Tennis Deuce probability to win

Suppose you’re at a “deuce” in the game of tennis. This means that to win the match, you need to be two points ahead of the other player (i.e. you need to score two points in a row).

The probability that you win a point at any given time is 0.25. What is the probability that you win the match?


Find the error in the following solution:

Let p be the probability that we win the match. Then we can write:
$ p = 0.25cdot[0.25 + 0.75cdot p] + 0.75cdot [0.25cdot p + 0.75cdot 0]$
p = 1/12

(this is incorrect)

All topic

Question: Should tennis umpire, Carlos Ramos, be fired if he is found guilty of Sexism like Serena Williams and the WTA accuses him of?

Question: Should tennis umpire, Carlos Ramos, be fired if he is found guilty of Sexism like Serena Williams and the WTA accuses him of?

Question: Should tennis umpire, Carlos Ramos, be fired if he is found guilty of Sexism like Serena Williams and the WTA accuses him of?

All topic

Question: How much was the tennis racquet worth that Serena Williams broke?

Question: How much was the tennis racquet worth that Serena Williams broke?

Question: How much was the tennis racquet worth that Serena Williams broke?

This past Saturday at the US Open, Serena Williams broke her tennis racquet out of anger. How much do you think the racquet was worth?

All topic

Strange Behavior for trying to Predict Tennis Millionaires with Keras (Validation Accuracy)

I’m trying to make an NN with Keras to predict the ATP players that will get more than US$1 million in prize money based on their weight and height (from a dataset I mined some weeks ago), but I have been getting a weird behavior especially for the validation accuracy. Sometimes it gets to 84-85%, which is reasonable since SVMs and GaussianNB seem to be able to hit only 83.3% at best (check this post for more info), but sometimes it gets only around 15% accuracy. And the accuracy mostly doesn’t change at all if I add capacity or more epochs. I guess one of the weirdest trends in this problem is that the loss is comparably quite small when I get low accuracies:

The test and validation losses are quite small, but the accuracy is terrible.

All of the code is available in this repo (specially the ATP NN.ipynb and the atp_python_2018-08-27_1-1500.json), but the main part of it is:

model = Sequential()
model.add(Dense(20, activation = 'relu', input_shape = (2,)))
model.add(Dense(20, activation = 'relu'))
model.add(Dense(2))
model.compile(optimizer = 'adam', loss = 'categorical_crossentropy', metrics = ['accuracy'])
model_training = model.fit(x = hw_a, y = prize_a_bin, epochs = 4, validation_split = 0.1)

At first, I thought this was happening because the validation split done by Keras would be getting somewhat improper sets that were not very consistent with the rest of the data, since the millionaires are only 10% of the whole dataset, but that doesn’t seem to be the case, the weirdness persists. The only pattern I can kind of recognize is that the normal performance and the strange one are compementary, i.e., if one is 85%, the other will be 100% – 85% = 15%. Is that linked to some mistake I’ve made?

On a sidenote, since I’m a beginner with Keras, should I have specified the last layer’s activation function? I assume he is doing either a softmax or a sigmoid by default, but it seems make no difference if I specify either of them. I wonder why with only class (either millionaire or not), you have reshape y into a to_categorical and have two units – instead of two – in the output layer.

All topic

Bad companies on a tennis tournament

$n geq 4$ players participated in a tennis tournament. Any two players have played exactly one game, and there was no tie game. We call a company of four players $bad$ if one player was defeated by the other three players, and each of these three players won a game and lost another game among themselves. Suppose that there is no bad company in this tournament. Let $w_i$ and $l_i$ be respectively the number of wins and losses of the $i$-th player. Prove that $$sum^n_{i=1} left(w_i – l_iright)^3 geq 0.$$

All topic

Tennis Davis Cup Graz

Tennis Davis Cup Graz

Tennis Davis Cup Graz

Dominic Thiem, Thiem, Alex de Minaur, Thiem Davis Cup, de Minaur

All topic

Are transgender people allowed to play tennis on the WTA/ATP tour?

Are transgender people allowed to play tennis on the WTA & ATP tours as their non-original gender? I know that Renee Richards was the first one to play at a Grand Slam, about 20 years ago.

Does the rulebook accept deny entry currently for people who have changed sex? Are the rules different on ITF & ATP/WTA circuit?

I know this question can be asked of any sport, but I am restricting it to tennis only.

All topic

Question: Remember when white girls used to dominate tennis?

Question: Remember when white girls used to dominate tennis?

Question: Remember when white girls used to dominate tennis?

All topic

Portable lights for playing tennis at night?

I’m looking for a way to play outdoor tennis on unlit courts at night. I had the idea to bring some kind of portable lighting. Has anyone tried this? Is it effective? Is there a way to do this for a reasonable cost and setup time?

Would floodlights be effective for this? If so, what kinds of attributes should I look for?

I do not have access to either a generator or an electrical outlet in the locations where I play, so presumably I’d need to use something that could work with rechargeable batteries.

All topic

Question: Will Serena Williams play in any more tennis matches?

Question: Will Serena Williams play in any more tennis matches?

Question: Will Serena Williams play in any more tennis matches?

All topic