As Sheldon is on the train, during his life's rediscovering, he is thinking back to how things could've been different. He was thinking about how things would've happened had he been using the roll of the dice for the last 7 years instead of the last 2.

Flashback:

Sheldon and Leonard are at the sperm bank and with the roll of the dice, Sheldon stays and maturbates into a cup hoping for a potential Nobel winner.

Later that same day they meet their new neighbor.

"Hi"

"Hi"

"Hi"

Sheldon having rolled the dice in his head speaks up first ahead of Leonard, "Hi, I'm Sheldon. This is my roommate Leonard. We live across the hall."

"I'm Penny. Nice to meet you."

Later that night after Penny comes over and meets Raj and Howard. She's remarking how smart Sheldon is, sitting in his spot and telling him to sit next to her, in other words going out of her way to flirt with Sheldon. He is oblivious to it. He keeps hitting the wrong roll of the dice so he doesn't respond the way he wants to. She then asks if she can take a shower. Leonard shows her the bathroom and where the towels and stuff are and he leaves.

Just after the shower turns on, Sheldon finally hits the right roll and gets up and to everybody's shock, goes into the bathroom.

"It's about time you came in here." says Penny.

"Sorry for the wait. I kept hitting snake eyes."

"Would you like to join me?"

"With pleasure"

End of flashback:

If only he had started rolling dice back then. He would've ended up with the girl he loved instead of Amy.