Introduction
The probability index (running count) tells you how many more low cards than high cards have been dealt. But is a running count of +6 equally significant when there are 5 decks remaining versus 1 deck remaining? Clearly not.
The adjusted probability — commonly called the true count — normalizes the running count by the number of decks remaining. This gives you a per-deck measure of the deck’s composition shift, which is far more useful for making decisions.
The Formula
The calculation is straightforward:
True Count = Running Count / Decks Remaining
For example:
- Running count of +6 with 2 decks remaining → True count = +3
- Running count of +6 with 6 decks remaining → True count = +1
- Running count of +3 with 1 deck remaining → True count = +3
The same running count of +6 means very different things depending on how many cards are left in the shoe.
Why Adjustment Matters
Consider a shoe with a running count of +10. Sounds impressive. But context matters:
| Running Count | Decks Remaining | True Count | Interpretation |
|---|---|---|---|
| +10 | 1 | +10 | Extreme advantage — very rare |
| +10 | 2 | +5 | Strong advantage |
| +10 | 5 | +2 | Mild advantage |
| +10 | 8 | +1.25 | Barely above neutral |
A running count of +10 spread across 8 remaining decks means only slightly more low cards per deck have been dealt than high cards. The probability shift is minimal. But concentrate that same +10 into a single remaining deck, and the composition is drastically altered.
Estimating Remaining Decks
To calculate the true count in practice, you need to estimate how many decks remain in the shoe. This is covered in depth in the deck estimation article, but here’s the quick version:
- Watch the discard tray. The height of the discard pile tells you how many decks have been dealt.
- Subtract from total. If the shoe started with 6 decks and about 2 decks are in the discard tray, approximately 4 remain.
- Round to halves. You don’t need exact precision — estimating to the nearest half-deck is sufficient.
Worked Examples
Example 1: Early in the Shoe
- 6-deck shoe, about 1 deck dealt
- Running count: +4
- Decks remaining: ~5
- True count: +4 / 5 = +0.8 ≈ +1
- Interpretation: Essentially neutral. The count hasn’t concentrated enough yet.
Example 2: Mid-Shoe
- 6-deck shoe, about 3 decks dealt
- Running count: +6
- Decks remaining: ~3
- True count: +6 / 3 = +2
- Interpretation: Moderate advantage. The remaining cards are noticeably high-card rich.
Example 3: Deep in the Shoe
- 6-deck shoe, about 5 decks dealt (approaching the cut card)
- Running count: +4
- Decks remaining: ~1
- True count: +4 / 1 = +4
- Interpretation: Strong advantage. Even a modest running count becomes significant with few cards left.
True Count and Statistical Edge
The true count correlates directly with the player’s statistical edge. As a rough guideline:
| True Count | Approximate Edge Shift |
|---|---|
| 0 | House edge (~0.5% with basic strategy) |
| +1 | Roughly break-even |
| +2 | ~+0.5% player edge |
| +3 | ~+1.0% player edge |
| +4 | ~+1.5% player edge |
| +5 | ~+2.0% player edge |
These numbers vary by specific rules, penetration, and other factors. But the relationship is approximately linear: each +1 true count adds roughly 0.5% to the player’s edge.
Handling Negative True Counts
The same logic applies in reverse:
- True count of -2 means the remaining deck is rich in low cards
- The house edge increases beyond its base level
- This is useful information: it tells you the current conditions are unfavorable
Mental Math Tips
Dividing by 2 or 4 is easy. Dividing by 3 or 5 is harder. Some tips:
- Divide by 2: Half the running count. RC +7 → TC ≈ +3.5
- Divide by 3: Think in thirds. RC +9 → TC = +3. RC +7 → TC ≈ +2.3
- Divide by 4: Half, then half again. RC +10 → +5 → +2.5
- Divide by 5: Divide by 10, then double. RC +8 → +0.8 → +1.6
Don’t worry about decimal precision. Rounding to the nearest integer is good enough for practical use.
Key Takeaways
- The true count adjusts the running count for the number of decks remaining
- True Count = Running Count / Decks Remaining
- A high running count deep in the shoe is worth much more than the same count early
- Each +1 true count shifts the edge by roughly 0.5% in the player’s favor
- Estimating remaining decks to the nearest half-deck is sufficient
- The true count is what drives both betting and playing decisions
Next Steps
Now that you understand the true count, learn how to use it for bet sizing — the strategy for adjusting your wagers based on your statistical edge. Practice with the True Count drill in 21 Sharp.