.44%. One in 227. That does sound rare.
But that is the chance of “starting from this hand, the next eight are all Banker.” That is not how you watch a table. You scan every starting point in the shoe. Seventy-four hands give 67 possible starts, and both sides count — well over a hundred times more chances.
This is multiple comparisons: the more chances you look at simultaneously, the higher the odds of seeing an extreme one. Everyone falls for it, and it is the main engine behind “tonight was unusually lucky/strange.”
How the numbers were produced
Exact recursion, not a simulation estimate.
Track the state “current run length r, current side,” step forward 74 hands, and accumulate all the probability mass where no run of length k has yet occurred. Then subtract from one:
P(at least one run of k) = 1 − P(never reaches k in 74 hands)Recursion is exact — no sampling error. To confirm the implementation is right, we also simulated 60,000 shoes with the full drawing rules and recorded the longest run in each:
| Run length | 60,000 shoes | Exact recursion | Diff |
|---|---|---|---|
| 5 | 92.70% | 92.64% | +0.06 |
| 6 | 70.12% | 69.88% | +0.24 |
| 7 | 43.43% | 43.39% | +0.04 |
| 8 | 24.08% | 24.00% | +0.08 |
| 9 | 12.73% | 12.51% | +0.22 |
| 10 | 6.42% | 6.34% | +0.08 |
| 12 | 1.57% | 1.57% | −0.00 |
Everything lands inside 0.25 percentage points — the sampling noise of the simulation itself. Two entirely different methods, one answer.
A widespread wrong denominator
A lot of writing puts a shoe at 60 hands, which systematically understates runs:
- Run of 6: 61.7% at n=60 versus 69.9% at n=74
- Run of 8: 19.6% at n=60 versus 24.0% at n=74
Four points does not sound like much, but it turns “one shoe in 4.2” into “one shoe in 5.1.” Manufactured rarity accumulates exactly like this.
And after eight in a row?
The next hand is still Banker 45.86%, Player 44.62%, Tie 9.52%.
Not “due to break,” not “the dragon continues.” The cards were shuffled; what came before is not transmitted to the next card in any form. This is not our position; it is the definition of the game.
You can enter any road into the road-reading engine on the home page and watch it compute how often that shape appears in random play — and watch the three numbers for the next hand refuse to move.
Read next: The real probabilities and the house edge · Why staking plans cannot work · How to read baccarat roads · The third card rule
FAQ
How rare is a run of eight?
Not rare. The chance of at least one run of 8 inside a single shoe is 24% — roughly one shoe in four.
Is a long streak more likely to break?
No. After the shuffle each hand is independent. However long the run, the next hand is still Banker 45.86%. There is no exception to this.
Then why do long runs feel so rare?
What feels rare is a specific run at a specific spot. What you are actually doing is scanning all 74 decided hands of a shoe at once, which is dozens of times more chances.