**Pig** is a folk jeopardy dice game with simple rules: Two players race to reach 100 points. Each turn, a
player repeatedly rolls a die until either a 1 ("pig") is rolled or the player holds and
scores the sum of the rolls (i.e. the *turn total*). At any time during a
player's turn, the player is faced with two decisions:

**roll**- If the player rolls a**1**: the player scores nothing and it becomes the opponent's turn.**2 - 6**: the number is added to the player's turn total and the player's turn continues.

**hold**- The turn total is added to the player's score and it becomes the opponent's turn.

**Problem:** Compute and report the
probabilities of the possible scoring outcomes from a hold-at-20 Pig turn.

The following is a dynamic programming algorithm that approaches the problem by computing the probability of passing through each score on the way to the final outcome:

- Create a floating-point array
*score*with indices from 0 through 25 (hold value + 5). Initialize all entries to 0.0, except initialize index 0 to 1.0. - For each increasing index
*i*from 0 through 19 (hold value - 1): - Let
*p*be*score*[*i*]*.* - Set
*score*[*i*] to 0.0. - Add p to
*score*[0],*score*[*i*+ 2],*score*[*i*+ 3],*score*[*i*+ 4],*score*[*i*+ 5],*score*[*i*+ 6]

At the beginning of each iteration *i,* *score*[*i*] is
the probability of passing through score *i.* After all iterations,
the remaining positive values are the probabilities of their respective score
outcome probabilities.

**Input Format:** (no input)

**Output Format:**

- On the first line, print "Score" and "Probability" separated by a tab.
- After computing the probabilities of outcomes, print a table line for each possible score outcome in increasing order of score. For each score outcome, print the score, a tab, and the probability of that score outcome.

**Sample Transcript:**

Score Probability 0 0.624541 20 0.099713 21 0.094991 22 0.074189 23 0.054196 24 0.035198 25 0.017173

**Extra Exercises: **

- What is the expected average score outcome for hold-at-20?
- Additionally allow the user to specify the hold value. What is the probability of reaching 100 in a single turn?