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Humanity's Last Code Exam / 2013_B / Hey, Better Bettor

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atcoder

question content

# Problem Description Recent recessions have not been kind to entertainment venues, including the gambling industry. Competition is fierce among casinos to attract players with lots of money, and some have begun to offer especially sweet deals. One casino is offering the following: you can gamble as much as you want at the casino. After you are finished, if you are down by any amount from when you started, the casino will refund

x\%

of your losses to you. Obviously, if you are ahead, you can keep all of your winnings. There is no time limit or money limit on this offer, but you can redeem it only once. For simplicity, assume all bets cost 1 dollar and pay out 2 dollars. Now suppose

x

is 20. If you make 10 bets in total before quitting and only 3 of them pay out, your total loss is 3.2 dollars. If 6 of them pay out, you have gained 2 dollars. Given

x

and the percentage probability

p

of winning any individual bet, write a program to determine the maximum expected profit you can make from betting at this casino, using any gambling strategy. ## Input The input consists of a single test case. A test case consists of the refund percentage

x

(0 \leq x < 100)

followed by the winning probability percentage

p

(0 \leq p < 50)

. Both

x

and

p

have at most two digits after the decimal point. ## Output Display the maximum expected profit with an absolute error of at most

10^{-3}

. ### Sample Input 1

Plain-text mathematical notation (without MathML)

# Problem Description

Recent recessions have not been kind to entertainment venues, including the gambling industry. Competition is fierce among casinos to attract players with lots of money, and some have begun to offer especially sweet deals. One casino is offering the following: you can gamble as much as you want at the casino. After you are finished, if you are down by any amount from when you started, the casino will refund x% of your losses to you. Obviously, if you are ahead, you can keep all of your winnings. There is no time limit or money limit on this offer, but you can redeem it only once.

For simplicity, assume all bets cost 1 dollar and pay out 2 dollars. Now suppose x is 20. If you make 10 bets in total before quitting and only 3 of them pay out, your total loss is 3.2 dollars. If 6 of them pay out, you have gained 2 dollars.

Given x and the percentage probability p of winning any individual bet, write a program to determine the maximum expected profit you can make from betting at this casino, using any gambling strategy.

## Input

The input consists of a single test case. A test case consists of the refund percentage x (0≤x<100) followed by the winning probability percentage p (0≤p<50). Both x and p have at most two digits after the decimal point.

## Output

Display the maximum expected profit with an absolute error of at most 10^(−3).

### Sample Input 1

Original LaTeX notation

# Problem Description

Recent recessions have not been kind to entertainment venues, including the gambling industry. Competition is fierce among casinos to attract players with lots of money, and some have begun to offer especially sweet deals. One casino is offering the following: you can gamble as much as you want at the casino. After you are finished, if you are down by any amount from when you started, the casino will refund \( x\% \) of your losses to you. Obviously, if you are ahead, you can keep all of your winnings. There is no time limit or money limit on this offer, but you can redeem it only once.

For simplicity, assume all bets cost 1 dollar and pay out 2 dollars. Now suppose \( x \) is 20. If you make 10 bets in total before quitting and only 3 of them pay out, your total loss is 3.2 dollars. If 6 of them pay out, you have gained 2 dollars.

Given \( x \) and the percentage probability \( p \) of winning any individual bet, write a program to determine the maximum expected profit you can make from betting at this casino, using any gambling strategy.

## Input

The input consists of a single test case. A test case consists of the refund percentage \( x \) \((0 \leq x < 100)\) followed by the winning probability percentage \( p \) \((0 \leq p < 50)\). Both \( x \) and \( p \) have at most two digits after the decimal point.

## Output

Display the maximum expected profit with an absolute error of at most \( 10^{-3} \).

### Sample Input 1

Code

0 49.9


### Sample Output 1

Code

0.0


### Sample Input 2

Code

50 49.85


### Sample Output 2

Code

7.10178453

question title

Hey, Better Bettor

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upstream_id / Original problem ID: 2013_B
task_id: 261405c3-0c2b-58ff-bc78-86bc6aab08b4
task_key: ICPC~2dWorld~2dFinals--examples--2013~5fB
task_revision_id: 2
config / split: ICPC-World-Finals / examples

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