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.

https://tobykingsman.wordpress.com/2016/02/17/markov-chains-and-tennis/comment-page-1/

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:

https://s0.wp.com/latex.php?latex=P+%3D+p%5E4+%2B+4p%5E4%281-p%29+%2B+10p%5E4%281-p%29%5E2+%2B+%5Ccfrac%7B20p%5E5%281-p%29%5E3%7D%7B1-2p%281-p%29%7D&bg=ffffff&fg=808080&s=0

BUT

On this website (stack exange)

https://math.stackexchange.com/questions/1126327/probability-of-winning-a-game-in-tennis

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:

https://image.ibb.co/c86Wy9/Schermata_da_2018_08_09_15_05_26.png

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

r/https://s0.wp.com/latex.php?latex=P+%3D+p%5E4+%2B+4p%5E4%281-p%29+%2B+10p%5E4%281-p%29%5E2+%2B+%5Ccfrac%7B20p%5E5%281-p%29%5E3%7D%7B1-2p%281-p%29%7D&bg=ffffff&fg=808080&s=0

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

submitted by Nevin Manimala Nevin Manimala /u/luchins
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