Playing the odds?

[BusterFlush]

Here is the scenario. I play in a weekly home game that is very competitive. The first two hours is a limit Hold'em game and then a NL tournament is played.
After weird run of cards during the first session and into the tournament, I was in decent chip position and had just raised with 5-5 at UTG+1 and taken the blinds. The game is 10 handed and I am now UTG with 8-8. If I raise again 3x BB as before I am likely to receive action if not more.
Regarding weird run of cards, this 8-8 was my 10th small pairs (9 or under) during the course of the night without flopping a set. My thought was the odds were with me to flop a set and I would push this hand if needed. After making a 3x BB raise, a MP went all-in and action was folded to me. The raiser is a good math player and reads well. I had twice as many chips as him and had to call 900 more into a 1,650 pot. I called and the MP had two overs and I flopped my set.
The correct result occurred but was it the correct play?

[tigerite]

"The odds are with me" is nonsense, cards have no memory. You are the same odds against flopping the set with this hand as you were with all the previous small pairs, the way you are thinking leads to "gambler's ruin" and is a fallacy.

Yea I agree. Just because you havent hit a set doesnt mean you are "due". I think it was a good play if you wanted to be in a coinflip but even still it wasnt an incorrect play. But thinking that you will hit a set because you hadnt in the previous attempts is foolish.

[BusterFlush]

Thank you for the replies. I understand the cards do not have memories. If my odds are 1 in 7 to to flop a set and I have not in the previous 9 pocket pairs, isn't the probability increased to on the 10th? Not guaranteed, just more likely? Or is the argument that each pair is an individual event and past and future results should not factor in one's play?

[tigerite]

The latter. Your thinking is like the fools who play roulette tables, they see 10 reds in a row, then think the probability has somehow changed from 18/37 that the next number will be black. It's complete fallacy.