Black Jack Appendix 13
In playing blackjack online
one problem I often face is not knowing how many decks are being used. This is a
particular problem with Real Time Gaming casinos. The help files often do not
indicate this rule, as well as other rules, and customer support are notorious
for giving incorrect information on their own rules. So I devised a test to help
determine the number of decks. This test is based on the player's first two
cards and the dealer's first two.
The following table shows the probability for various configurations of the
initial four cards in blackjack. Note the probabilites for a suited pair. Of all
the hands I feel this is the best to test for, given both it's frequency and
correlation to number of decks.
| 4-Card Hand |
1 deck |
2 decks |
4 decks |
6 decks |
8 decks |
| 4 singletons |
0.676110 |
0.63692 |
0.618504 |
0.612530 |
0.609573 |
| Non-suited pair |
0.304250 |
0.286614 |
0.278327 |
0.275638 |
0.274308 |
| Suited pair |
|
0.047769 |
0.069582 |
0.076566 |
0.080006 |
| Two non-suited pairs |
0.010372 |
0.009771 |
0.009488 |
0.009397 |
0.009351 |
| Two suited pairs |
|
0.000271 |
0.000593 |
0.000725 |
0.000796 |
| Two pair - 1 suited |
|
0.003257 |
0.004744 |
0.00522 |
0.005455 |
| 3 of a kind - 3 suits |
0.009220 |
0.008685 |
0.008434 |
0.008353 |
0.008312 |
| 3 of a kind - 2 suits |
|
0.006514 |
0.009488 |
0.010441 |
0.010910 |
| 3 of a kind - 1 suit |
|
|
0.000527 |
0.000773 |
0.000909 |
| 4 of a kind - 4 suits |
0.000048 |
0.000045 |
0.000044 |
0.000044 |
0.000043 |
| 4 of a kind - 2 suits (3&1) |
|
|
0.000033 |
0.000048 |
0.000057 |
| 4 of a kind - 2 suits (2&2) |
|
0.000017 |
0.000037 |
0.000045 |
0.000050 |
| 4 of a kind - 3 suits |
|
0.000136 |
0.000198 |
0.000218 |
0.000227 |
| 4 of a kind - 1 suit |
|
|
0.000001 |
0.000002 |
0.000003 |
| Total |
1 |
1 |
1 |
1 |
1 |
To determine the number of decks in an online blackjack game keep a tally of
both the total number of hands played and the number of suited pairs. Only count
a hands as a suited pair if the other two are singletons. For example one suited
pair and one non-suited pair does not count. In a single deck game the ratio of
suited pairs to total hands will obviously be zero. In double deck this ratio
will be about 4.8%. In a 4-deck game the ratio increases to 7.0%. After that the
differences are too subtle are to tell without a gigantic sample.
Of course if you ever notice three of the same card on the screen at once
that rules out a double deck game immediately. Despite my lack of faith in
customer support knowing their own rules I would suggest at least asking. If
they give you an incorrect answer, and you can prove it, you may get some free
money in your account as a way of thanks. This has happened to me several times.
Unfortunately it takes a fairly large sample size to have confidence in the
number of decks between 2 and 4. After 250 hands the probability that the sample
mean in a 2-deck game will be greater than 6.96% (the 4-deck theoretical mean)
is 5.29%. Likewise the probability that the sample mean in a 4-deck game will be
less than 4.78% (the 2-deck theoretical mean) is 8.76%. Increasing the sample
size to 500 these numbers become 1.11% and 2.76%. At 1000 the numbers are 0.06%
and 0.34%.
