Blackjack and Card Math

Insurance and Side Bets in Blackjack

How blackjack insurance and similar add-on side bets are priced, with hypothetical arithmetic, and why they generally carry a higher casino edge than the main game.

On this page
  1. The main game and the add-ons
  2. How the insurance bet works
  3. A hypothetical calculation
  4. Even money
  5. Why insurance feels attractive
  6. Other side bets
  7. Reading the table

The main game and the add-ons

Blackjack is a game of chance with a built-in casino advantage. No strategy, system, pattern or timing changes the odds in the player’s favor over time, and most players lose money over time. Insurance and side bets are extras placed on top of the main hand, and they are priced separately. As a rule, they carry a larger edge than the main game, so they add to the expected cost of playing rather than reduce it. Nobody should gamble money they cannot afford to lose.

How the insurance bet works

When the dealer’s upcard is an ace, the dealer may have a natural, which requires a ten-value card in the hole. Before the dealer checks, players are offered insurance. The rules are:

  • The insurance bet costs up to half of the original bet.
  • It pays 2 to 1 if the dealer has a natural.
  • It loses if the dealer does not, and the hand then continues as normal.

Despite the name, insurance does not protect the main bet in the usual sense. It is a separate wager on one question: is the dealer’s hole card a ten-value card?

A hypothetical calculation

Imagine a single-deck game, a player bets $10 and the dealer shows an ace. To keep the arithmetic simple, assume that the player’s own cards are unknown to the calculation, so there are 51 cards unseen from the player’s point of view, 16 of which are ten-values (the tens, jacks, queens and kings).

  • The chance the hole card is a ten-value card is 16/51, about 31.4 percent.
  • The chance it is not is 35/51, about 68.6 percent.

The insurance costs $5 and pays $10 when it wins (2 to 1, so $10 profit on a $5 stake).

Average result over 51 equally likely hole cards: 16 wins of $10 and 35 losses of $5 give 160 - 175 = -$15. Divided by 51, that is about -$0.29 per $5 insurance bet, or about -5.9 percent of the amount wagered on insurance.

For the bet to break even, the hole card would need to be a ten-value card one time in three, since a 2 to 1 payout is fair only at odds of 1 in 3. In a single deck the real chance is slightly below 1 in 3 (16/51 is about 0.314), and that gap is the casino’s edge. When several decks are in use, the proportion of ten-values stays close to 4 in 13, about 0.308, so the bet is worse for the player, and the edge on insurance is somewhat larger. The relevant fact for a player is that the payout is set below what the odds would justify.

A player who happens to see more ten-values in other hands at the table has a different picture, but that is a matter of what has been dealt rather than a change in the way the bet is built, and it does not make insurance a general bargain.

Even money

Sometimes a player holding a natural is offered “even money” when the dealer shows an ace. This is the same decision as taking insurance on a natural, written differently. Accepting even money gives a certain payout of 1 to 1 on the main bet. Declining means the player’s natural either pays 3 to 2 or pushes, if the dealer also has a natural. The sure thing feels comforting, which is a good example of how framing effects can make a pricing decision feel like a safety decision.

Why insurance feels attractive

Insurance feels like protection against a bad outcome, and that is its appeal. A player with a strong hand may want to hedge, much as the logic behind hedging bets is that a partial cover reduces risk. In fact it only changes the shape of the result, with a smaller chance of a large outcome and a larger chance of a small one, and it adds an extra wager with its own negative expected value. Over many hands, the player is paying a premium that is not covered by the payout.

Other side bets

Many blackjack tables offer side bets that pay on features of the first cards, such as whether the first two cards are a pair, or whether the player’s cards and the dealer’s upcard form a poker-like hand. Each has its own pay table. Because they are separate wagers, their edges are not the main game’s edge. Typical features:

  • Large advertised top payouts that attract attention.
  • Low probability of winning on any one hand.
  • A casino edge that is often several percent and sometimes considerably more, depending on the pay table, which varies between tables.

A hypothetical example: a side bet wins with a probability of 1 in 30 and pays 25 to 1. On a $1 bet, the average result is (25 × 1/30) - (29/30 × 1) = 25/30 - 29/30 = -4/30, about -$0.13. That is a 13 percent edge, many times larger than the edge on the main hand under good rules. Actual figures differ for real side bets, but the structure is the same: a rare event paid at a price lower than its true odds.

Side bets are also appealing because of the pace of variable rewards: an occasional large payout interrupts a long run of small losses and holds attention. The payout percentages of such bets are typically lower than the main game’s, though that is not displayed prominently.

Reading the table

If a table offers side bets, they are optional, and the posted pay table shows what each pays. Adding one raises the amount wagered per hand and, on average, the cost of the session. Skipping them does not make the main game a winning one, but it keeps the cost closer to the main game’s lower edge.

The takeaway is that insurance and side bets are priced as entertainment extras, with the casino retaining a larger share than on the base hand. Decide on a budget before playing, expect to lose over time, and reach out to local support services if gambling is causing difficulty.

The complete guide to blackjack and card math

How Blackjack Works: Rules, Hands and Dealer Procedure
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