The dealer shows an ace, the table pauses, and the box asks: insurance? It pays 2:1 if a ten-value card sits in the hole — which makes it a pure probability question with a famous answer and an important exception. This calculator prices the bet exactly: for a fresh shoe of any size, and for a counted shoe via the Hi-Lo true count, where the “sucker bet” verdict genuinely flips.
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How to Use the Calculator
- Decks in shoe: 1 to 8 — deck count nudges the fresh-shoe numbers slightly.
- Insurance bet amount: typically half your main bet; the tool prices whatever you enter.
- True count (optional): leave 0 for an uncounted, roughly fresh shoe. If you keep a Hi-Lo count, enter the current true count — this is the input that can turn the bet profitable.
The result shows the implied probability of a ten in the hole, the 2:1 payout, the expected value in dollars, and the return per dollar staked.
The Core Math: One Third Is the Line
Insurance wins when the hole card is a ten-value. With a 2:1 payout, the break-even condition is simple:
Ten-values are 16 of 52 ranks — 30.77% of a full deck — so a neutral shoe always sits below the line. Removing the dealer’s visible ace helps marginally, which is why smaller shoes are a touch cheaper:
| Decks | P(ten in hole), fresh shoe | Insurance EV |
|---|---|---|
| 1 | 31.37% | −5.88% |
| 2 | 31.07% | −6.80% |
| 4 | 30.92% | −7.25% |
| 6 | 30.87% | −7.40% |
| 8 | 30.84% | −7.47% |
Off a fresh shoe, every row is a worse bet than the game you interrupted to place it. That is the whole basis of the standard advice — and the advice is incomplete, because nothing forces the shoe to stay neutral.
Where the Verdict Flips: The Counted Shoe
Insurance is unusual among side bets: it depends on exactly one quantity, ten-density, which is precisely what a Hi-Lo count tracks. Each point of true count raises the insurance return by roughly 2.4 percentage points, so from a six-deck baseline of −7.40% the bet crosses zero around true count +3 — the classic “insurance index,” and historically the single most valuable counting deviation. The calculator applies this linear approximation; at extreme counts it is an estimate of a real but noisier edge, and the input is capped where the linear model stops being meaningful.
Two worked cases:
- Fresh six-deck shoe: 311 unseen cards after the dealer’s ace, 96 tens — P = 30.87%, EV = 3 × 0.3087 − 1 = −7.40%. A $50 insurance bet donates $3.70 on average. Decline.
- Ten-rich shoe: 50 cards left, 20 of them tens — P = 40.00%, EV = +20.00%. The same $50 bet now returns $10.00 on average. This is the situation the true-count input exists to detect.
“Even Money” Is Insurance Wearing a Suit
When you hold a natural against a dealer ace, the offer of guaranteed even money is mathematically identical to insuring your blackjack: you trade a 30.87%-ish chance of a push for a locked 1:1 payout, surrendering the 3:2 premium the rest of the time. Off a neutral shoe the guaranteed dollar costs about 4% of expected value — the same arithmetic in friendlier packaging, and it flips positive at the same true-count line as the plain side bet.
Beyond Insurance: The Other Ace-Up Decisions
The ace up forces more than one choice. Whether to surrender a stiff hand, hit a marginal total, or stand belongs to per-action mathematics — the side-by-side EV of every move — which is the job of our Decision EV Calculator; the honest deterrent example is 16 vs 10, where standing runs at −54.04% per dollar and late surrender’s fixed −50.00% is the cheapest exit. For the win-push-lose picture of a made hand, the Hand Equity Calculator covers every standing total.
Related Blackjack Tools
- Blackjack Decision EV Calculator — Hit, stand, double, split and surrender, priced per action
- True Count Calculator — Converting a running count into the number this tool needs
- Card Counting Calculator — The edge behind the deviations
- Blackjack Expected Value Guide — House edge by rules and what it costs per hour