I think the odds as articulated suffer for only going out two decimal places. Let me explain why I think so and hopefully someone smarter than me can confirm or deny:
Heads-up, after the flop, there are 7 cards accounted for. The most extreme odds are generated by requiring two exact cards from the deck. Example like Heffmike's need-to-draw-two-to-quads, or this one: AcKc vs 7c2h, flop comes 2c3c4c. The dude with the 7 can only win if the 5c and 6c come up. That's 1/45 times 1/44, or one chance in 1,980, or about six times harder to nail than 3/1000.
At a full table your odds are a little better as fewer cards are left. There your odds are one in 930, still three times harder than 3/1000.
actually, it's the same scenario, because your 1/45 x 1/44 math implies it matters which order the cards come on the turn and river - which it doesn't.
so it's actually 2/45 (5c or 6c on turn) and 1/44 (whichever one didn't come on the turn spikes the river) to make 2/1980 or.....
1/990. Back where we started.
Boy, it's like I was a math/science major at one point in my life.
5 comments:
sure, easy, top set vs. running perfectperfect quads, happens all the time :-)
http://twodimes.net/h/?z=7423668
pokenum -h 7d 6s - ah ad -- as 2c 7h
Holdem Hi: 990 enumerated boards containing As 2c 7h
cards win %win lose %lose tie %tie EV
6s 7d 1 0.10 989 99.90 0 0.00 0.001
Ad Ah 989 99.90 1 0.10 0 0.00 0.999
triplets are even rarer.....hahahaha
I think the odds as articulated suffer for only going out two decimal places. Let me explain why I think so and hopefully someone smarter than me can confirm or deny:
Heads-up, after the flop, there are 7 cards accounted for. The most extreme odds are generated by requiring two exact cards from the deck. Example like Heffmike's need-to-draw-two-to-quads, or this one: AcKc vs 7c2h, flop comes 2c3c4c. The dude with the 7 can only win if the 5c and 6c come up. That's 1/45 times 1/44, or one chance in 1,980, or about six times harder to nail than 3/1000.
At a full table your odds are a little better as fewer cards are left. There your odds are one in 930, still three times harder than 3/1000.
Mathies? Yes? No?
actually, it's the same scenario, because your 1/45 x 1/44 math implies it matters which order the cards come on the turn and river - which it doesn't.
so it's actually 2/45 (5c or 6c on turn) and 1/44 (whichever one didn't come on the turn spikes the river) to make 2/1980 or.....
1/990. Back where we started.
Boy, it's like I was a math/science major at one point in my life.
Dad of twins here. Looks like you've used up all your run good for a while.
Congrats!
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