Last Updated: April 1, 2019

# Baccarat Insurance at Marina Bay Sands

## Introduction

At some baccarat tables, the player may make mid-state proposition bets, generally with the purpose of insuring a winning hand. I discuss such bets in general in my page on baccarat insurance. To avoid that page getting too long, this page focuses on those insurance bets at the Marina Bay Sands in Singapore.

As usual, when writing about baccarat, to avoid confusion, I use lower case when referring to players playing the game and upper case when referring to bets.

## Player Win after Four Cards

The following table shows situations where players may bet on a Player win after four cards are dealt. Insurance bets win on a Player win, lose on a Banker win, and push on a Tie.

### Player Win after Four Cards

Player
Total
Banker
Total
Pays Probability
Player Win
Probability
Banker Win
Probability
Tie
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

## Banker Win after Four Cards

The following table shows situations where players may bet on a Banker win after four cards are dealt. Insurance bets win on a Banker win, lose on a Player win, and push on a Tie.

### Banker Win after Four Cards

Player
Total
Banker
Total
Pays Probability
Player Win
Probability
Banker Win
Probability
Tie
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

## Player Win after Five Cards

The following table shows situations where players may bet on a Player win after five cards are dealt. Insurance bets win on a Player win, lose on a Banker win, and push on a Tie.

### Player Win after Five Cards

Player
Total
Banker
Total
Pays Probability
Player Win
Probability
Banker Win
Probability
Tie
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

## Banker Win after Five Cards

The following table shows situations where players may bet on a Banker win after five cards are dealt. Except in situations where Player has a total of nine, insurance bets win on a Banker win, lose on a Player win, and push on a Tie. When the Player does have nine points, insurance bets on the Banker win on a tie and lose on a Player win.

### Banker Win after Five Cards

Player
Total
Banker
Total
Pays Probability
Player Win
Probability
Banker Win
Probability
Tie
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

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