Balanced and Unbalanced Counts, and What the Difference Costs
Updated
A balanced system counts a full shoe down to exactly zero, so you must divide by the decks remaining to get a usable number. An unbalanced one does not, so you skip the division entirely. That is the whole distinction — and the cost of the shortcut is smaller than people expect.
- Balanced (Hi-Lo, Zen, Omega II, Wong Halves): shoe counts to zero, divide for the true count.
- Unbalanced (KO, Red 7): no division, act on the running count.
- KO’s betting correlation is 0.970 — higher than Hi-Lo’s 0.963.
- The convenience costs almost nothing. Precision at the table matters more.
What a counting system is actually approximating
Every card that leaves the shoe changes your edge by a specific amount. We computed that amount for each rank by removing one card and recalculating the entire game:
| Card removed | Effect on your edge |
|---|---|
| Ace | -0.0952% |
| 2 | +0.0637% |
| 3 | +0.0731% |
| 4 | +0.0975% |
| 5 | +0.1243% |
| 6 | +0.0731% |
| 7 | +0.0454% |
| 8 | -0.0027% |
| 9 | -0.0330% |
| 10, J, Q, K | -0.0830% |
A counting system is a rounding of that table into whole numbers you can add in your head. Hi-Lo rounds it to +1, 0 and −1. Level-two systems use a finer grid. How well the rounding matches the real numbers is the betting correlation.
Where the balance comes in
Hi-Lo has twenty cards worth +1 and twenty worth −1 per deck, so a full shoe counts to zero. That balance is what makes the division work: a running count of +6 with three decks left is genuinely +2 per deck.
KO adds the seven to the plus side, so a deck counts to +4 rather than zero. You cannot divide a number with a built-in drift, so instead you start the count at a negative number that depends on the deck count and watch for a fixed trigger.
What the shortcut costs
Less than nothing on betting: KO’s correlation is 0.970 against Hi-Lo’s 0.963. The unbalanced version tracks betting slightly better, not worse.
Where unbalanced systems genuinely lose ground is playing decisions: without a true count you cannot apply index numbers precisely, so the deviations in brief get cruder. For most players that is a small loss and the division was the bigger risk.
How these numbers were produced
For each card rank, we removed one card from a six-deck shoe and recomputed the house edge across every possible player hand and dealer upcard. The difference is that card’s effect of removal.
Betting correlation is then the correlation between a system’s tags and those effects, weighted by how often each rank appears. Our figures reproduce the published correlations for all eight systems to two decimal places, which is the check that the method is sound. More on how we compute.
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By Martin Kosek · every number on this site is computed by us, not copied.
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