Ask a Hi-Lo counter when to take insurance and the usual answer is a number: a true count of about +3. Published index lists state it, and our Illustrious 18 guide repeats it. A list gives the trigger, though, not what the bet returns on either side of it.
So we measured it. The simulation behind our article on how often you win a blackjack hand produced about 62 million rounds, and every round with an ace up recorded the true count a counter would have when insurance is offered, plus whether the hole card was a ten-value card.
The short version: insurance without a count is a losing bet, plainly stated. With a count, the return climbs steadily and crosses zero close to the published index, though only by a slim margin at +3 itself.
The arithmetic that sets the bar
Insurance pays 2 to 1 and wins only when the dealer's hole card is a ten-value card: ten, jack, queen or king. Call that chance p. Per unit insured the bet wins 2 units with chance p and loses 1 unit otherwise, so its expected return is 2p - (1 - p) = 3p - 1, which breaks even at p = 1/3, or 33.33 percent.
That is the whole frame. In an average shoe the hole card under an ace is a ten slightly less than one time in three, which is why commonly published figures, cited in our insurance explainer, put the house edge on insurance near 7 percent, and why basic strategy declines it. The bet flips only if p rises above one third, and what moves p is the composition of the cards not yet seen. Hi-Lo tracks that approximately (tens and aces count -1, 2 through 6 count +1), so a high count usually means a ten-rich remainder.
What we measured
The simulation ran about 62.09 million rounds of six deck blackjack: dealer stands on soft 17 and peeks for blackjack, blackjack pays 3:2, double on any two cards, double after split, split to four hands, one card to split aces, no surrender, cut card at 75 percent, one player following basic strategy from the app's 4 to 8 deck chart.
The dealer had an ace up in 4,773,621 of those rounds, 7.69 percent, about one in thirteen. At each one the Hi-Lo count was taken as a counter would have it at the offer: the running count of everything already dealt, plus the player's two cards and the dealer's ace, divided by the decks not yet seen, hole card included. That raw true count was floored to a whole number and, separately, rounded, and the round recorded whether the hole card was a ten.
Across all ace up rounds the hole card was a ten 30.84 percent of the time, so insurance returned -7.48 percent of the amount insured, in line with the commonly published edge of about 7 percent. Even money came out about the same: on the 218,556 rounds where the player held a natural, the ten share was 30.77 percent and the return -7.70 percent. Even money is insurance settled early, as the explainer shows.
21 TrainerFree on iPhone and Android. Instant right or wrong feedback with a clear explanation on every hand.
Get the app
The return at each floored count
Ace up rounds by floored true count, with the return per unit insured and its standard error:
| Floored true count | Share of ace up rounds | Hole card a ten | Insurance return | Standard error |
|---|---|---|---|---|
| -3 | 7.52 | 29.14 | -12.59 | 0.23 |
| -2 | 13.80 | 29.85 | -10.45 | 0.17 |
| -1 | 21.35 | 30.56 | -8.33 | 0.14 |
| 0 | 22.94 | 31.34 | -5.98 | 0.13 |
| +1 | 10.70 | 32.20 | -3.41 | 0.20 |
| +2 | 5.97 | 32.94 | -1.19 | 0.26 |
| +3 | 3.39 | 33.50 | +0.49 | 0.35 |
| +4 | 1.98 | 34.50 | +3.51 | 0.46 |
| +5 | 1.10 | 35.48 | +6.43 | 0.63 |
| +6 | 0.63 | 36.13 | +8.39 | 0.83 |
| +7 | 0.34 | 36.54 | +9.62 | 1.14 |
| +8 or more | 0.38 | 38.84 | +16.51 | 1.08 |
Counts below -3, 9.90 percent of ace up rounds together, all returned -15 percent or worse.
Two patterns matter. The chance of a ten under the ace climbs steadily: 29.85 at -2, 30.56 at -1, 31.34 at 0, 32.20 at +1, 32.94 at +2, about three quarters of a point per true count in that range. That is consistent with the count tracking the share of tens left in the shoe. The climb is steady, not exactly linear, so treat the figure as local.
The return column then crosses zero between +2 and +3: -1.19 at +2, +0.49 at +3. Our Illustrious 18 article gives the rule as insurance at a Hi-Lo true count of about +3, per Schlesinger's published list, ranked first among the deviations. The measured crossing is consistent with that number, with one caveat about precision.
How rarely the line is met
The +3 row is also where the measurement is least decisive. Its return of +0.49 percent sits only about 1.4 standard errors above zero, and that standard error treats rounds as independent when rounds from one shoe are correlated, so the real uncertainty is larger. The data is consistent with the true value being slightly negative, zero, or higher. The +4 row, +3.51 with a standard error of 0.46, is the first clearly positive count. An index is the point where the decision flips, not a promise of profit at that exact count.
A floored +3 or higher came up in 7.81 percent of ace up rounds (the rounded rows above add to 7.82). Ace up rounds are themselves 7.69 percent of all rounds, so the opportunity appears in about 0.6 percent of all rounds, roughly one in 166. Most of the time an ace shows, the count is below the line and the answer is still no; high counts are uncommon, as our measurement of true count frequencies shows.
Floored or rounded: the same counts, different labels
Rounding the same raw counts to the nearest whole number (halves up) instead of flooring them tells a subtler story.
| Rounded true count | Share of ace up rounds | Hole card a ten | Insurance return | Standard error |
|---|---|---|---|---|
| -1 | 19.19 | 30.23 | -9.32 | 0.14 |
| 0 | 24.66 | 30.98 | -7.06 | 0.13 |
| +1 | 14.53 | 31.86 | -4.42 | 0.17 |
| +2 | 7.93 | 32.52 | -2.44 | 0.23 |
| +3 | 4.54 | 33.27 | -0.20 | 0.30 |
| +4 | 2.56 | 33.97 | +1.92 | 0.41 |
| +5 | 1.48 | 34.89 | +4.67 | 0.54 |
| +6 | 0.80 | 35.73 | +7.18 | 0.73 |
| +7 | 0.48 | 36.42 | +9.27 | 0.96 |
| +8 or more | 0.52 | 38.28 | +14.83 | 0.92 |
Under rounding, +3 still measures slightly negative at -0.20 percent, within noise of zero, and +4 positive at +1.92. Nothing about the game changed. A floored +3 holds raw counts from +3 up to just under +4 and a rounded +3 holds +2.5 up to just under +3.5, so the floored bucket sits half a count higher; a raw +3.7 is a floored +3 but a rounded +4. Our measurements of flooring versus rounding and the rounding conventions behind index numbers cover this in detail. Which convention a published index list assumes depends on the source, and these measurements cannot tell you, so read a count against the table that matches how it was converted.
What this measurement leaves out
This is six decks only; other deck counts shift the numbers. The count divides by the exact decks remaining, which no player has: a player estimates that denominator from the discard tray, and deck estimation is a skill with its own errors. The simulation seated one player, so the only cards from the current round in the count were the player's two and the dealer's ace; a full table puts more cards on the felt before the offer, as our piece on counting at a full table describes.
The standing cautions apply too. Counting cards with your head is legal in the United States, but casinos are private businesses that may refuse service to suspected counters. No technique removes risk: a positive average on insurance is a long-run figure, not a promise about any single hand. Everything above describes one decision at one moment, not advice about bet sizes at any count.
Drilling the line
The practical skill is narrow: hold the count, convert it when an ace shows, compare it with the index, and decide. The Pro upgrade in 21 Trainer teaches four counting systems, Hi-Lo, KO, Omega II and Zen, with a true count drill and index deviation training covering the Illustrious 18. Our guide to memorizing index numbers puts insurance first in the study order.
For a player who is not counting, the answer stays the one basic strategy always gave: no. Without a count, insurance is a losing bet, and in this simulation it cost 7.48 percent of the amount insured on average.
21 Trainer ProHi-Lo, KO, Omega II and Zen, with a true count drill and index deviation training covering the Illustrious 18.
Get the app
Frequently asked questions
What true count do you need to take insurance in blackjack?
The commonly published Hi-Lo index is about +3, per Schlesinger's list, where insurance tops the Illustrious 18. Our simulation is consistent with it: with the count floored, insurance returned +0.49 percent of the amount insured at +3, only about 1.4 standard errors above zero, and +3.51 at +4, clearly positive. With the count rounded, +3 came out slightly negative at -0.20 percent.
Is insurance a good bet if you are not counting cards?
No. Across 4,773,621 ace up rounds in our simulation, the hole card was a ten 30.84 percent of the time and insurance returned -7.48 percent of the amount insured, consistent with the commonly published house edge of about 7 percent. Without a count, decline every time, even money included.
Is even money on a blackjack the same as insurance?
Yes. Even money is insurance settled early: insuring a blackjack for the maximum produces one unit either way, so the casino just hands you the unit. When the player held a natural in our simulation, the ten share was 30.77 percent and the return -7.70 percent, close to the -7.48 percent for all ace up rounds.
How often is the count high enough to make insurance worth it?
Rarely. A floored true count of +3 or higher came up in 7.81 percent of ace up rounds, and ace up rounds are about one in thirteen, so the opportunity appears in roughly 0.6 percent of all rounds, about one in 166. Most of the time an ace shows, the count says no.
What do you need to practice to use the insurance index?
An accurate running count, a sound deck estimate, a true count conversion done the same way every time, and the index itself. The Pro upgrade in 21 Trainer teaches four counting systems, Hi-Lo, KO, Omega II and Zen, with a true count drill and index deviation training covering the Illustrious 18, all with virtual chips on iPhone and Android.