[KJL]

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What are the odds (and the math) of flopping exactly 1 pr from two non-paired cards? I've seen anywhere from 27-30%

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1-[(44/50)*(43/49)*(42/48)]= a 32.5% chance to make a pair or better, when holding 2 no-paired cards.
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What are the odds of making a straight by the river (pre-flop odds, that is) of connectors (87o etc.)?


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This is actually hard to do because different connectors make a different number of straights.
For AK and A2:
[4*4*4*C(47,2)]/C(50,5)=~3%
For KQ and 23:
[2*4*4*4*C(47,2)]/C(50,5)=~6.5%
For QJ and 34:
[3*4*4*4*C(47,2)]/C(50,5)=~10%
For all other connectors:
[4*4*4*4*C(47,2)]/C(50,5)=~13%
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And for 1-gap connectors?


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For AQ and A3:
[4*4*4*C(47,2)]/C(50,5)=~3%
For KJ and 24:
[2*4*4*4*C(47,2)]/C(50,5)=~6.5%
For all others:
[3*4*4*4*C(47,2)]/C(50,5)=~10%
Note: The numbers 1-gapers only include when you use both of your hole cards to make the straight. It does not include the times when you hold AQ and the board reads JT98x I will add these calculations later, if you want.