NEWTDOG101
Visionary
Silver Level
B
BlueNowhere
Legend
Silver Level
50C3/11C3 = 118.78 or 117.78 to 1. As a percentage 0.842%.
50C3 is the number of ways that 3 cards can fall given the 50 remaining in the deck. 11C3 is the number of ways 3 to the flush fall given that there's 11 left in the deck. divide one by the other gives you the percent. 11C3 gives you the total combinations of flush flops given you hold two. 50C3 is total combos that flop can land on.
Yea I rule at maths.
50C3 is the number of ways that 3 cards can fall given the 50 remaining in the deck. 11C3 is the number of ways 3 to the flush fall given that there's 11 left in the deck. divide one by the other gives you the percent. 11C3 gives you the total combinations of flush flops given you hold two. 50C3 is total combos that flop can land on.
Yea I rule at maths.
Samango
Legend
Silver Level
I'm not familiar with that notation Blue. What is C in 50C3, and I'm surprised that you can divide one resultant number by the other to arrive at the result ( because the usual way that I'm familiar with, would be three separate calculations for each card on the flop, multiplied together) Can you show me the workings of the way you do it?
B
BlueNowhere
Legend
Silver Level
Yea multiplying together works fine in this scenario but can get impossible when you do things that aren't this simple, hence me using the notation I did as that's what I usually use. The C is the the notation used for combinations in nCr, it's a button on a calculator that saves you having to put into your calculator n!/(r!(n-r!)). It's what is used to find the number of combinations when order doesn't matter.
Basically if you think about it it makes sense. If the total number of combos that make your flush can be represented with 11C3 so in total there will be 165 combos of flushes that you can flop. then the total different flops that are possible is 50C3 which is 19600. so to work out the chance of flopping one of the 165 combos from a total of 19600 combos you just divide one by the other. It's just the same as if you have 20 apples in a basket and 5 are red the chance of choosing a red apple is total red/total apples. Then if you want two reds apples in a row the way you calculate the chance is 5C2 (the way you can choose two red apples from 5). Then you would divide this number by the total ways you can choose two apples (20C2)
So the working is basically 11C3/50C3 for the probability, that can be written as (11!/3!8!)/(50!/3!47!). Now if you simplify this it becomes (11x 10x9/3x2x1)/(50x49x49/3x2x1). Which can be simplified to 11x10x9/50x49x48 which is the form you stated of just multiplying all the individual odds together. This would just be the correct way to represent it and can be used for more complex things which can't just be thought of in the sense of multiplying probabilites together.
11!/3!8! can be sinplified to 11x 10x9/3x2x1 because 11x10x9x8x7x6x5x4x3x2x1/(3x2x1)x(8x7x6x5x4x3x2x1). The underlined parts cancel out to give the answer 11x 10x9/3x2x1 Apply the same logic to 50C3.
Hopefully I've explained that so you understand it.
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Samango
Legend
Silver Level
Thanks Blue, that is good. I don't have an nCr button on any of my calculators though, but I get the factorial division that it is doing.
How odd that you would even consider that I hadn't looked on a scientific calculator before posting that... and odd too that you would believe that because you think that they all have it, that they all do. Nope
Attachments
Samango
Legend
Silver Level
Apparently the max height for an attachment is 280 (same as the Windows calculator pic) which is why I rotated the other one
It seems really dumb to me to bias the orientation of attachment to landscape view 620w x 280h. It is never going to be a problem to scroll down the page if necessary.
It seems really dumb to me to bias the orientation of attachment to landscape view 620w x 280h. It is never going to be a problem to scroll down the page if necessary.
