All right folks.
First off, please understand that having a 1st-card advantage means that the player has somehow found out what the first card of the as-yet undealed coup is.
This is at worst cheating or at best, if the dealer or procedures are weak, advantage play.
1st-card advantage is essentially a study of all the possible card permutations that start with Ace through to King that result in a Player, Banker or Tie result from the remaining cards in the shoe.
The 2 tables below show that knowing that the 1st card is a 1-5 or 10-K, would give a small advantage on the Banker wager. Knowledge of the 1st card being 6-9 would give an increasing advantage on the Player wager, with knowing a 1st card as being 9 giving a 21% advantage on the Player wager.
Below is a table that shows the probabilities before the start of the shoe:
Card Value: | Player Win | Banker Win | Tie | Player Win % | Banker Win % | Tie % | Player Exp | Banker Exp | Tie Exp |
1 | 159,747,170,699,264 | 189,857,873,692,672 | 34,887,130,646,784 | 41.5476% | 49.3789% | 9.0736% | -0.0783 | 0.0536 | -0.1834 |
2 | 160,408,944,947,200 | 188,725,567,889,408 | 35,357,662,202,112 | 41.7197% | 49.0844% | 9.1959% | -0.0736 | 0.0491 | -0.1724 |
3 | 161,429,794,906,112 | 187,253,976,461,312 | 35,808,403,671,296 | 41.9852% | 48.7016% | 9.3132% | -0.0672 | 0.0428 | -0.1618 |
4 | 162,751,823,355,904 | 184,376,516,966,400 | 37,363,834,716,416 | 42.3290% | 47.9533% | 9.7177% | -0.0562 | 0.0323 | -0.1254 |
5 | 166,618,505,969,664 | 179,969,323,315,200 | 37,904,345,753,856 | 43.3347% | 46.8070% | 9.8583% | -0.0347 | 0.0113 | -0.1128 |
6 | 173,075,882,563,584 | 170,168,183,390,208 | 41,248,109,084,928 | 45.0141% | 44.2579% | 10.7279% | 0.0076 | -0.0297 | -0.0345 |
7 | 185,770,147,510,272 | 157,451,915,216,896 | 41,270,112,311,552 | 48.3157% | 40.9506% | 10.7337% | 0.0737 | -0.0941 | -0.0340 |
8 | 206,999,120,039,936 | 140,506,916,139,008 | 36,986,138,859,776 | 53.8370% | 36.5435% | 9.6195% | 0.1729 | -0.1912 | -0.1342 |
9 | 215,108,869,548,032 | 132,334,879,180,800 | 37,048,426,309,888 | 55.9462% | 34.4181% | 9.6357% | 0.2153 | -0.2325 | -0.1328 |
0 | 638,608,023,052,288 | 761,607,414,185,984 | 137,753,262,916,608 | 41.5228% | 49.5203% | 8.9568% | -0.0800 | 0.0552 | -0.1939 |
This table shows the same 16 cards in for each card value, so technically, halfway through the shoe:
Card Value: | Player Win | Banker Win | Tie | Player Win % | Banker Win % | Tie % | Player Exp | Banker Exp | Tie Exp |
1 | 2,404,712,210,944 | 2,862,066,979,328 | 525,341,662,848 | 41.5170% | 49.4131% | 9.0699% | -0.0790 | 0.0543 | -0.1837 |
2 | 2,414,405,553,152 | 2,845,665,957,888 | 532,049,342,080 | 41.6843% | 49.1299% | 9.1857% | -0.0745 | 0.0499 | -0.1733 |
3 | 2,427,320,125,440 | 2,826,650,029,056 | 538,150,698,624 | 41.9073% | 48.8016% | 9.2911% | -0.0689 | 0.0445 | -0.1638 |
4 | 2,441,864,919,040 | 2,787,715,898,880 | 562,540,035,200 | 42.1584% | 48.1294% | 9.7122% | -0.0597 | 0.0356 | -0.1259 |
5 | 2,510,828,003,328 | 2,709,937,753,088 | 571,355,096,704 | 43.3490% | 46.7866% | 9.8644% | -0.0344 | 0.0110 | -0.1122 |
6 | 2,609,779,693,056 | 2,562,217,828,352 | 620,123,331,712 | 45.0574% | 44.2363% | 10.7063% | 0.0082 | -0.0303 | -0.0364 |
7 | 2,801,721,069,056 | 2,369,605,165,568 | 620,794,618,496 | 48.3712% | 40.9108% | 10.7179% | 0.0746 | -0.0951 | -0.0354 |
8 | 3,123,172,254,720 | 2,113,348,414,464 | 555,600,183,936 | 53.9210% | 36.4866% | 9.5923% | 0.1743 | -0.1926 | -0.1367 |
9 | 3,240,895,371,776 | 1,993,736,233,472 | 557,489,247,872 | 55.9535% | 34.4215% | 9.6250% | 0.2153 | -0.2325 | -0.1338 |
0 | 9,633,645,025,280 | 11,472,680,607,744 | 2,062,157,779,456 | 41.5808% | 49.5185% | 8.9007% | -0.0794 | 0.0546 | -0.1989 |