Probability of flopping a royal flush?

[poker_nut]

Just wanted to know:

If you held, say Kh Jh, then what is the probability that you will flop a royal flush?

Thanks in advance.

Poker_nut.

[balsamono]

There are 50 unseen cards. There are 50*49*48 possible flops, but this counts [2c 5h 9d] and [5h 9d 2c] as different flops. There are 6 different ways of arranging 3 specific cards, so there are 50*49*48/6=19600 different combinations of cards that can flop. Only one of these give you a royal flush, so the chance is 1/19600, or about 0,005 %. I think this is correct, but it's getting late here...

[balsamono]

I'll even try to calculate the probability of making a royal flush by the river. You need a specific three-card hand on the board, so you have to calculate the number of three-card hands you can choose from a five-card board. The first of the two cards you don't use in your hand can be in 5 different positions, and the second in 4 positions. There are 5*4 ways of selecting two arranged positions from five positions. Because the arrangement doesn't matter here, divide by two. 5*4/2=10, so there are 10 different 3-card hands on a 5-card board. Any of these can be [Ah Qh Th]. The probability of making a royal flush if you play until the river, is therefore 1/1960 or about 0,05 %.

[kimchi]

[ QUOTE ]
so the chance is 1/19600, or about 0,005 %.

[/ QUOTE ]

I've played 40k hands and I've flopped a Royal Flush once, and rivered another (both in the same week [img]/images/graemlins/cool.gif[/img])

So this means I'm due to flop another soon..........