The purpose of this appendix will be to show why the player should insure then split aces against an ace in Realtime Gaming casinos using 2 or 4 decks. It will also show why to take insurance with two eights or 11 against a dealer ace in a 2-deck game, but not a 4-deck game. If you are not familiar with the rules of this game please see my Realtime Gaming review. Tables are shown for both 2 and 4 decks, the most common configurations for Realtime Gaming casinos. In my experience Realtime Gaming casinos use four decks, which explains why I advise only taking insurance with two aces against an ace in my Realtime Gaming basic strategy.
The following table shows the expected return of all affected hands assuming the dealer does not have a blackjack. These numbers can be found in my blackjack appendix 9.
Expected values, no dealer BJ - 2 decks
Dealer
Player
Hit
Dbl./Split
A
A,A
-0.067327
0.157378
A
8,8
-0.531321
-0.493242
A
6,5
0.121079
0.16665
A
7,4
0.118882
0.1615
A
8,3
0.117332
0.150867
A
9,2
0.116041
0.141065
Expected values, no dealer BJ - 4 decks
Dealer
Player
Hit
Dbl./Split
A
A,A
-0.065388
0.129936
A
8,8
-0.536768
-0.508893
A
6,5
0.11171
0.134492
A
7,4
0.110619
0.131911
A
8,3
0.109865
0.126656
A
9,2
0.109244
0.121847
Considering the possibility of a blackjack the following table shows the expected value of doubling and splitting the same plays. These numbers can be derived from table 1 and a probability of blackjack of 32/101 for 2 decks and 64/205 for 4 decks. These tables clearly show why the player should never double or split if the dealer has a possible blackjack.
Expected values, possible dealer BJ - 2 decks
Dealer
Player
Hit
Dbl./Split
A
A,A
-0.362827
-0.526148
A
8,8
-0.679813
-0.970631
A
6,5
-0.234114
-0.519813
A
7,4
-0.235615
-0.523332
A
8,3
-0.236674
-0.530596
A
9,2
-0.237556
-0.537292
Expected values, possible dealer BJ - 4 decks
Dealer
Player
Hit
Dbl./Split
A
A,A
-0.357169
-0.53502
A
8,8
-0.681387
-0.974409
A
6,5
-0.23536
-0.531886
A
7,4
-0.236111
-0.533661
A
8,3
-0.236629
-0.537276
A
9,2
-0.237057
-0.540583
The cost of insurance on a half unit bet in a 2-deck game is (32/101)*1 + (69/101)*(-0.5) = -0.024752475. Likewise the cost in a 4-deck game is (64/205)*1 + (141/205)*(-0.5) = -0.031707317. The next two tables show the expected return of hitting without taking insurance, and doubling and splitting with taking insurance, both assuming a possible dealer blackjack. The last column shows the correct play.
