strange odds question?

DennisG

I am trying to figure out the math on this..

difference of odds between royal flush and 7 card straight flush.

I know the royal is 1:650k ish..but..how do I go about determining the 7 card straight flush? I know is isn't a valid hand..but was just a topic of discussion...

There are still 32 possiblilities of it in a deck, and only 4 in the royal flush...but it does require two extra cards..??

SuitedPair

Find the total number of seven card hands possible and divide by 32.... I think

Would do the math for you but my mind is a bit....hazy

MickeyHoldem

As you stated there are 32 possible 7 card straight-flushes. There are 4 royals that can be combined with any 2 of the remaining 47 cards, or 4x(47choose2)=4324. 4 of these would be 7 card straight-flushes that include the royal, leaving 4320 non-seven card royals.

... so you are 135 times more likely to get a royal flush* as aposed to a seven card straight flush.


*of the non-seven card variety