Different tennis odds formulas

Hello, this nice website explains trought a Markov process the game score in tennis and the passage from one state to another. It’s a very nice to read.


But I don’t understand one thing and I am getting confused… He says (you can read it on the website)

”So the final equation for the probability of Player A winning the game is:



On this website (stack exange)


one guy asks for the same question, and one other guy using Bernulli process he calculates a formula for the probability for a tennis player to win the game and it is:


WHY this formula is different from the first one I have red on that website? (this below)


I can not explain that ”10” and ”20”… where do they came from ?

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