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Baccarat Insurance
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Introduction
Recently, I've been noticing an increasing number of Asian casinos introducing insurance bets for baccarat after a few initial cards have been dealt. These bets are typically designed to provide coverage for a stronger hand, protecting against losses or ties for hands that tot up to 9.
To make things clearer, I use an uppercase 'Player' when discussing the betting term and a lowercase 'player' for the individual engaged in the game.
Unless stated differently, an insurance bet on the Banker is a winning proposition if the Player hand ultimately prevails, and the opposite holds true as well.
Exceptions:
- When the hand total is a 9, the insurance wins if there's a tie, but the bet loses in all other circumstances.
- Insurance placed on a 0-0 score for the Banker hand after five cards has a winning potential in the case of a tie; otherwise, it results in a loss.
All statistics presented on this page are derived from a game using eight decks of cards.
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Marina Bay Sands — Singapore
Information can be found in my page on Insurance Options for Baccarat at Marina Bay Sands .
Asia Gaming
Information can be found in my page on Baccarat Insurance at Asia Gaming .
Star Cruises
Star Cruises, known for its voyages to East Asian nations, provides baccarat insurance in its onboard casinos. Below is my interpretation of the rules based on an internal company document outlining the game’s procedures. It appears that the insurance bet is capped at the value of the original stake, although I am uncertain when the cards are revealed as players seem to have discretion in this matter.
Insuring a Natural
If either the Player or Banker holds a natural 8 or 9, there’s an option to insure against a tie for 9 or a loss for 8.
Natural Insurance
| Points | Pays | Prob. Win | Prob. Loss | Prob. Draw | Expected Value |
|---|---|---|---|---|---|
| 9 | 9 | 0.905475 | 0.000000 | 0.094525 | -0.054754 |
| 8 | 7 | 0.810911 | 0.094938 | 0.094151 | -0.146347 |
Insuring a 3-Card Player Hand When the Banker Hand is Unknown
The upcoming table illustrates a scenario in which the Player has received a third card while the Banker has not revealed any cards. In this scenario, insurance is placed on the Player's hand, which wins if it ties at a total of 9. A win for the Banker occurs in all other cases.
3-Card Player Insurance Against Unknown Banker Hand
| Player Points | Pays | Player Win | Banker Win | Tie Win | Expected Value |
|---|---|---|---|---|---|
| 9 | 9 | 0.923233 | 0.000000 | 0.076767 | -0.232331 |
| 8 | 7 | 0.846404 | 0.076904 | 0.076693 | -0.308079 |
| 7 | 4 | 0.769274 | 0.153882 | 0.076844 | -0.153748 |
| 6 | 3 | 0.683625 | 0.230965 | 0.085410 | 0.009271 |
| 5 | 1.5 | 0.603527 | 0.308001 | 0.088471 | -0.141525 |
| 4 | 1 | 0.513984 | 0.392562 | 0.093454 | -0.121423 |
Banker Insurance After Four Cards Have Been Dealt
The following table addresses a situation where the Player has revealed three cards while the Banker has shown two. Insurance is available in four specific scenarios where the Banker's totals are equal. In a 0-0 scenario, the insurance bet is victorious in the event of a tie; other scenarios reward payouts only if the Player wins.
Insurance after Four Cards Exposed
| Player Points | Banker Points | Pays | Player Win | Banker Win | Tie Win | Expected Value |
|---|---|---|---|---|---|---|
| 0 | 4 | 1 | 0.368065 | 0.578663 | 0.053272 | -0.210599 |
| 1 | 4 | 1 | 0.343812 | 0.602820 | 0.053368 | -0.259008 |
| 2 | 4 | 1 | 0.319906 | 0.627004 | 0.053090 | -0.307099 |
| 3 | 4 | 1 | 0.295920 | 0.591577 | 0.112503 | -0.295658 |
| 0 | 5 | 1.5 | 0.319950 | 0.638715 | 0.041335 | -0.158790 |
| 1 | 5 | 1.5 | 0.283814 | 0.674655 | 0.041531 | -0.248934 |
| 2 | 5 | 1.5 | 0.248356 | 0.650906 | 0.100738 | -0.278371 |
| 3 | 5 | 1.5 | 0.271182 | 0.628151 | 0.100667 | -0.221377 |
| 4 | 5 | 1.5 | 0.294993 | 0.604412 | 0.100595 | -0.161923 |
| 0 | 6 | 3 | 0.248749 | 0.721860 | 0.029391 | 0.024389 |
| 1 | 6 | 3 | 0.200798 | 0.710369 | 0.088833 | -0.107975 |
| 2 | 6 | 3 | 0.212631 | 0.698539 | 0.088830 | -0.060646 |
| 3 | 6 | 3 | 0.224458 | 0.687609 | 0.087932 | -0.014235 |
| 4 | 6 | 2 | 0.236160 | 0.675002 | 0.088838 | -0.202682 |
| 5 | 6 | 2 | 0.248909 | 0.662332 | 0.088759 | -0.164513 |
Banker Insurance Following Five Revealed Cards
In the next table, we look at a case where the Player has three cards exposed and the Banker has two. Insurance is only available in four situations where the Banker's totals match. In the instance of a 0-0 tie, the insurance bet claims victory if a tie occurs, while other cases reward payouts based on the Player's win.
Insurance after Five Cards Exposed
| Player Points | Banker Points | Pays | Player Win | Banker Win | Tie Win | Expected Value |
|---|---|---|---|---|---|---|
| 0 | 0 | 2 | 0.000000 | 0.695236 | 0.304764 | -0.085707 |
| 1 | 1 | 7 | 0.077013 | 0.615304 | 0.307683 | -0.076214 |
| 2 | 2 | 3 | 0.154018 | 0.538302 | 0.307680 | -0.076249 |
| 3 | 3 | 2 | 0.231517 | 0.460953 | 0.307530 | 0.002080 |
Resorts World Sentosa
These rules were communicated to me through an internal company document, which might not be current. It mentions that insuring a 2-card Banker hand totaling 6 against a Player hand totaling 5 would result in a payout of 3 to 1, theoretically giving the player an edge of 8.44%. I am unsure about the current validity of this rule.
Banker Insurance After Four Cards Revealed
The next table reveals the odds for insuring a Banker bet when the Player's total is lower after four cards have been dealt. Insurance bets are considered wins if the Player ultimately prevails.
Banker Insurance after Four Cards Have Been Revealed
| Player Points | Banker Points | Pays | Player Win | Banker Win | Tie Win | Expected Value |
|---|---|---|---|---|---|---|
| 0 | 5 | 2 | 0.319950 | 0.638715 | 0.041335 | 0.001185 |
| 1 | 5 | 2 | 0.283814 | 0.674655 | 0.041531 | -0.107027 |
| 2 | 5 | 2 | 0.248356 | 0.650906 | 0.100738 | -0.154193 |
| 3 | 5 | 2 | 0.271182 | 0.628151 | 0.100667 | -0.085786 |
| 4 | 5 | 2 | 0.294993 | 0.604412 | 0.100595 | -0.014426 |
| 0 | 6 | 3 | 0.248749 | 0.721860 | 0.029391 | 0.024389 |
| 1 | 6 | 3 | 0.200798 | 0.710369 | 0.088833 | -0.107975 |
| 2 | 6 | 3 | 0.212631 | 0.698539 | 0.088830 | -0.060646 |
| 3 | 6 | 3 | 0.224458 | 0.687609 | 0.087932 | -0.014235 |
| 4 | 6 | 3 | 0.236160 | 0.675002 | 0.088838 | 0.033478 |
| 5 | 6 | 3 | 0.248909 | 0.662332 | 0.088759 | 0.084397 |
| 0 | 7 | 4 | 0.154340 | 0.769393 | 0.076268 | -0.152035 |
| 1 | 7 | 4 | 0.153216 | 0.769718 | 0.077066 | -0.156852 |
| 2 | 7 | 4 | 0.153224 | 0.769708 | 0.077068 | -0.156814 |
| 3 | 7 | 4 | 0.154128 | 0.768806 | 0.077066 | -0.152294 |
| 4 | 7 | 4 | 0.153211 | 0.769725 | 0.077065 | -0.156882 |
| 5 | 7 | 4 | 0.154124 | 0.768810 | 0.077066 | -0.152312 |
Player Insurance After Four Cards Have Been Revealed
This table outlines the odds for securing a Player bet when the Banker total is lower after four cards have been revealed. Insurance bets are rewarded if the Banker ends up winning.
Player Insurance after Four Cards Have Been Revealed
| Player Points | Banker Points | Pays | Player Win | Banker Win | Tie Win | Expected Value |
|---|---|---|---|---|---|---|
| 5 | 4 | 2 | 0.597782 | 0.289715 | 0.112503 | -0.018352 |
| 6 | 0 | 2 | 0.692222 | 0.231515 | 0.076263 | -0.229191 |
| 6 | 1 | 2 | 0.692651 | 0.230281 | 0.077068 | -0.232089 |
| 6 | 2 | 2 | 0.692656 | 0.230281 | 0.077063 | -0.232094 |
| 6 | 3 | 2 | 0.693562 | 0.230272 | 0.076166 | -0.233019 |
| 6 | 4 | 3 | 0.692650 | 0.230277 | 0.077073 | -0.001817 |
| 6 | 5 | 3 | 0.691743 | 0.231193 | 0.077065 | 0.001835 |
| 7 | 0 | 3 | 0.769393 | 0.154340 | 0.076268 | -0.306374 |
| 7 | 1 | 3 | 0.769718 | 0.153216 | 0.077066 | -0.310068 |
| 7 | 2 | 3 | 0.769708 | 0.153224 | 0.077068 | -0.310037 |
| 7 | 3 | 3 | 0.768806 | 0.154128 | 0.077066 | -0.306422 |
| 7 | 4 | 4 | 0.769725 | 0.153211 | 0.077065 | -0.156882 |
| 7 | 5 | 4 | 0.768810 | 0.154124 | 0.077066 | -0.152312 |
Banker Insurance Following Five Cards Being Revealed
The next table presents the odds for insuring a Banker bet when the Player's total is lower after five cards are exposed. Insurance bets win if the Player prevails.
Banker Insurance after Five Cards Have Been Revealed
| Player Points | Banker Points | Pays | Player Win | Banker Win | Tie Win | Expected Value |
|---|---|---|---|---|---|---|
| 1 | 1 | 6 | 0.077013 | 0.615304 | 0.307683 | -0.153227 |
| 1 | 2 | 7 | 0.077011 | 0.845973 | 0.077016 | -0.306895 |
| 1 | 3 | 7 | 0.076989 | 0.845742 | 0.077269 | -0.306818 |
| 1 | 4 | 7 | 0.076032 | 0.847902 | 0.076065 | -0.315676 |
| 1 | 5 | 7 | 0.075882 | 0.848080 | 0.076039 | -0.316907 |
| 1 | 6 | 7 | 0.076783 | 0.846428 | 0.076789 | -0.308945 |
| 2 | 3 | 4 | 0.154252 | 0.768763 | 0.076986 | -0.151755 |
| 2 | 4 | 4 | 0.153694 | 0.768986 | 0.077320 | -0.154208 |
| 2 | 5 | 4 | 0.152675 | 0.772494 | 0.074831 | -0.161793 |
| 2 | 6 | 4 | 0.153579 | 0.770093 | 0.076329 | -0.155778 |
| 3 | 4 | 1.5 | 0.231953 | 0.690731 | 0.077316 | -0.342802 |
Player Insurance Following Five Cards Being Revealed
This table outlines the odds for insuring a Player bet when the Banker total is lower after five cards have been revealed, with winning bets contingent upon a Banker win.
Player Insurance after Five Cards Have Been Revealed
| Player Points | Banker Points | Pays | Player Win | Banker Win | Tie Win | Expected Value |
|---|---|---|---|---|---|---|
| 5 | 0 | 2 | 0.613890 | 0.309497 | 0.076613 | 0.005104 |
| 5 | 1 | 2 | 0.614788 | 0.308293 | 0.076919 | 0.001799 |
| 5 | 2 | 2 | 0.615134 | 0.307946 | 0.076920 | 0.000758 |
| 5 | 3 | 2 | 0.616392 | 0.306687 | 0.076921 | -0.003018 |
| 5 | 4 | 2 | 0.617492 | 0.305417 | 0.077090 | -0.006658 |
| 6 | 0 | 3 | 0.691042 | 0.232147 | 0.076811 | 0.005400 |
| 6 | 1 | 3 | 0.691983 | 0.231249 | 0.076768 | 0.001764 |
| 6 | 2 | 3 | 0.692490 | 0.230743 | 0.076767 | -0.000261 |
| 6 | 3 | 3 | 0.693904 | 0.230225 | 0.075870 | -0.003228 |
| 6 | 4 | 3 | 0.694015 | 0.229293 | 0.076692 | -0.006137 |
| 6 | 5 | 3 | 0.692008 | 0.230948 | 0.077044 | 0.000838 |
| 7 | 0 | 4 | 0.768423 | 0.154764 | 0.076812 | -0.149365 |
| 7 | 1 | 4 | 0.769115 | 0.153977 | 0.076908 | -0.153207 |
| 7 | 2 | 4 | 0.769616 | 0.153613 | 0.076771 | -0.155163 |
| 7 | 3 | 4 | 0.769562 | 0.153673 | 0.076766 | -0.154871 |
| 7 | 4 | 4 | 0.770610 | 0.152621 | 0.076769 | -0.160127 |
| 7 | 5 | 4 | 0.769077 | 0.153838 | 0.077085 | -0.153726 |
| 7 | 6 | 4 | 0.768408 | 0.154635 | 0.076956 | -0.149867 |
| 8 | 0 | 7 | 0.845811 | 0.077381 | 0.076809 | -0.304147 |
| 8 | 1 | 7 | 0.846393 | 0.076700 | 0.076907 | -0.309496 |
| 8 | 2 | 7 | 0.846178 | 0.076905 | 0.076918 | -0.307846 |
| 8 | 3 | 7 | 0.846655 | 0.076766 | 0.076579 | -0.309293 |
| 8 | 4 | 7 | 0.847738 | 0.076573 | 0.075688 | -0.311724 |
| 8 | 5 | 7 | 0.846555 | 0.076427 | 0.077018 | -0.311569 |
| 8 | 6 | 7 | 0.845958 | 0.077253 | 0.076789 | -0.305184 |
| 9 | 0 | 8 | 0.923190 | 0.000000 | 0.076810 | -0.308709 |
| 9 | 1 | 8 | 0.923094 | 0.000000 | 0.076906 | -0.307850 |
| 9 | 2 | 8 | 0.923090 | 0.000000 | 0.076910 | -0.307808 |
| 9 | 3 | 8 | 0.923153 | 0.000000 | 0.076847 | -0.308380 |
| 9 | 4 | 8 | 0.923583 | 0.000000 | 0.076417 | -0.312246 |
| 9 | 5 | 8 | 0.923586 | 0.000000 | 0.076414 | -0.312278 |
| 9 | 6 | 8 | 0.923200 | 0.000000 | 0.076800 | -0.308800 |
