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Blackjack insurance and even money calculator: take it or not?
The dealer shows an ace and offers insurance. Enter your two cards and the table, and see what insurance or even money is worth in exactly this spot.
Inputs
Cards seen at other seats (optional)
Only cards dealt in this round. Leave both at 0 if you play alone.
Even money pays +1.000 bet now. Declining averages +1.039 bets: your blackjack is paid unless the dealer also has one, which is a push. The gap is 0.039 of your bet.
The dealer's second card is unknown and could be any card you have not seen. Even money is paid at 1 to 1 whatever the blackjack payout. Insurance is decided before you play your hand; at a no-hole-card table it is settled when the dealer draws the second card, which is a ten just as often, so the hole-card rule does not change these numbers.
What insurance is
When the dealer's up card is an ace, the table offers insurance: a side bet of up to half your main bet that the dealer has blackjack. It pays 2 to 1. If the dealer has blackjack you lose the main bet and the insurance pays; if not, the insurance is lost and the hand goes on.
Why insurance loses on average
A 2 to 1 payout breaks even when the dealer's hole card is a ten exactly 1 time in 3, and wins on average only when tens come more often than that. Ten-value cards are 16 of every 52, a little under a third. With 6 decks and only the dealer's ace known, the hole card is a ten 30.87% of the time (96/311), so insurance keeps 7.40% of every amount you put on it. If your own two cards are not tens, the share rises a little (31.07%), but the bet still loses 6.80%.
Even money is insurance in disguise
With a blackjack against an ace, the dealer offers "even money": you are paid 1 to 1 at once instead of waiting. At a 3:2 table that is the same as insuring your blackjack. Taking it gives exactly +1 bet. Declining gives 1.5 bets unless the dealer also has blackjack, which is a push: on average +1.039 bets with 6 decks. Declining is better by 0.039 of your bet, the same house edge the insurance bet carries, applied to half a bet.
At a 6:5 table the answer flips
If a blackjack pays only 6 to 5, declining averages 1.2 bets times the share of rounds with no dealer blackjack: +0.831 bets with 6 decks. Even money at 1 to 1 is +1, so taking it is better by 0.169 of your bet. This is a cost of the 6:5 payout, not a reason to play there. What 6:5 costs over a session: payout calculator.
Do the other cards on the table matter?
A little. Every ten you see at other seats makes a dealer blackjack slightly less likely, and every other card slightly more likely. It takes a lot of low cards in one round to push the share of tens past 1 in 3. Online games run by a random number generator usually shuffle the cards for every round, so only the cards dealt in this round count.
More on how the bet works: blackjack insurance.
How it is worked out
The hole card is equally likely to be any card you have not seen, so the chance of a dealer blackjack is the number of unseen ten-value cards divided by the number of unseen cards – an exact fraction. Insurance then averages 2 × p − (1 − p) per amount staked. The same formula, checked by our own independent simulation for 6 and 8 decks, gives the figures on the side bets page.
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