Yugi is the one.

The moment Yugi completed the Millenium Puzzle his life changed permenantly. The puzzle created another mind/soul within him. In times when he or his close friends are in danger, Yugi will transform into this other person, know as the Game King or Yami no Yugi.

There is a slight difference in appearance of the two Yugi's. As you can see, the Game King is slightly taller than the normal Yugi. When engaging a punishment or right after transformation, a glowing sennen eye will briefly appear on the Game King's forehead.

The King of Games, Yami no Yugi will engage a 'Game of Darkness' or 'Game of Death' against any rival or person who threatens him or his friends.

The game itself is described to be similar to Russian Roulette. The game is played in different ways but has the same basic plot. The game is offered. The rival accepts. He loses and is punished. Quite often the loser loses his sanity, sometimes even their life.

Yugi has one main rival. Seto Kaiba. After Kaiba was punished by Yami no Yugi for stealing Yugi's Grandfather's 'Blue Eyes White Dragon', Kaiba swore to get his revenge and has attempted many times to defeat Yugi. Kaiba once said to Yugi,

Yugi Mutou is in love with Anzu Mazaki but as expected he is very shy. Anzu soons realize that there is another face to Yugi after she was saved by him a few times. She eventually fell in love with Yami no Yugi.

Yugi loves Anzu, but Anzu loves Yami no Yugi, and Yami no Yugi 'kinda' loves Anzu but also loves games. It just goes in a loop.