The Illustrious 18 & Fab 4: deviation charts

Why a play "flips": the crossover

For any hand, each available action has an expected value that depends on the composition of the remaining shoe — which the true count summarizes. As the count rises, the EV of standing on 16 vs 10 rises (the dealer busts more) while the EV of hitting falls (you bust more). The two curves cross at some true count. That crossover is the index number:

Every index in the tables below was found the same way basic strategy itself was: exhaustive simulation at each count level, action by action. Nothing is judgment; each number is a measured crossover.

Notice the indices are two-sided. Positive indices activate an aggressive play as the count rises ("double 10 vs 10 at +4 or above"). Negative indices retreat from basic strategy as the count falls ("hit 13 vs 2 at −1 or below") — because a low-card-rich shoe makes your stiff hands safer to hit and the dealer's stiffs safer from busting.

The flagship: insurance at +3

Basic strategy says never take insurance, and for a neutral shoe that's provably right. Insurance is a side bet that the dealer's hole card is a ten, paying 2:1. Let p be the fraction of tens among the unseen cards:

So insurance is a bad bet until tens make up more than a third of the unseen cards — and the count tells you precisely when that happens. Each point of Hi-Lo true count raises the ten density of the remaining shoe by roughly half a percent; the density crosses 33.3% at a true count of about +3. Above that, "never take insurance" is no longer advice, it's a mistake. This single index is worth more than any other deviation because a dealer ace shows up constantly and the flipped EV applies to your whole wager — which, at +3, is a big one.

Why only 18 (and 4)?

There are hundreds of computable indices. Don Schlesinger's analysis in Blackjack Attack showed the value is brutally concentrated: a small set of plays — frequent hands, big EV swings — delivers the large majority of all play-variation profit, and the long tail of exotic indices adds almost nothing while multiplying the memorization load and the error rate. HisIllustrious 18 (the core plays) plus theFab 4 (the four late-surrender indices) became the standard syllabus for exactly this reason: maximum EV per unit of memory.

The charts

Indices apply to multi-deck (4–8 deck) games and key off thetrue count. Each row overrides yourbasic strategy chart only when the count condition is met — at every other count, basic strategy stands. Where surrender appears, it assumes late surrender is offered; if it isn't, fall back to the basic strategy play.

Dealer hits soft 17 (H17)

Dealer stands on soft 17 (S17)

A warning about misapplied deviations

Every index play is a bet that your count is right. Deviate on a wrong count and you've made a play that's worse than basic strategy in the actual composition you're facing — you'd have been better off knowing nothing. This is why deviations are the last layer of the learning path, not the first: their value is conditional on flawless execution of everything underneath.

Frequently asked questions