ChuckTs asked in a PM:
what are the odds that 64o will outflop AA/KK?
Ok, let's look at that...
You get 3 cards on the flop and let's say, by outflop, you mean a hand that beats AA/KK after the flop.
The easiest example is we flop our straight. We can do this with 235, 357, or 578. Oh boy, this is going to get intricate... sorry in advance. The first card must be a 2,3,5,7,or 8. Make a diagram as we go and it will be easier to see I'm sure, but I'm just going to talk myself to the solution as I type... lol. The chances of that first card being one we need are 20/48 or 5/12. That was easy! The next card needs to be one of the remaining cards so odds of that are not as easy to calculate. If, for example, the first card is a 2, the next card must be a 3 or 5. However if first card is a 5, the next card can be any of our remaining cards. Let's break it down into 2 ways to think about it:
First Card Is _______Next Card Must Be ______3rd card on flop Must be _______"The Math" ________Frequency of Event (Odds)
2 __________________3 or 5 ______________whichever needed (5 or 3)_________TO do for homework (LOL)
3 _________________2 or 5 or 7 __________whichever of those 2 needed
5 __________________2 or 3 or 7 or 8________further divided a la above
7 __________________3 or 5 or 8 __________WILL BE THE SAME process as if 3 is "first card" on flop
8 _________________5 or 7 _________________Ditto, same reasoning as if 2 is "first card" on flop
Now-- easier way... one card must be a 5: so Probability of 5 on flop = 1 - (probability of no 5 on flop) = 44/48 x 43/47 x 42/46 = 1 - 76.57% (rounded) = 23.43% of chance of 5 on flop. Multiply that by the chance of: i. a 2 and 3 on flop PLUS ii. 3 and 7 on flop PLUS iii. 7 and 8 on flop.
Do the math for these and then apply the same reasoning to possibility of 2 4's on flop, 2 6's on flop and both a 4 and 6 on flop. Then you will have your answer. I can do the math for you if you want, but it's a good exercise for the reader at home.