Yahtzee is a game of chance like dice or poker. The numbers of ways the outcomes ( straight rolling ) is 240 .
Probability of hitting a large straight is 240 / 7776 = 1/32
Yahtzee is the one of dice game that uses five standard six-sided dice. After rolling each die, the player can decide which die to keep and which to reroll. Goals include many different types of combinations, many of which originate from poker.
The two types of combinations that players must roll are called roads: small roads and large roads. Similar to poker straights, these combinations consist of consecutive dice. A small straight uses 4 out of the 5 dice and a large straight uses all 5 dice. Since the dice rolls are random, we can use probability to analyze the likelihood of hitting large straight on a single roll. Assumes that the dice used are fair and independent of each other. Now, you need to know how many ways you can roll a big/ large straight. Here it is more difficult than calculating the sample size. Big straights are harder to roll than small straights, but it’s easier to count the number of times you’ve rolled a big straight than the number of times you’ve rolled a small straight.
Next, determine the number of ways to get a straight by rolling the given dice. To get a nice straight with dice {1, 2, 3, 4, 5}, you can arrange the dice in any order. It turns out that you just swap the five dice. There are 5! = 120 ways to do this. There are two dice combinations that form the large Straight, each with 120 ways to roll, so there are 2 x 120 = 240 ways to roll the large Straight.
Now the probability of hitting a big/ large straight can be calculated with simple division. Since there are 240 ways to get the big straight in one roll, and 7776 rolls 5 dice, the odds of getting the big straight are 240/7776, close to 1/32, and lie 3.1%.
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