Blackjack Insurance Calculator

Defaults are Main Bet 100 dollars and Dealer Shows Ace checked. Insurance is offered only when the upcard is an ace. Submit. Insurance Cost is 50.00 (half the main bet), Insurance EV is −7.69%, and Recommendation is Decline. The side bet pays 2:1 if the hole card is a ten-value rank. Under the infinite-deck approximation used here, that hole card is a ten with probability 4/13, not the 1/3 that would make 2:1 a fair price.

Uncheck Dealer Shows Ace. Cost becomes 0, EV is N/A, and Recommendation is Not available. That is the correct control: insurance is not a generic hedge against losing the main bet; it is a side wager that exists only against an ace. Re-check the box and raise Main Bet to 250. Cost becomes 125; EV percentage stays −7.69% because the edge does not depend on stake; Recommendation remains Decline.

The EV line is a percentage of the insurance stake, not of the main bet. A −7.69% edge on a 50 insurance bet is about 3.85 dollars of expected loss on that side bet, independent of whether the main 100 wins, loses, or pushes. Even money in lieu of insurance, when offered on a player blackjack, is the same wager in disguise: you are accepting a sure even-money win instead of 3:2, which is equivalent to taking insurance.

This calculator does not ask for the count. At a true count of roughly +3 or higher, the ten-density can push the hole-card ten probability above 1/3 and flip the EV non-negative. The engine never sees a count, so it will keep saying Decline at the 4/13 baseline. If you are not counting, treat that as the whole answer. If you are counting, do not use this tool for the take/decline decision.

Worked identity: bet 100, ace true → cost 50, EV −7.69%, Decline. Repeat with bet 40 → cost 20, same percentage, Decline. The 2:1 payout is already inside the 3p−1 formula; you do not enter a payout field. Reload defaults whenever you want to see the canonical negative-edge illustration that matching-the-book writers have used since the 1960s.

Insurance is a side bet that the dealer’s hole card is a ten-value card when the upcard is an ace. It is sold as protection for the main wager. It is priced as a 2:1 proposition on a 1:2 stake. The educational purpose of this calculator is to show that the price is wrong at a neutral shoe: the fair probability for a 2:1 payout is 1/3, while a fresh pack has 16 tens in 52 cards, 4/13 ≈ 0.3077, which is below 1/3. The house keeps the difference.

The wager appears in Thorp’s Beat the Dealer as the canonical example of a side bet with a large, stable edge against an uncounting player and a count-sensitive flip for a card counter. Casino marketing still uses the word “insurance,” which implies hedging. Mathematically you are buying a separate even-money-style bet whose correlation with the main hand is incomplete: you can win insurance and lose the main, win both, or lose both.

Limits of this implementation: infinite-deck 4/13, no removal of the player’s cards, no distinction between 10, J, Q, K, no peek-error model, no European no-hole-card variant where insurance may not be offered the same way. Main Bet is only used to scale the cost as bet/2. The recommendation is Decline whenever the ace box is checked, because 3×(4/13)−1 is negative. Take would require a positive EV that this baseline never produces.

History: some jurisdictions experimented with even-money buttons on player blackjacks, which are insurance in a trench coat. Others forbade insurance to speed the game. Online RNG blackjack still offers it because it is profitable and optional. Continuous shufflers keep the ten-density near 4/13, so counting never rehabilitates the bet there. Live 6D shoes can, in principle, but only with a count and a large enough remaining pack.

Do not confuse insurance with surrender, which forfeits half the main bet to skip the resolution, or with “taking even money because I have blackjack.” This tool only prices the hole-card ten proposition. It will not tell you whether the main hand of 20 versus ace is strong; that is a different decision already made by basic strategy (stand). The side bet can be declined while the main bet is played out. Default 100 on an ace remains Decline at −7.69%.

Insurance is a side bet that the dealer's hole card is a ten-value rank when the upcard is an ace. It is offered only against an ace. The cost is half the main stake. The side bet pays two to one if the hole card is a ten, jack, queen, or king. Fairness for a two-to-one payout would require the hole card to be a ten with probability one third. A fresh pack has sixteen ten-value cards among fifty-two, so the infinite-deck probability is 4/13, about 0.3077, which sits below one third. Thorp treated this proposition in Beat the Dealer as the canonical example of a side bet with a large, stable edge against an uncounting player.

Derivation of the displayed mean uses one unit staked on insurance. With probability p the hole card is a ten and the even-money-style ledger records a win of two; with probability one minus p the unit is lost. Expected value equals two p minus (1 − p), which simplifies to 3p − 1. Substitute p = 4/13: 12/13 − 1 = −1/13 ≈ −0.076923, printed as −7.69%. Fairness would require 3p − 1 = 0, hence p = 1/3. The ratio 4/13 is short of 1/3 by 1/39, and that gap is the house edge. Decline off the top at a neutral shoe.

Finite-shoe correction does not rescue the bet. Six decks hold ninety-six tens in three hundred twelve cards, still four thirteenths if nothing has been seen. After the ace upcard is removed, ninety-six tens remain in three hundred eleven cards, about 0.3087, still below one third. Removing player tens would lower p; removing player small cards would raise it. This lecture ignores those composition shifts, matching an uncounted price. Hi-Lo true count of roughly plus three is the folklore index at which ten-density can push p across one third on a six-deck shoe. Without a count, the recommendation remains Decline whenever the ace is showing.

Worked default. Main stake one hundred implies insurance cost fifty. Percentage mean does not scale with stake; the dollar mean on the side bet is minus 0.076923 times fifty, about minus 3.85. Even money offered on a player blackjack is the same wager in disguise: accepting a sure even-money win instead of three to two is equivalent to taking insurance. Unchecking the ace makes the side bet unavailable, cost zero. Raising the main stake to two hundred fifty raises cost to one hundred twenty-five and leaves the percentage at minus 7.69.

Assumptions. Independent ranks, four ten-value ranks equally likely, dealer peek resolving blackjack before the main hand when insurance loses. Correlation with the main wager is incomplete: you can win insurance and lose the main, win both, or lose both. The word insurance is marketing. The arithmetic is a two-to-one proposition priced above the physical frequency of tens. Continuous shufflers pin ten-density near four thirteenths, so counting never rehabilitates the bet there.