Blackjack Formula
The Blackjack Formula by Arnold Snyder
BA + PA + RA + SA = % PROFIT
BA = Betting Advantage
PA = Playing Advantage
RA = Rule Advantage
SA = Starting Advantage
SA = DA + v
h = number of units of high bet
n = number of decks
c = percent dealt out
x = number of extra players
BC = betting correlation
PE = playing efficiency
v = sum of effects of rule variations
DA = deck advantage
STARTING ADVANTAGE BY NUMBER OF DECKS
| DECKS | DECK ADVANTAGE |
|---|---|
| 1 | + .02 |
| 2 | .31 |
| 3 | .43 |
| 4 | .48 |
| 5 | .52 |
| 6 | .54 |
| 8 | .58 |
| 9 |
| DECKS | |||||||
| Variation | 1 | 2 | 3 | 4 | 5 | 6 | |
|---|---|---|---|---|---|---|---|
| (1) | No dbl on 11 | – .820 | – .775 | – .760 | – .753 | – .748 | – .745 |
| (2) | No dbl on 10 | -. 150 | – .480 | – .470 | – .465 | – .462 | – .460 |
| (3) | No dbl on 9 | – .130 | – .103 | – .094 | – .090 | – .087 | – .085 |
| (4) | No dbl 8,7,6 | .000 | .000 | .000 | .000 | .000 | .000 |
| (5) | No soft dbl | – .130 | – .107 | – .099 | – .095 | – .092 | – .091 |
| (6) | Hits soft 17 | – .190 | – .205 | – .210 | – .213 | – .214 | – .215 |
| (7) | No splitting non-aces | – .014 | – .027 | – .031 | – .033 | – .034 | – .035 |
| (8) | No splitting aces | – .160 | – .170 | – .173 | – .175 | – .176 | – .174 |
| (9) | No splitting non-aces | – .210 | – .230 | – .237 | – .240 | – .242 | – .243 |
| (10) | No hole card | – .100 | – .108 | – .110 | – .111 | – .112 | – .113 |
| (11) | Dbl after splits | +.140 | +.140 | +.140 | +.140 | +.140 | +.140 |
| (12) | Dbl any # cards | +.240 | +.232 | +.230 | +.229 | +.228 | +.227 |
| (13) | Dbl on 11 after split | +.070 | +.070 | +.070 | +.070 | +.070 | +.070 |
| (14) | Dbl on 14 after split | +.050 | +.050 | +.050 | +.050 | +.050 | +.050 |
| (15) | Re-split Aces | +.030 | +.055 | +.063 | +.067 | +.070 | +.072 |
| (16) | Draw to Split Aces | +.140 | +.140 | +.140 | +.140 | +.140 | +.140 |
| (17) | Surrender | +.024 | +.054 | +.065 | +.070 | +.073 | +.075 |
| (18) | Surrender (Hits Soft 17) |
+.030 | +.065 | +.077 | +.082 | +.086 | +.088 |
| (19) | Early Surrender | +.630 | +.630 | +.630 | +.630 | +.630 | +.630 |
| (20) | Early Surrender (Hits Soft 17) |
+.730 | +.730 | +.730 | +.730 | +.730 | +.730 |
| (21) | 2 to 1 Pay Off | +2.320 | +2.285 | +2.273 | +2.267 | +2.264 | +2.262 |
SYSTEM COMPARISONS
| System | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | X | A |
| Wong’s halves | +1.5 | +1 | +1 | +1.5 | +1 | +1.5 | 0 | -1.5 | -1 | -1 |
| Revere Point Count | +1 | +2 | +2 | +2 | +2 | +1 | 0 | 0 | -2 | -2 |
| Dubner/Hi-Lo | +1 | +1 | +1 | +1 | +1 | 0 | 0 | 0 | -1 | -1 |
| Ian Anderson | +1 | +1 | +1 | +2 | +1 | +1 | 0 | -1 | -1 | -2 |
| Revere Advanced (’73) | +2 | +2 | +3 | +4 | +2 | +1 | 0 | -2 | -3 | 0 |
| Uston Point Count | +1 | +2 | +2 | +3 | +2 | +2 | +1 | -1 | -3 | 0 |
| Hi-Opt II | +1 | +1 | +2 | +2 | +1 | +1 | 0 | 0 | -2 | 0 |
| Revere Advanced +/- | +1 | +1 | +1 | +1 | +1 | 0 | 0 | -1 | -1 | 0 |
| Einstein/Hi-Opt | 0 | +1 | +1 | +1 | +1 | 0 | 0 | 0 | -1 | 0 |
| Canfield Expert | 0 | +1 | +1 | +1 | +1 | +1 | 0 | -1 | -1 | 0 |
| Gordon | +1 | +1 | +1 | +1 | 0 | 0 | 0 | 0 | -1 | 0 |
| Ten Count | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | -2.5 | +1 |
