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.

The short version
Every figure here is computed with our own solver and checked against an independent reference. The calculator applies the same numbers to your table.

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 removedEffect 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.

Ace -0.0952% 5 +0.1243% 10, J, Q, K -0.0830% 8 -0.0027%
This is what a counting system is trying to approximate. The five is the most valuable card to see leave; the eight barely matters.

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.

Keep reading

The KO countthe unbalanced standard Which to pickthe honest comparison The true countwhat balanced systems need

By Martin Kosek · every number on this site is computed by us, not copied.

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