3 card poker odds maths

Ok smart guys time to make yourselves feel clever and me sound dumb. I have a little math question. I read the wizard of odds 3 card poker probablilty page..

I tried to work it out for myself, the odds of getting hands.

Heres my calculation for getting a pair..

52 cards

The first card that is dealt I think is irrelavant, you will get some kind of card that’s for sure.

So lets say we have the 5 of diamonds

The probablilty of getting another 5 of a different suit to make a pair on the second card is 3/51 and on the third card is 3/50(presuming we didn’t get one the first time) 0.58% + 0.6% = 1.18%

But according to the wizard of odds page, the probability of getting a pair is 16.94%

Please tell me why the wizard is right and I am wrong :(

thanks - please dont say becasue he's smart and im not..:/ i just genuinely cant work it out. I did do some basic statistics in maths with permutations and combinations and that but this calculation is WAY off and its making my head hurt.

Consider these three cases to make a pair:

1) The second card is a 5, and the third card is not a 5: p1 = (3/51)(48/50) = 5.647%

2) The second card is not a 5, but the third card is a 5: p2 = (48/51)(3/50) = 5.647%

3) The second card is not a 5, but the third card is the same rank as the second card: p3 = (48/51)(3/50) = 5.647%

p1 + p2 + p3 = 16.94%


Also, the following will help you with your percentage calculations: 3/50 = 6/100 = 6% (not 0.6%)

that makes great sense, thanks for taking the time to write that out.