Blackjack Card Counting Simulator

The Blackjack Card Counting Simulator implements a Hi-Lo true-count conversion, not a full shoe simulator. Two inputs: Running Count (default 5) and Decks Remaining (default 6, step 0.5, range 0.5–8). True Count is running / decks. Player Edge is the linear rule of thumb (TC − 1) × 0.5 percent. On the defaults, TC = 5/6 ≈ 0.833, displayed as 0.8 to one decimal, and Player Edge = (0.833 − 1) × 0.5 = −0.0833…%, displayed as −0.08%. The count is slightly positive; the estimated edge is still slightly negative because the intercept sits at TC = +1, the usual Hi-Lo break-even under common rules.

Type Running Count = 0, Decks Remaining = 6: TC = 0.0, edge = (0 − 1) × 0.5 = −0.50%. That −0.50% is the off-the-top player expectation the formula assumes for a basic-strategy player before the count moves. Type Running Count = 12, Decks Remaining = 3: TC = 4.0, edge = (4 − 1) × 0.5 = +1.50%. Type Running Count = 5, Decks Remaining = 5 (the regression check in SorteCalc’s tests): TC = 1.0, edge = 0.00%. That is the design hinge.

Decks Remaining is the hard part in a real pit. You estimate by eye from the discard tray. Halves are allowed (3.5 decks left) because a six-deck shoe is not always at an integer. The engine floors the input at 0.5 so you cannot divide by zero. Running Count can be negative: −8 with 4 decks left is TC = −2.0 and edge = −1.50%. Hi-Lo running counts of that size happen; they mean the remaining cards are rich in low cards, which is bad for the player.

The page does not keep a running count for you, does not know the hole card, and does not recommend a bet spread. It converts the two numbers you already have into a true count and a linear edge sketch. If your running count is wrong, the 0.8 and −0.08% are precisely converted nonsense. If the table is a single-deck pitch game, do not leave Decks Remaining at 6.

Compare a six-deck TC of 0.8 with a double-deck TC of 0.8: the formula gives the same edge. That is the point of true count — density of extra tens, not the raw running total. Edward O. Thorp’s original Ten-Count was a different tagging system; Harvey Dubner’s Hi-Lo and Stanford Wong’s Professional Blackjack popularized the conversion you are looking at.

Card counting is a family of tagging systems that keep a running total of how far the remaining shoe has drifted from a fresh composition. Hi-Lo, the system this page uses, assigns +1 to 2–6, 0 to 7–9, and −1 to ten-value cards and aces. The running count is their sum as cards come out. Because a running +5 in a full six-deck shoe is dilute, and a running +5 with one deck left is concentrated, you divide by decks remaining to get a true count: extra high cards per remaining deck.

Edward O. Thorp’s Beat the Dealer (1962) used a Ten-Count and made the casino problem public. Harvey Dubner presented Hi-Lo at a 1963 conference; Stanford Wong’s books turned it into the retail standard. Julian Braun’s IBM simulations and later Peter Griffin’s The Theory of Blackjack measured how much expected value moves per true-count point. The popular summary is “about 0.5% of extra player edge per true-count point above the break-even count,” with break-even near TC +1 under typical 6-deck, S17, DAS, late-surrender-off rules. SorteCalc hard-codes that summary: edge% = (TC − 1) × 0.5.

What the tool is not: a shoe simulator, a strategy engine, or legal advice. Many jurisdictions treat using a count as legal if you use your brain and illegal if you use a device; that is not this page’s topic. The linear map ignores rule variation (H17, no DAS, 1.5:1 blackjack, continuous shuffling machines). A CSM resets the count every hand; Decks Remaining never falls, and counting dies. The map also ignores bet-spread heat, table max, and the fact that the true count is an estimator, not an oracle — you discretize decks remaining by eye.

The default TC ≈ 0.83 with a slightly negative edge is pedagogical. A modest positive running count in a deep six-deck shoe is not yet an advantage. Wong’s “wonging” (entering only at high counts) exists because of that intercept. If you leave the defaults and think “plus five, I must be ahead,” the −0.08% is the correction. Griffin’s more refined regressions use a slightly different slope and a rules-dependent intercept; this page uses the classroom slope.

Use it to convert a count you already keep, to see how fast edge flips around TC +1, and to remember that Thorp’s insight was density, not a lucky streak.

A lecture on how to convert a running count into a true count and a linear edge sketch starts with division, not with a shoe of cards. Hi-Lo tags low cards plus one, neutrals zero, tens and aces minus one. The running total is their sum as cards come out. Density, not the raw total, is what matters: a running plus five in a full six-deck shoe is dilute; the same plus five with one deck left is concentrated. True count is running divided by decks remaining. Defaults: running 5, decks 6, so 5/6 ≈ 0.833, shown as 0.8 to one decimal.

Player edge as a percent is the classroom line (true count − 1) × 0.5. Plug in 5/6: (5/6 − 1) × 0.5 = (−1/6) × 0.5 = −1/12 ≈ −0.0833 percent, shown as −0.08 percent. The count is slightly positive; the estimated edge is still slightly negative because the intercept sits at true count plus one, the usual Hi-Lo break-even under common six-deck, stand-on-soft-17, double-after-split rules. A neutral shoe at true count 0 is therefore about −0.50 percent, the off-the-top basic-strategy leak this sketch assumes. Running 5 with 5 decks left is the hinge: true count 1.0, edge 0.00 percent. Running 12 with 3 decks left: true count 4.0, edge +1.50 percent.

Edward O. Thorp’s Beat the Dealer, 1962, used a Ten-Count and made the casino problem public. Harvey Dubner presented Hi-Lo in 1963; Stanford Wong’s books turned the conversion into the retail standard. Peter Griffin’s The Theory of Blackjack measured how expected value moves per true-count point. The popular summary is about half a percent of extra player edge per point above the break-even count. Julian Braun’s simulations sit behind those slopes. This page is that linear sketch, not a composition-dependent strategy table and not a shoe simulation that deals cards.

What the arithmetic is not must be said twice. Continuous shuffling resets the count every hand; decks remaining never falls, and counting dies. Knock-out is unbalanced and does not divide by decks the same way; feeding that running total into this formula applies Hi-Lo to the wrong integer. Thorp’s Ten-Count used a ratio of remaining tens to others; do not mix systems. Decks remaining is estimated by eye from the discard tray, so binning error is the usual noise. A single-deck pitch game must not be left at 6 decks remaining.

Assumptions: Hi-Lo tags, true-count division, linear expected value, half a percent per point, break-even at plus one, decks remaining without error. A modest plus-five in a deep six-deck shoe is not yet an advantage; Wong’s habit of entering only at high counts exists because of that intercept. The arithmetic of 5/6 and −1/12 is exact either way. Griffin’s finer regressions use a slightly different slope and a rules-dependent intercept; the classroom slope is what you are looking at. Index plays such as the Illustrious 18 are out of scope.