Red Dog Math

Didn't see this in the Red Dog section, but what are the odds of a straight flush occurring (three consecutive, suited cards) given a 6-deck shoe?

There are 312 x 311 x 310 / 6 = 180,479,520 different combinations of 3 cards from 6 decks.

If you include AKQ as a "straight flush" (as opposed to a 3-card Royal), the number of straight flushes is:
12 (Ace-low through Queen-low) x 4 (4 suits) x 6 (there are six different cards in the deck for the low card - i.e. if it is 567 of spades, there are 6 cards that are the 5 of spades) x 6 (middle card) x 6 (high card) = 10,368.

The probability = 10,368 / 280,479,520, or about 1 in 17,407.

Quote: ThatDonGuy

There are 312 x 311 x 310 / 6 = 180,479,520 different combinations of 3 cards from 6 decks.

If you include AKQ as a "straight flush" (as opposed to a 3-card Royal), the number of straight flushes is:
12 (Ace-low through Queen-low) x 4 (4 suits) x 6 (there are six different cards in the deck for the low card - i.e. if it is 567 of spades, there are 6 cards that are the 5 of spades) x 6 (middle card) x 6 (high card) = 10,368.

The probability = 10,368 / 280,479,520, or about 1 in 17,407.

The Ace is considered high in Red Dog when figuring the spread. Is it also considered high for the purposes of this question? If it is, then the number of straight flushes possible would be reduced from 12 to 11 (2-low through Q-low). Probability of a straight flush in three cards would then be: About 1 in 18,990.

Quote: ThatDonGuy

There are 312 x 311 x 310 / 6 = 180,479,520 different combinations of 3 cards from 6 decks.

If you include AKQ as a "straight flush" (as opposed to a 3-card Royal), the number of straight flushes is:
12 (Ace-low through Queen-low) x 4 (4 suits) x 6 (there are six different cards in the deck for the low card - i.e. if it is 567 of spades, there are 6 cards that are the 5 of spades) x 6 (middle card) x 6 (high card) = 10,368.

The probability = 10,368 / 280,479,520, or about 1 in 17,407.

You multiplied 30,079,920 (312x311x310) by 6 instead of dividing by 6. Therefore, the amount of 3 card sequences is 5,013,320, which when compared to the 10,368 strght flushes would give the true odds of 483-1.

I got 482.997 to 1. bUT I MAY BE WRONG.

I think the fact that in Red Dog, the straight flush must be dealt with the two "outside cards" first and then the third inside card thrid may impact the odds.

For example if the first two cards in Red Dog were: 6h & 7h....the hand woud be over and treated as a push so you would never draw the third card required to complete the straight flush (i.e. 5h).

The example straight flush above would have to come 5h/7h & then 6h or 7h/5h and then 6h.

So order is important in straight flushes actually appearing in Red Dog, not sure that was considered above.

Thank you, Paradigm, I hadn't specified that. Good Point!

Okay, so given that 1) Ace can be high or low in response to Ayecaramba's post, and 2) order does matter, what are the odds?