What are the odds of rolling 3 of a kind with 4 dice?
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Calculate the probability of 3 of a kind in Yahtzee: Probability of 3 of a kind = 3 of 1 Kind and any unequal 4th & 5th die/All Possible Rolls Show
Total Combos of 2 non-equal die positions = 2 * (4,5)(3,5)(2,5)(1,5)(3,4)(2,4)(1,4)(2,3)(1,3)(1,2) Three of a kind combos of 1 = 10 * 20 Total Possible Die Roll Combos = 6 * 6 * 6 * 6 * 6 Probability of 3 of a kind = 12007776 Using our GCF calculator, we reduce top and bottom by 48, to get Probability of 3 of a kind = 25162 What is the Answer?Probability of 3 of a kind = 25/162 How does the Yahtzee-1st Roll Calculator work?Calculates the probability of various scoring hands in the game of Yahtzee on the 1st roll of the dice. What 4 concepts are covered in the Yahtzee-1st Roll Calculator?gamesprobabilitythe likelihood of an event happening. This value is always between 0 and 1. What are some example calculations for the Yahtzee-1st Roll Calculator?Yahtzee-1st Roll Calculator VideoTags:Add This Calculator To Your Website Odds are what dice games are all about. Using your judgment to decide when to hold or try for a combination is the skill element in a dice game. The tables here show the odds of achieving specified outcomes with a number of dice and using your educated judgement to decide when a roll has a reasonable chance of winning will give you the edge. Knowing these odds will give you an advantage over other players. Combination (rolled with...)5 Dice4 Dice3 Dice2 DiceSpecific Pair7.3 to 19.8 to 113 to 135 to 1Any Pair1.2 to 1*1.25 to 11.4 to 15 to 1Any Pair or Better9.8 to 1*2.6 to 1*1.25 to 1Specific Two Pair64 to 1215 to 1Any Two Pair3.3 to 113 to 1Any Two Pair or Better1.25 to 15 to 1Specific Three-of-a-Kind38 to 164 to 1215 to 1Any Three-of-a-Kind5.5 to 19.8 to 135 to 1Any Three-of-a-Kind or Better3.7 to 19.3 to 1Specific Full House777 to 1Any Full House25 to 1Any Full House or Better16 to 1Specific Four-of-a-Kind310 to 11295 to 1Any Four-of-a-Kind51 to 1215 to 1Any Four-of-a-Kind or Better49 to 1Specific Five-of-a-Kind7775 to 1Any Five-of-a-Kind1295 to 1* Odds are in favour of achieving outcome not against. Odds of improving Poker handsKeep a pair and roll three to improve to...Five-of-a-Kind215 to 1Four-of-a-Kind or Better13 to 1Full House or Better5 to 1Three-of-a-Kind or Better1.25 to 1Two Pairs or Better2.6 to 1 in favourKeep three-of-a-kind and roll two to improve to...Five-of-a-Kind35 to 1Four-of-a-Kind or Better2.3 to 1Full House or Better1.25 to 1Keep four-of-a-kind and roll one to improve to...Five-of-a-Kind5 to 1 Just as one die has six outcomes and two dice have 62 = 36 outcomes, the probability experiment of rolling three dice has 63 = 216 outcomes. This idea generalizes further for more dice. If we roll n dice then there are 6n outcomes. We can also consider the possible sums from rolling several dice. The smallest possible sum occurs when all of the dice are the smallest, or one each. This gives a sum of three when we are rolling three dice. The greatest number on a die is six, which means that the greatest possible sum occurs when all three dice are sixes. The sum of this situation is 18. When n dice are rolled, the least possible sum is n and the greatest possible sum is 6n.
Forming SumsAs discussed above, for three dice the possible sums include every number from three to 18. The probabilities can be calculated by using counting strategies and recognizing that we are looking for ways to partition a number into exactly three whole numbers. For example, the only way to obtain a sum of three is 3 = 1 + 1 + 1. Since each die is independent from the others, a sum such as four can be obtained in three different ways:
Further counting arguments can be used to find the number of ways of forming the other sums. The partitions for each sum follow:
When three different numbers form the partition, such as 7 = 1 + 2 + 4, there are 3! (3x2x1) different ways of permuting these numbers. So this would count toward three outcomes in the sample space. When two different numbers form the partition, then there are three different ways of permuting these numbers. Specific ProbabilitiesWe divide the total number of ways to obtain each sum by the total number of outcomes in the sample space, or 216. The results are:
As can be seen, the extreme values of 3 and 18 are least probable. The sums that are exactly in the middle are the most probable. This corresponds to what was observed when two dice were rolled. View Article Sources
Cite this Article Format mla apa chicagoYour Citation Taylor, Courtney. "Probabilities for Rolling Three Dice." ThoughtCo. https://www.thoughtco.com/probabilities-for-rolling-three-dice-3126558 (accessed January 3, 2023). What are the odds on rolling three of a kind with dice?Each of the dice rolls is an Independent Event, that is the outcome from anyone dice roll has no impact whatsoever on the outcome of any other dice roll. The probability of all three happening is the product of the three probabilities: 1 × (1/6) × (1/6) = 1/36.
What are the odds of rolling 3 sixes with 4 dice?6x6x6 = 216. Therefore, the probability of a triple is 6/216 = 1/36. If dice is rolled, what is probability that 1 is obtained in even number of throws?
What are the odds of rolling 3 of a kind with 5 dice?Which comes out to ~0.15.
What are the odds of rolling 4 dice the same?What is the probability that four dice show the same number? 6 / (6 x 6 x 6 x 6) = 1 / (6 x 6 x 6) = 1 in 216.
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