Card Counting in Blackjack

Hi-Lo is a widely taught count because every card is worth one of three values. Each card seen, in any hand at the table, is added as it appears. A full deck holds twenty low cards and twenty high ones, so counting a whole deck through always ends at zero.

The running count is the plain sum of the tags since the last shuffle. On its own it is misleading in a shoe game, because the same surplus of high cards means much more when few cards are left than when many are. Six extra high cards spread over five remaining decks hardly change the mix, while the same six in the last deck change it a great deal.

The true count corrects for that by dividing the running count by the number of decks still to be dealt. A running count of +6 with three decks left is a true count of +2. The same +6 with two decks left is +3, and with six decks left it is +1. Decks remaining are judged by eye, from the height of the stack in the discard tray, and rounding to the nearest half deck is close enough.

The rule: Bets and decisions follow the true count, not the running count: the running count divided by the decks still to come is the figure the tables on this page are read against.

This is the effect of removal: one card of the rank is taken out of a single deck, every other rule stays at the reference game's, and the player's expected result is measured again. A positive figure means the player gains when that card is gone. Figures are in percentage points of the starting wager.

The dealer must draw to every total from 12 to 16, and a small card is exactly what turns such a hand into a 17 or better instead of a bust. The player, who may stand on those totals, needs them far less. Take small cards out and the dealer busts more often. Take tens and aces out and the player loses three things at once: fewer blackjacks paid at 3:2 while the dealer's are paid only at even money, fewer doubles that land on a ten, and fewer dealer busts.

The removal figures show where Hi-Lo simplifies. The 5 is the most valuable card to see leave, followed by the 4, while the 2 is worth well under the 5 yet gets the same tag. The 7 helps the player when removed and the 9 hurts, but both count as zero, and the ace is worth more than any single ten. Counts that weight cards more finely follow the table more closely and are harder to keep. Hi-Lo trades a little accuracy for a tally that can be kept at speed, and because there are four ten-value ranks for every other rank, the tens carry most of its signal.

A six-deck shoe with two decks dealt and four left, the remaining cards tilted to match each true count, the reference rules otherwise, and perfect play for the cards that remain. At a true count of zero the four decks left play like a freshly shuffled four-deck game. Each step up the count moves the main game about 0.51 percentage points toward the player.

The count earns nothing on its own. A counter gains only by betting more when the true count is high and less, or nothing, when it is low, so the large bets land on the hands where the player is ahead. At a flat bet the rounds dealt at good counts and at bad ones roughly cancel, and the result drifts back toward the ordinary house edge.

Insurance is where the count changes a decision most clearly. Because it pays 2:1, it comes out ahead only once tens make up more than one card in three of those still unseen. In the shoe described above it still costs the player 0.29% at a true count of +3, and at +4 it turns, leaving the player ahead by 2.03%. Below that point it should be refused like any other side wager; what it costs when nobody keeps a count, deck by deck, is shown on the blackjack insurance page. A few chart plays shift at high or low counts as well, and they are worth learning only once the tags and the true count come without effort.

Counting needs cards to leave the shoe and stay out. An online table run by a random number generator deals every hand from a full, freshly shuffled set of decks, so the count is zero at the start of every round and the edge is always the off-the-top figure, 0.41% for the reference game. That is how every free blackjack demo in our library deals, which makes the demos useful for learning the tags and practicing basic strategy but not for testing a count.

A continuous shuffling machine does the same thing in a physical casino: the discards go back into the machine after each round, so no depletion ever builds up. Live tables dealt from a real shoe can be counted in principle, but many reshuffle after only part of the shoe, and the count seldom reaches the higher rows of the table above before the cards go back in.

The key point: On a random number generator, a continuous shuffler or a game that reshuffles early, keeping a count changes nothing, and the edge is the same on every hand.

Keeping a mental tally of the cards is a use of information every player at the table can see, and it is not cheating. Using a device or outside help to track cards is a different matter, and it is against the law in many places. A casino, however, is a private business and sets its own terms of play. It may limit a player's bets, shuffle sooner, or decline that player's action at blackjack altogether, and at an online table the terms of the site apply in the same way.

Counting does not change the house edge of the game itself, and the gain it offers is small against the swings of play, so it is better treated as a way to understand how the game works than as a source of income.