Poker Forum > Strategy
How many times does Kings run into Aces pre flop
noble1:
probability forum please ;D
Swinebag:
--- Quote from: coprey on January 28, 2009, 13:32:53 PM ---
0.03875536896 does this equate to 3.86%?
--- End quote ---
its actually 3.88 % (to 2 d.p.)
--- Quote from: coprey on January 28, 2009, 13:32:53 PM ---
How do you arrive at the following calculation:
(11 x 10 x 9 x 8 x 7)/(1 x 2 x 3 x 4 x 5)
--- End quote ---
It is using the formula for working out how many combination there are from choosing 6 from 11 (which is identical to choosing 5 from 11)
the formula is
number of combinations choosing r (aces winning 6 times) from n (11 races) =
n!/(n-r)! r!
the "!" notation is factorial, e.g. 4! = 1 x 2 x 3 x 4, 7! = 1 x 2 x 3 x 4 x 5 x 6 x 7
the above formula cancels down to give the calculation you quoted. We need to use it because in the case of the Aces winning 6 out of 11 races against Kings, there is no specific race that the aces have to win. For example, Aces could have held up the first 6 times, or the last 6 times or they could have held up in the 1st, 2nd, 4th, 8th, 9th and 10th race. In fact there are 462 different ways that Aces can beat kings 6 out of 11 times.
An simpler example of this calculation in action is used in lucky 15 or lucky 31 bets at the bookies. If you pick 5 horses in a lucky 31 there are 10 possible doubles, namely
1,2
1,3
1,4
1,5
2,3
2,4
2,5
3,4
3,5
4,5
Using the formula you get 10 by using n=5 and r =2 and this simplifies to (5 x 4)/(1 x 2)
bring your maths exercise book with you to Walsall colin, and you can do a few examples when you are card dead....I"ll mark it in the break ;D
noble1:
if you working out doubles rob say like in your example of 5 selections you could also work it out in your head by adding 4,3,2,1 =10 doubles
4 selections = 3+2+1=6 doubles
7 selection = 6+5+4+3+2+1=21 doubles
would that be ok?
Swinebag:
--- Quote from: noble1 on January 28, 2009, 14:14:05 PM ---
if you working out doubles rob say like in your example of 5 selections you could also work it out in your head by adding 4,3,2,1 =10 doubles
4 selections = 3+2+1=6 doubles
7 selection = 6+5+4+3+2+1=21 doubles
would that be ok?
--- End quote ---
for doubles only, yes.
noble1:
can i have £5 e/w on your next 5 selections please? ;D
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