Pai Gow math help

Hi all,

According to Wizard, there are 6,172,088 flushes, 184,644 straight flushes, and 26,020 royal flushes out of 154,143,080 possible hands. What I'd like to do is pull out the natural flushes, straight flushes, and royal flushes. If the hand has a joker in addition to the natural hand, that's okay.

Thanks!

=permut(13,5)*4

Quote: Deucekies

Hi all,

According to Wizard, there are 6,172,088 flushes, 184,644 straight flushes, and 26,020 royal flushes out of 154,143,080 possible hands. What I'd like to do is pull out the natural flushes, straight flushes, and royal flushes. If the hand has a joker in addition to the natural hand, that's okay.

Thanks!

I'm having trouble understanding what you are asking.

First, we are discussing the seven-card hands, correct?

1. There are straight flushes that can be 5, 6 or 7 cards long -and the 5-or 6-card straight flushes may or may not have additional cards in the suit of the straight flush.

2.There are natural flushes that can be 5, 6 or 7 cards long that do not contain a sequence of 5 or more consecutive ranks and therefore are not straight flushes.

The reason you need to worry about all of this is, for example, that a 6-card straight flush can be double (or triple) counted as also being two different combinations of a five card straight flush. If a 7 card hand that contains a 5-card straight-flush also has one or two other suited cards, then the hand also is several combinations of a 5-card natural flush hand. You have to be very careful with your combination formulas to avoid double-counting.

Consider this combination of seven cards: A-h, K-h, Q-h, J-h, T-h, 9-h, 4-h
1. It contains a royal flush.
2. It contains a K-high straight flush.
3. It also contains 19 different 5 card flushes ranging from AKQJ9 down to QJT94.


So, are you asking:

1. How many 7-card hands can form a natural 5-card royal flush, i.e., without the assistance of a joker even if a joker is present in the hand?
2. How many 7-card hands that are not included in the royal flush category above can form a natural (5-card or longer) straight flush (without the assistance of a joker) ?
3. How many 7-card hands that are not included in either the royal flush category or the straight flush category above will contain a natural (5-card or longer) flush -that is, at least 5 suited natural cards even if a joker is present in the hand?

That sounds right. Hopefully this answers your question.

Imagine the pay table on the Fortune bonus had a line for "Wild Flush" and one for "Natural Flush", "Wild Straight Flush" and "Natural Straight Flush", etc.