For the benefit of those not familiar with the Dragon Bonus, it is a side bet that pays based on the margin of victory in baccarat. It pays 30 to 1 for a margin of victory of 9 and the nine-point hand was not a natural.
The average number of hands in a baccarat shoe is 80.884, but let's just say 81 to make the math easier.
Using the binomial formula, the following table shows the probability of 0 to 10 30-1 wins in 81 hands.
Dragon Bonus 30-1 Wins per Shoe
WinsProbability 10 0.0000000002 9 0.0000000047 8 0.0000000857 7 0.0000013607 6 0.0000186536 5 0.0002163066 4 0.0020630955 3 0.0155401441 2 0.0866801257 1 0.3182950376 0 0.5771851856 Total 1.0000000000
The table shows the probability of exactly eight 30-1 wins is 0.0000000857, or 1 in 11,670,083.
The probability of eight or more wins is 0.0000000907, or 1 in 11,029,777.
This question is asked and discussed in my forum at Wizard of Vegas.