True count conversion explained

The true count is the running count divided by the number of decks still to be dealt. It converts a raw tally into a per-deck concentration so that the same number means the same thing whether the shoe is fresh or nearly finished. Every betting ramp and every index play for a balanced system like Hi-Lo is expressed in true count, so a counter who cannot convert accurately is working from the wrong numbers.

The formula

True count = running count ÷ decks remaining

Wizard of Odds gives the example of a running count of +7 with about four decks left: 7 ÷ 4 = 1.75, which he rounds to +2. BlackjackInfo uses +6 with three decks left for a true count of +2. Wikipedia defines the true count as the running count divided by the number of undealt decks.

Three things follow directly from the formula:

1. The true count has the same sign as the running count.
2. For a fixed running count, the true count rises as the shoe is dealt down, because the divisor shrinks.
3. Early in a shoe the divisor is large, so the true count rarely moves far from zero. Most of the usable information arrives in the back half of the shoe.

Worked examples

The fourth and sixth rows show how the convention matters. A running count of +7 over four decks is +1 or +2 depending on whether you floor or round, and that is precisely the gap between “bet the minimum” and “raise” on many ramps. The last row shows why deep penetration is valuable: with three-quarters of a deck left, a modest running count of +3 becomes a true count of +4.

Mental arithmetic is easier if you think in half-decks and keep the division approximate. “+9 over about three and a half decks” is “a bit under +3”, and that is usually enough. Precision only matters when you are near a threshold, and then it is worth pausing to do the sum properly.

Estimating decks in the discard tray

You cannot see the undealt cards, but you can see the discard tray. In a six-deck game:

Decks remaining = 6 − decks in the discard tray

Some players also subtract the cards currently on the table, but at table speed this is a refinement; the cards on the felt are at most a fraction of a deck and are about to be in the tray anyway.

To learn tray heights, stack one, two, three and four decks at home and look at them from the angle you will see the tray at a table. Then practise with random stacks and check. Most counters estimate to the nearest half deck in six-deck games and to the nearest quarter deck in single- and double-deck games. A half-deck error at four decks remaining changes a +8 running count from 8 ÷ 4 = +2 to 8 ÷ 3.5 ≈ +2.3 or 8 ÷ 4.5 ≈ +1.8, which rarely changes a decision. The same half-deck error at one deck remaining is enormous: +8 becomes +8, +16 or +5.3. Estimation needs to be sharpest at the end of the shoe, which is also where the big bets are.

If the shoe is behind a cut card and you can see the undealt stack, you can estimate from either end. Use whichever is easier to see from your seat.

Flooring, rounding and half-counts

Published systems differ in how they handle fractions:

• Truncation (floor towards zero): +1.75 becomes +1, −1.75 becomes −1. This is the conservative convention and the one many simulation-derived index tables assume. Norm Wattenberger’s true count analysis notes that his simulations use truncation with half-deck or quarter-deck estimation, and that the estimation method itself changes which true counts occur and how often.
• Rounding to nearest: +1.75 becomes +2. Wizard of Odds uses this in his example.
• Half-count resolution: keep +2.5 as +2.5. More precise, more work, and only useful if your ramp and indices are expressed in halves.

None of these is wrong, but the index numbers and betting ramp you use were generated under one of them, and silently mixing conventions pushes you slightly off the intended thresholds. The Illustrious 18 indices quoted on this site follow the Wizard of Odds presentation; use them with his convention.

Why the true count drives both betting and playing

Betting. The player’s advantage in a balanced count rises roughly in step with the true count, which is why betting ramps are stated in true count rather than running count. A ramp that says “4 units at +3” is a ramp in true count; a running count of +3 with five decks left is a true count of well under +1 and gets the minimum bet. Bet spreads and bankroll covers ramps in detail.

Playing. Index numbers are true-count thresholds at which a basic strategy decision flips. The best known is insurance at a true count of +3 or more in Hi-Lo, and standing on 16 against a 10 at a true count of 0 or more. A running count of +3 alone is not enough to take insurance in a six-deck game; it must be +3 per deck remaining. Using running counts for index plays is a common and expensive beginner error.

Both uses depend on the same number, so the conversion is done once per decision point: before you place a bet, and again at any hand where an index might apply.

How often the true count is actually useful

A fresh six-deck shoe spends most of its life near zero. Wattenberger’s simulations find that a six-deck game shows a true count of zero or lower about 71% of the time, and that the count calls for a raised bet somewhere between 10% and 35% of hands depending on rules, penetration and strategy. The practical consequence is that a counter plays the majority of hands at the table minimum and at a house edge, and earns the overall advantage from the minority of hands where the true count is high. This is also why penetration matters so much: a shoe cut at four decks never reaches the depths where small running counts become large true counts.

Unbalanced counts: skipping the conversion

Systems such as KO and Red 7 are deliberately unbalanced so that a full shoe does not sum to zero. By starting the running count at a negative number chosen for the number of decks, the running count itself approximates the true count at the point that matters for betting. Wattenberger’s analysis contrasts these with balanced systems that require a true count conversion. The trade-off is explored in card counting systems compared. If true count estimation is the part of counting you find hardest, an unbalanced count is a legitimate solution rather than a shortcut.

Related reading

• Hi-Lo card counting tutorial
• Bet spreads and bankroll for counters
• Illustrious 18 index plays
• How a shoe game is dealt