Quote Originally Posted by RoyalStraight
1. The first and most obvious of reasons is that any given 2 pair is composed of 4 cards where the 3 of a kind is composed of only 3 cards. Therefore if we take that as 3/4=75% which we subtract from 100% and get 25%. Simply put, 2 pair is worth an average of 25% more than 3 of a kind. Therefore it should be ranked higher.
Yes, but 4/3=133% and if we subtract 100% from that we get 33%. It is clear that this hints that 3 of a kind should be higher.

2. The win rate of 2pair over any given 20,000 hands is nearly 16.5% higher than the win rate of 3 of a kind. Far more hands are won with 2 pair than are won with 3 of a kind. If over a 200 hand session you are dealt two pair 3% of the hands and we divide this by its wins rate over 3 of a kind(16.5), we get 0.18181818>. And for the 3 of a kinds we divide the aproximately 1.5% of the time we get 3 of a kind by the same 16.5 difference we get 0.090909>. As you can clearly see, the long run overall worth of 2 pair is more than double that of 3 of a kind! We have been accepting the mathematical error of 3 of a kind beating 2pair for all these years and i am the first to discover it and do the math for myself. If this does not convince you that 2pair should beat 3 of a kind then continue reading my other reasons below.
The 1.5% and 3% numbers are made up, making any and all conclusions futile.

3. If we were to play every hand to the river, (which I do not recommend but can be used as a profitable strategy in higher stakes games) we would see that we get 2pair nearly 16.5 percent more than 3 of a kind making it that much more valuable and clearly showing why it should be ranked higher than 3 of a kind.
We get 1pair even more.. so 1pair should be the highest paying hand evah?