Carcassonne Dice

An unusual event happened when playing Carcassonne dice recently. Please can someone explain the probability of it happening?

There are NINE 6-sided dice. On one side of each there is a particular design (a building crane; i.e. 1/6 chance on one die). You have 3 throws. One of the win conditions is to accumulate 9 cranes after having 3 throwing attempts.

Throw 1 I got 6 cranes out of 9 dice (I put 6 cranes aside)

Throw 2 I got 2 cranes from the 3 remaining dice (I then put 2 cranes aside, now I have 8 cranes)

Throw 3 I got 1 crane from the remaining die (I now have the win condition of 9 cranes)

This feels extremely lucky - please can someone tell me the odds of this happening?

I get .000418, or around 1 in 2,392. I am not the math expert here, so hopefully someone will either confirm or debunk my answer. My pre calculation guess was 1 in a million......

Quote: SOOPOO

I get .000418, or around 1 in 2,392. I am not the math expert here, so hopefully someone will either confirm or debunk my answer. My pre calculation guess was 1 in a million......

I'll confirm your answer—0.000418108—or about 1 in 2392.

This is the probability for getting 9 cranes in any sequence of three (or less) throws. The OP's particular sequence occurs about 1 in 83,000.

Sorry, I cannot show the math at the moment.

Quote: PeeMcGee

I'll confirm your answer—0.000418108—or about 1 in 2392.

This is the probability for getting 9 cranes in any sequence of three (or less) throws. The OP's particular sequence occurs about 1 in 83,000.

Sorry, I cannot show the math at the moment.

Thank you both, that was really quick and helpful