High Card only count

How many 5 card poker hands only have a high card, i.e no pair, straight, flush, e.t.c? A breakdown of high cards would also be appreciated.

I do know what is special about 23457 off-suited - any card improves it.

• Not entirely sure what you mean? Any hand without at least a pair is a "high card" hand. Are you looking for a formula to calculate how many there are? – Toby Booth Jan 26 '15 at 13:44
• I can't see how you would go about it other than laying out every hand and counting those whose highest score is high card. – JMP Jan 26 '15 at 14:51
• See this link en.wikipedia.org/wiki/Poker_probability – paparazzo Apr 13 '17 at 22:58

2 Answers

From the Wikipedia article on Poker Hands:

Of the 2,598,960 possible five-card combinations, {formula elided} 1,302,540 do not contain any pairs and are neither straights nor flushes. As such, the probability of being dealt "no pair" in a five-card deal is approximately 50.11%

In seven-card poker, the frequency of such "no pair" is 23,294,460; the probability of being dealt one is approximately 17.4%.[4][Note 3]

The article also has the formula for calculating it, which didn't translate well to this site.

If you mean distinguishable hands, 1277.

http://www.suffecool.net/poker/7462.html

If you mean all hands, dantiberian's 1302540 is correct.