Learn / True Count vs Exact Composition
True Count summarises the shoe in one number. The exact composition keeps every rank.
Both describe the cards that remain. A count compresses them into a single figure; the
composition records how many cards of each rank are left.
How the Hi-Lo True Count is formed
Tag the cards, add the tags, divide by the decks remaining.
Hi-Lo is a widely used counting system. Each card seen changes a Running Count; the True
Count scales that number to the size of the shoe that is left.
Tags
+1, 0 or −1
2, 3, 4, 5 and 6 count +1. 7, 8 and 9 count 0. 10, J, Q, K and A count −1.
Running Count
The Sum of the Tags
The tags of every card seen since the shuffle are added together.
True Count
Per Deck Remaining
The Running Count divided by the number of decks still in the shoe.
156 cards left
→
156 ÷ 52 = 3 decks remaining
Running Count +6
→
True Count = +6 ÷ 3 = +2
OOB derives the number of decks remaining from the exact number of cards left rather than
from an estimate, and shows the True Count as a reference metric.
What the count keeps — and what it leaves out
One number cannot hold ten rank counts.
The True Count measures the overall balance between low cards and high cards, scaled to
the remaining shoe. To fit into one number, it treats many different shoes as equal.
Keeps
The Low/High Balance
Whether more low cards (2–6) or more high cards (10s and aces) have left the shoe, per deck remaining.
Merges
All Low Ranks Alike
Removing a 2 or a 6 changes the count by the same amount, although the two ranks affect hands differently.
Ignores
7, 8 and 9
Their removal does not change the Running Count. It reduces the cards remaining, so the True Count can still change.
Combines
Tens and Aces
Tens and aces share one tag, although they play different roles in blackjacks, soft hands and doubles.
Before
→
Running Count +6, 156 cards left: +6 ÷ 3 = +2
After 26 cards of 7, 8, 9
→
Running Count still +6, 130 cards left (2.5 decks): +6 ÷ 2.5 = +2.4
What the exact composition keeps
The remaining number of every rank: ten numbers instead of one.
OOB records how many cards of each rank — A, 2, 3, 4, 5, 6, 7, 8, 9 and 10/J/Q/K —
are left after every exposed card. For a uniform draw from that composition, before any
further conditioning, the probability of a rank being the next card is its remaining count
divided by the cards remaining (the ratio shown in the
Methodology). It is not a
universal formula once more is known — for example, after a dealer peek has shown that
the hole card does not complete a blackjack.
409 cards left
→
a rank with 31 cards left: 31 ÷ 409 ≈ 7.6% chance of being the next card, for a uniform draw
Same total
→
a rank with 25 cards left: 25 ÷ 409 ≈ 6.1%
Two shoes with the same True Count can hold different numbers of a given rank, and so
different next-card probabilities.
A published example
Same True Count. Different shoe. Different highest-EV action.
The published pair shares the same rules, player hand, dealer upcard, Running Count (+3)
and cards remaining (409), so the True Count is identical: 156/409 ≈ +0.38. The
remaining compositions differ, and OOB selects Stand in one state and Hit in the other.
What the pair does and does not show.
It shows that a count can leave out information that changes a decision. It does not
show how often decisions differ, does not measure an average improvement, and does not
show that counting is useless. The margins in the pair are small, and every available
action EV in both states is negative.