Incredible Blackjack Hand Last Saturday night I played at Bally's in Atlantic City and got a hand I could not believe. Dealer had 9 and I was dealt 2 8s. I split the 8s and was given a third card. It was an 8 so I split them again. The next card I was dealt was a fourth 8. This has happened to me three other times in my life, so no big deal. The fifth card was again an 8 and the sixth consecutive 8 followed. No one at the table or the dealer or even the pit boss had ever seen that before. I do not even know how to start calculating what the odds are in getting 6 straight cards of the same denomination from an 8 deck shoe, which holds 416 cards. Can you help me?

Calculations from symmetricuser were all perfect when trying to calculate the probability of taking, for example, 6 8's in a row. Even though you ask for 6 cards in a row, of any denomination, so you are not forcing the number. Therefore, you have to multiply that for all the 13 possible denominations.
$$13\times \frac{\binom{32}{6}}{\binom{415}{6}} \approx 1.72\times 10^{-6},$$
