# Yahtzee Odds

Yahtzee! Shouting this with excitement is the ambition of every Yahtzee player. It is the aim of this article to have a more detailed look at odds and probabilities of Yahtzee, in hope that you, the player, will assess the information given here to maximize your Yahtzee skills.

Chris Young and his 300 games

In December of 2007, an experienced Yahtzee player by the name of Chris Young decided to conduct and experiment to try and determine if there is a measured probability of getting certain scores in Yahtzee. Using an Electronic hand device, which guaranteed the fulfillment of Yahtzee rules, yielded the following results:

Out of 300 games, 105 Yahtzees were rolled; this is one in every 2.85 games.

127 Low scores were rolled and 277 high scores with no Yahtzee. The highest with one Yahtzee was 326, with two Yahtzees  - 437, and with three – 504.

Yahtzee Probabilities

Rolling a Yahtzee on your first roll is the lowest of all – 0.08%. Probability for a Yahtzee on your second roll would be approximately 1.23%. Same case applied on Three Rolls would be a 3.43%. Adding these three together brings to the result showing that by chance, a player could expect a Yahtzee once in every 21 turns.

Other Probabilities

Pair - going for 3 of a kind, probability with 2 rolls is 66.5%, and 42.1% with one roll.

2,3,4,5 – going for a Large Straight, probability with 2 rolls is 55.6%, with one roll 33.3%.

"Gut shot" – going for a Large Straight, probability with 2 rolls is 30.6%, with one roll 16.7%.

"Open-ended" small straight – going for a Small Straight, probability with 2 rolls is 80.2%, with one roll 55.6%.

"Gut shot" Small Straight – going for a Small Straight, probability with 2 rolls is 51.8%, with one roll 30.6%.

"Double-gutted" Small Straight – going for a Small Straight with 2 rolls is 55.6%, with one roll 33.3%.

2 Pair – going for a full house with 2 rolls is 55.6%, with one roll 33.3%.

3 of a kind – going for 4 of a kind with 2 rolls is 51.8%, with one roll 30.6%.

Pair – going for 4 of a kind with 2 rolls is 22.3%, with one roll 7.4%.

No Pair – going for 3 of a kind with 2 rolls is 36.1%, with one roll 13.2%.

3 of a kind – going for Yahtzee with 2 rolls is 9.3%, with one roll 2.8%.

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