Lakers make final cuts but keep forwards Metta World Peace and Thomas Robinson

As the Lakers wrapped up practice Monday, veteran forwards Metta World Peace and Thomas Robinson stood next to each other on the sideline.

While 10 of their teammates scrimmaged, World Peace tapped Robinson on the shoulder and directed his eyes away from the action. Robinson nodded for a second, as if it were a teaching moment. Then they each broke out in laughter, and were left smiling as a late-game scenario played out in front of them.

There was good reason for the pair to loosen up, if only for a day or two. World Peace and Robinson were the last two players kept on the Lakers’ 15-man regular-season roster after the team waived center Yi Jianlian and guard/forward Anthony Brown on Monday morning.

Lakers Coach Luke Walton said after Monday’s practice that Yi wanted to look for other opportunities after playing the last four seasons in China. With the addition of free-agent center Timofey Mozgov, and a goal of developing young centers Tarik Black and second-round pick Ivica Zubac,Walton said the 28-year-old Yi wants “bigger minutes than we had available.”

Brown, who played 20.7 minutes per game as a rookie last season, was hurt by the Lakers’ depth at his spot.

“That was tough. Just with the team we have and so many young guys, and we have so many twos and threes as it is right now,” Walton said of the decision to waive Brown. “With Nick [Young] playing as well as he’s playing, and signing [Luol] Deng and drafting Brandon [Ingram], it was tough to find him opportunities out there.

“As much as I liked [Brown] and as well as he was playing, Metta World Peace and [Thomas Robinson], they were bringing it every single day and they were giving us the toughness that I think we need.”

Seven of the Lakers’ 15 players will be younger than 25 when the Lakers open the season against Houston at Staples Center on Wednesday. Walton said the experience of World Peace, who turns 37 next month, and Robinson (25 and with his sixth NBA team) played into the final roster decisions.

World Peace in particular gives the rebuilding Lakers a veteran presence. He played on the Lakers’ 2010 championship team with Walton, who is four months younger than World Peace. And Walton sees great value in a player who can provide the insight of a coach.

“It’s weird. At the end of my career I feel like I’m at the beginning,” World Peace said Monday, as he prepares for his 17^th year in the league. “I’ve got a goal. My personal goal is to reach 20 years.”

Robinson, who was drafted fifth overall by the Sacramento Kings in 2012, has had trouble sticking with a franchise for more than one season. Walton said he is “shocked” by that after watching Robinson during the preseason, but admitted the Lakers were not thinking about him during the off-season.

The 6-foot-10 forward changed that by showing up to summer scrimmages at the Lakers’ practice facility. Walton noticed that Robinson’s team usually won, and extended a training camp invite. Robinson made the most of his limited playing time in exhibition games and was often the last player to leave the court after practices.

If he does earn minutes this season, Robinson will provide relentless energy on defense and in rebounding and will try to stretch the court with a developing shooting touch.

“More relieved, I won’t say I’m excited, because I made the team but nothing is done yet,” Robinson said. “I shouldn’t have been in that position, but things happen the way they happen. I worked my way out of it, and now I just have to keep going.”

When practice finished, 13 players filtered off the court and into the locker room. The two that remained were Robinson and World Peace. Robinson took jump hooks. World Peace shot corner threes.

They worked on opposite ends of the court but were really one in the same: Looking to maximize an opportunity by playing as if their jobs were still on the line.

jesse.dougherty@latimes.com

Twitter: @dougherty_jesse