Share this

Last Updated: March 01, 2011

Baccarat Insurance


Introduction

I have been hearing more and more about casinos in Asia offering insurance bets in baccarat after four or five cards have been dealt. These are generally made to protect a stronger hand against losing, or in the case of a 9, a tie.

To avoid confusion, I capitalize Player when referring to the bet, and use lower case when referring to the person playing the game.

Except as noted, insurance on the Banker hand wins when the Player hand ends up winning, and vise versa.

Exceptions:

  • Insurance on a 9-point hand will win in the event of a tie and lose otherwise.
  • Insurance on the Banker hand on a 0-0 score after five cards will win in the event of a tie and otherwise lose.

All figures in this page are based on an eight-deck game.

Star Cruises

Star Cruises is a cruise line that visits the east Asian countries. Their ships offer baccarat insurance in their casinos. The following is my best interpretation of their rules, based on a company document explaining the rules and procedures of the game. The insurance bet is limited to the amount of the original wager. It is unclear to me when the cards are exposed, but it seems the players have free will in this regard.

Insuring a Natural

If either Player or Banker has a natural 8 or 9, then he may insure it against a tie in the case of a 9 or a loss in the case of an 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 Against Unknown Banker Hand

The next table covers the situation where the Player has drawn a third card and the Banker has not turned over any cards yet. Insurance is taken on the Player hand and wins in the case of a tie with a Player 9. A Banker win occurs with all other player totals.

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 are Exposed

The next table covers the situation where the Player has exposed three cards and the Banker has exposed two. Insurance is offered only on four situations where the totals are equal on the Banker hand. In the 0-0 case, the insurance bet wins in the event of a tie, and all others pay on a Player win.

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 After Five Cards are Exposed

The next table covers the situation where the Player has exposed three cards and the Banker has exposed two. Insurance is offered only on four situations where the totals are equal on the Banker hand. In the 0-0 case the insurance bet wins in the event of a tie, all others pay on a Player 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 also came to me in the form of an internal company document, which may be outdated. It states that insuring a Banker 2-card 6 against a Player 2-card 5 pays 3 to 1, which would have a player advantage of 8.44%. I don't know if they still allow this.

Banker Insurance After Four Cards Exposed

The following table shows the odds for insuring a Banker bet when the Player has a lower total after four cards. Insurance bets win if the Player ends up winning.

Banker Insurance after Four Cards Exposed

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 Exposed

The following table shows the odds for insuring a Player bet when the Banker has a lower total after four cards. Insurance bets win if the Banker ends up winning.

Player Insurance after Four Cards Exposed

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 After Five Cards Exposed

The following table shows the odds for insuring a Banker bet when the Player has a lower total after five cards. Insurance bets win if the Player ends up winning.

Banker Insurance after Five Cards Exposed

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 After Five Cards Exposed

The following table shows the odds for insuring a Player bet when the Banker has a lower total after five cards. Insurance bets win if the Banker ends up winning.

Player Insurance after Five Cards Exposed

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