ScrabbleBet | Topcoder Archive

Problem Statement

One Saturday evening you are playing a game of online Scrabble. Your opponent is a very good player, but this time you managed to win. After a brief conversation, you are told: "I am clearly better than you, but one game is simply not enough to prove it." Your opponent then makess the following bet: "If we play 10 games, you will win less than 5 ... and this will happen every time, even if we try this 10 times in a row!".

You will solve a more general problem using the following parameters:
- an int trials denoting the number of meetings in which a set of games is played.
- an int games denoting the number of games that are to be played in each meeting.
- an int winsNeeded denoting the number of victories you need in one of the meetings to win the bet.
- an int winChance denoting the probability in percent of winning one particular game.

Return a double between 0 and 1, denoting the probability you have to win the bet.

Definition

Class:: ScrabbleBet
Method:: estimate
Parameters:: int, int, int, int
Returns:: double
Method signature:: double estimate(int trials, int games, int winsNeeded, int winChance)
(be sure your method is public)

Notes

Your return value must have an absolute or relative error less than 1e-9.

Constraints

trials will be between 1 and 50, inclusive.
games will be between 1 and 20, inclusive.
winsNeeded will be between 1 and games, inclusive.
winChance will be between 0 and 100, inclusive.

Examples

```
2
```
```
2
```
```
1
```
```
50
```
```
Returns: 0.9375
```
There are 4 possible ways a meeting could evolve: - you lose both games. - you lose game 1 and you win game 2. - you win game 1 and you lose game 2. - you win both games. Your opponent has a 1/4 chance of not losing the bet after the first meeting. Since there are two meetings, your opponent's chances to win the bet are 1/4 * 1/4 = 1/16. Thus, you have a 15/16 chance to win the bet.
```
2
```
```
2
```
```
2
```
```
50
```
```
Returns: 0.4375
```
This time your opponent has a 3/4 chance of not losing the bet after one meeting and a 9/16 chance of not losing the bet after the two meetings. Your chances are now 1 - 9/16 = 7/16.
```
10
```
```
10
```
```
5
```
```
25
```
```
Returns: 0.5566860567603682
```
```
2
```
```
20
```
```
5
```
```
10
```
```
Returns: 0.08448495352665641
```
```
50
```
```
15
```
```
1
```
```
0
```
```
Returns: 0.0
```
```
50
```
```
17
```
```
16
```
```
100
```
```
Returns: 1.0
```
```
50
```
```
10
```
```
10
```
```
75
```
```
Returns: 0.9448701546682944
```

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