Card counting systems compared

Every card counting system assigns a number to each rank and adds them up; they differ in how finely they weight the ranks, whether the ace is counted, and whether the tags sum to zero. More detail buys a little accuracy at the cost of speed and error rate, and in six- and eight-deck games the published differences between the popular systems are small. This page sets the eight best-known systems side by side and explains what the comparison measures mean.

Tag values for eight systems

The tags below are as listed in Wikipedia’s card counting article.

Wong Halves is usually played with every tag doubled (1, 2, 2, 3, 2, 1, 0, −1, −2, −2) to avoid fractions; the proportions are identical.

Structural properties

Level, balance and ace treatment follow directly from the tags. The “sum per deck” column is the arithmetic: each rank has four cards, and 10–K is four ranks (16 cards).

Level is the largest tag magnitude. Level-one systems only ever add or subtract one, which is why they can be run at full table speed by most people after a few weeks of practice.

Balance decides whether a true count conversion is needed. A balanced count returns to zero at the end of every shoe, so the running count must be divided by decks remaining to be meaningful; see true count conversion. KO’s +4 per deck and Red 7’s +2 per deck are designed in: the player starts the running count at a negative offset chosen for the number of decks, and the running count then crosses zero at a point that approximates a useful true count. The cost is a running count that only approximates the true count at one depth (its pivot) and drifts elsewhere.

Ace treatment is the main design trade-off. The ace is the most valuable card for betting purposes because it drives naturals, but for playing decisions it behaves like a small card as often as a large one. Wikipedia summarises the consequence: counting the ace improves betting correlation but reduces playing efficiency. Hi-Opt I, Hi-Opt II and Omega II therefore set the ace to zero and expect serious users to keep a separate side count of aces for bet sizing, which is a second mental tally on top of the main count.

Betting correlation, playing efficiency and insurance correlation

Peter Griffin’s The Theory of Blackjack introduced three correlation measures that are still the standard way to compare systems:

• Betting correlation (BC): how closely the count tracks the player’s actual advantage, which governs when to raise the bet. Wikipedia describes it as a measure of how effectively a system identifies when the undealt cards offer a positive expectation.
• Playing efficiency (PE): how well the count identifies when to deviate from basic strategy. Wikipedia notes that without side counts PE can approach about 70%, and that PE matters most in single- and double-deck games where playing decisions are a larger share of the counter’s gain.
• Insurance correlation (IC): how well the count predicts when insurance is profitable, which is a question purely about the proportion of tens remaining.

Published per-system figures that could be verified for this page:

Both articles are Arnold Snyder’s comparisons republished by Las Vegas Advisor, which describe the method as a simplification of Griffin’s. The missing cells (KO, Hi-Opt I, Omega II and Wong Halves, and all insurance correlations) are not quoted here because no figure for them could be verified against a primary or reference source at the time of writing; secondary websites publish numbers, but they disagree with each other and rarely say which rules or deck count they assume. The general shape is not in dispute: ace-counted systems have higher BC and lower PE; ace-neutral systems the reverse; multi-level systems edge both up; and a system that tags the 10 but not the ace (Hi-Opt I) has the highest IC of its level because insurance depends only on tens.

What simulations show in shoe games

Snyder’s “Battle of the Babies” reproduces two sets of win-rate simulations for the three simplest systems. The figures are percentage win rates under the simulation conditions of each source, not promises for any real game.

Two things stand out. First, the three systems are within a few hundredths of a percent of each other in six- and eight-deck games; the choice of system matters far less than penetration, spread and accuracy. Second, the two sources disagree with each other by more than the systems disagree among themselves, which Snyder attributes to differences in how bets were matched between systems in the Knock-Out Blackjack runs. Treat any single published ranking with that in mind.

Snyder’s own 1981 ranking of a hundred systems put the Zen Count first and Hi-Lo eleventh under single-deck conditions, with the comment that under most conditions the superiority of the top systems is negligible.

When a simpler system is the better choice

Choose the simplest system you can run without error, then spend the saved effort on the things that move the result more:

• You play shoe games. Playing efficiency is worth least in six and eight decks, so a level-two or ace-neutral system gains little. Hi-Lo or KO is the sensible default.
• True count conversion is your weak point. KO or Red 7 removes it for betting. You lose some precision at depths away from the pivot, but you lose far more from botched division.
• You play single or double deck. Playing decisions matter more and the deck estimate is easier, so Hi-Opt II or Zen with an ace side count can justify itself for a disciplined player.
• You already count Hi-Lo at casino speed. Moving up a level is a marginal improvement; learning more index plays, finding deeper penetration and sizing the bet spread properly are not.

Whatever the system, the counter’s overall advantage in a multi-deck game is small. Wikipedia puts a typical six-deck counter at roughly 1% over the house, and that assumes good rules, deep penetration, a wide spread and no mistakes. A system that is 2% more efficient on paper but 20% slower at the table is a worse system.

Related reading

• Hi-Lo card counting tutorial
• True count conversion
• Card counting overview
• Deck count: single versus multi-deck