|
Percent Gain |
|
Average |
THORP |
BRAUN |
WONG |
HUMBLE |
Various sources |
No Insurance |
|
|
|
-0.4 |
|
|
Two decks |
-0.33 |
-0.35 |
-0.16 |
-0.4 |
-0.38 |
-0.35 |
Four decks |
-0.51 |
-0.51 |
|
-0.5 |
-0.54 |
-0.50 |
Five decks |
-0.29 |
|
-0.03 |
|
-0.54 |
|
Six decks |
-0.4 |
|
-0.05 |
|
-0.54 |
-0.6 |
|
|
|
|
|
|
|
Soft 17 |
|
|
|
|
|
|
Dealer hits soft 17 |
-0.2 |
-0.2 |
-0.2 |
-0.2 |
-0.2 |
|
Dealer hits soft 17 only with ace up |
|
-0.23 |
|
|
|
|
Dealer hits soft seventeen is optional |
|
-0.23 |
|
|
|
|
|
|
|
|
|
|
|
Double Down |
|
|
|
|
|
|
Double down on any two cards |
|
|
|
0.3 |
|
|
Double down on 10 & 11 only |
|
|
|
|
|
-0.26 |
Double down on 9, 10, 11 only |
|
|
|
|
|
-0.13 |
Forbid doubling down on |
|
|
|
|
|
|
all soft hands |
-0.15 |
-0.14 |
-0.1 |
-0.2 |
-0.14 |
|
Hard 8 |
O |
O |
|
|
|
|
Hard 9 |
-0.12 |
-0.14 |
-0.1 |
-0.1 |
-0.14 |
|
Hard 10 |
-0.54 |
-0.56 |
-0.5 |
|
-0.56 |
|
Hard 11 |
-0.85 |
-0.89 |
-0.8 |
|
|
|
Allow doubling down after splitting pairs |
0.12 |
|
0.14 |
0.1 |
0.1 |
0.13 |
Allow doubling down on any 3 cards |
0.19 |
0.19 |
|
|
0.19 |
|
Allow doubling down on 3 or more cards |
0.21 |
0.2 |
0.2 |
|
0.2 |
0.24 |
|
|
|
|
|
|
|
Split |
|
|
|
|
|
|
Draw any number of cards to split aces |
0.13 |
0.14 |
0.1 |
|
0.14 |
0.14 |
Forbid splitting aces |
|
-0.16 |
|
|
|
|
Forbid splitting any pair |
|
-0.46 |
|
|
|
|
Resplit aces |
|
|
|
|
|
0.02 |
Further splitting of pairs:
One deck |
|
0.05 |
|
|
|
|
Two decks |
|
0.08 |
|
|
|
|
Four decks |
|
0.11 |
|
|
|
|
All pairs 2 decks, unlimited draw to split aces |
|
0.06 |
|
|
|
|
In General |
|
|
|
|
0.05 |
|
all pairs except aces |
0.06 |
0.02 |
0.1 |
|
|
|
all pairs including aces |
0.2 |
|
0.2 |
|
|
|
|
|
|
|
|
|
|
Puerto Rican Rules |
|
|
|
|
|
|
One Deck |
|
-0.71 |
|
|
|
|
Two Decks |
|
-1.04 |
|
|
|
|
Surrender |
|
|
|
|
|
|
Surrender |
|
0.1 |
|
|
|
|
Late surrender (Las Vegas) |
0.05 |
|
0.06 |
|
0.06 |
0.02 |
Early surrender (Atlantic City) |
0.62 |
|
0.62 |
|
0.62 |
.62 - .72 |
|
|
|
|
|
|
|
Other |
|
|
|
|
|
|
Dealer shuffles when new player enters game |
|
|
|
-0.5 |
|
|
No Hole Card |
|
|
|
|
-0.13 |
|
Dealer wins ties |
|
|
|
|
-9 |
|
A,J of spades always wins double |
|
|
0.04 |
|
|
|
Blackjack is paid double |
2.32 |
2.32 |
|
|
|
2.32 |
Blackjack always wins but is paid even |
|
|
-2.06 |
|
|
|
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