Quote Originally Posted by Levian
Pyroxene, what are the odds for you to flop a pair (hole cards) while villain flops a higher pair (with his hole cards that both are above yours) in a heads up match?

So basically like:
You hold 78, villain holds QJ, What are the odds for you to flop a 7 or an 8 while villain flops a Q or a J?

And what are the odds if he's holding like Q-4?
Levian,

I am also new, and am going to attempt to answer your question because I want to practice calculating odds myself. I would love for someone to check my math, as I'm sort of treating this like a GRE practice question, so:

For the purposes of this exercise, it's not relevant to take into account that villain has two hole cards higher than yours, only that he has two hole cards different from yours. So, you are looking for the probability of him hitting one of his hole cards, and you hitting one of your hole cards, and the third card coming up a blank for both of you:

(6 * 6 * 38)/(50 * 49 * 48) = .01163

Since this can happen one of three ways, multiply that by 3 and you get .034898, or 3.5%

That's your answer for the 78 v QT problem, since it doesn't matter which hole card he hits, or which hole card you hit, either way you'll be behind.

For the 78 v Q4 question, since villain only has one hole card that can beat you, you just chop that percentage in half. There'll still be a 3.5% chance of you both hitting hole card, but only the higher card will put villain ahead. In other words:

(6 * 3* 38)/(50 * 49 * 48) * 3

These percentages only represent the chances of you and villain both hitting EXACTLY one pair.

Now, having done the math, I would recommend that, regardless, if you're playing suited connectors or gappers, and you pair the board with no draws, and there are overcards, you're probably gonna want to play the hand with extreme caution.