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[offaxis]

Banker 3 cards win 7
-7 (9,5,3)
+4 L
-1 (3,9,5)
0 (7,3,7)
+5 L
+4 L

[AsymBacGuy]

Let's see if we can get some help from additional mathematical considerations.

The probability to get a EZ dragon bonus is 2.25%, so we'll have on average about two occurences per every 100 hands dealt.

Of course not every Banker three card combination will get the same probability to produce a Dragon Bonus.

Zero-zero-7 will account the highest ratio by far: 19.2%;
the next more likely scenario is zero-2-5 (6%), then zero-1-six (4.8%) and so on.

So zero value cards and sevens will produce the highest number of Dragons, then there are zero value cards with 5s and 2s and zero value cards with 6s and 1s.

Despite of what the aforementioned system prescribes, we see that 3s and 4s might play an inferior role than zeroes, 7s, 5s, 2s, 6s and 1s.

Of course cards denying the possible appearance of Dragon Bonus are 8s and 9s for two distinct reasons:

- the likelihood to get naturals is higher when a deck is rich of those cards;

- any third card being an 8 or 9 (on both sides) more often than not will dictate a standing Banker hand (totally denying the DB possibility) or a total Player point higher than 7 and an outcome different than 7 when Banker takes an 8 or 9 as a third card.

So we could reconsider a perfect deck to be more likely to produce Dragon Bonus if it's (in descending order):

- particularly poor of 8s and 9s

- particularly rich of zero value cards

- particularly rich of 7s

- particularly rich of 5s, 2s, 6s and aces.

An interesting sidenote is trying to assess which B/P side is more likely to show up in those instances in a sort of "backup" betting plan.
Of course contemplating many classes of cards will get too numerous combinations, so we should get more help restricting our course of action. 

Since the most likely scenario to get a DB is a deck full of zero value cards and 7s and poor of 8s and 9s, we know that such situation will entice more standing 7s on each side, but one side will be 5% taxed with the other one being 1:1 payed.

So our best "backup" plan in those (rare) circumstances should be to bet the Player side with the hope to hit the DB bet.

as.