Ok I'm still bad at poker. That's good; less reason to be annoyed.
If you have AT in your hand against a MP raise with a reasonable range, you rather have the Flop AQ5 than AQT. This blow my mind, which shows that I still don't know sh*t. My estimate was that getting the T and hence the second pair would increase win chances by maybe 15-20%, but it decreases it by 6% compared to the 5.
Yeah I mean screw two pairs, who needs that.
As someone who doesn't play poker at all and doesn't know what MP raise means, is this just because people are more likely to have a straight in the AQT scenario than to beat you with 2 pair or something in the AQ5 scenario? Does it depend on number of players?
So MP is middle position, and raise means that the people before them folded and then they raise, i.e., bet something like three big blinds. And this matters we assume that people use different hands to raise from different positions. In this case, we assume middle position raises all these hands (and folds the rest):
So all the probabilities are against a randomly sampled hand from that set. So it depends on the position of your opponent, the number of players only matters indirectly. (Of course if your opponent actually raises every hand, then position no longer matters and these are just the wrong probabilities.)
Now my main takeaway from the two pairs being so bad here is that the importance of a second pair varies widely depending on circumstances. To choose an extreme example, suppose we're against the same range and have 65. Then with the Flop A52, we have ~37% to win, whereas with A56, we have 78%, so the second pair is extremely important. And it makes sense; there are no 5s in the opponent's range, so with one pair of 55 we win if the opponent hit nothing but lose to every pair, whereas with two pairs, we beat every pair. So that's a big difference.
But in the case of AT and a Flop of AQ5, we already have the best possible pair, so we're already beating most pairs of the opponent. And of course two pairs also loses to trips and straight and flushes, so there just aren't a lot of extra hands we beat. Specifically, the second pair is really good against AK and AJ since those were hands that we don't beat otherwise. Everything else, we either already beat without the second pair, or still lose to with the second pair.
And then yeah the straight, which you wouldn't think is that likely, seems to be a bigger factor than those few extra hands we beat. If opponent has KK, KQ, KJ, QJ, or even TT or JJ, then the extra T is bad for us. Conversely the 5 doesn't help your opponent at all, it's just a dead card, and we like dead cards since our hand is currently good.