I visited my younger cousins, John and Edmund, recently, and found them playing an interesting game. They would take turns to call out numbers until one of them declared themselves the winner. They would also alternate the person who would start the game.
Here are examples of some of the games they played (I've written John's answers in italics and Edmund's answers in bold)
3, 2, 3, 4, 4, 5, 5, 2, 3, 3, 4, 2, 2, 4, 5, 7, 6
At this point, John declared himself the winner.
2, 3, 2, 2, 1, 4, 1, 5, 6, 3, 5, 3, 3, 1, 1, 2
Again, John declared that he won at this point. After some consideration, Edmund reluctantly agreed.
As the afternoon wore on, the games tended to get longer. Here was another one won by John
1, 4, 1, 1, 4, 3, 5, 2, 2, 3, 3, 1, 2, 2, 4, 4, 3, 4, 3, 3, 2
Edmund was clearly having some difficulty beating his older brother but, eventually, he came through in the longest game I had witnessed.
4, 3, 5, 4, 6, 7, 4, 5, 3, 2, 6, 5, 5, 3, 1, 4, 5, 3, 3, 4, 5, 1, 4, 3, 7, 7, 1, 7, 1, 1, 7, 7, 1, 6, 6, 6, 6
"Yes! I win!" exclaimed Edmund.
I didn't really understand the rules of the game yet but I had a strategy I wanted to try and asked John if I could join in.
"Sure", said John, "4".
"4", I responded
"3", said John.
"3", I responded with confidence.
"2. I win!", exclaimed John.
I was a bit dumbfounded and looked over at Edmund who was chuckling in the corner. I couldn't understand how my strategy had lost so quickly. I accused them of making it all up but they insisted that it was a real game.
Can you explain how the game works?
Hint
John and Edmund's game is not their own creation, they are just playing the game in an unusual way.