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Fun Facts on Probabilities for Mooncake Dice Game

Fun Facts on Probabilities for Mooncake Dice Game


Every Mid-Autumn Festival here in the Philippines, the Chinese-Filipino community often commemorate such festivity by playing what we call "Pua Tiung Chiu" or Mooncake Dice Game.

Fun Facts on Probabilities for Mooncake Dice Game

What is Pua Tiung Chiu?
Pua Tiung Chiu is a basically a game of luck wherein each will take turns in rolling 6 dies in a glass bowl. Depending on the combination of the numbers, there are corresponding prizes awarded to the player, and if in case the luck is not on your side, you won't get anything.

Over the years I have played this game, I never won any of the first prize. Hence, due to this frustration, I decided to somehow estimate the probability of me getting any prizes on every roll.

Monte Carlo Simulation
When I shared this idea with my high school friends, I was surprised to find out that somebody already did a computation over this matter. Anyway, I haven't actually seen it, but this shall somehow reinforce the idea.

Also, since I do not know how to mathematically compute for the probabilities, I decided to just simulate a game via excel. I did 10,000 simulated dice throws, categorized each combination. and ultimately computed the probabilities based from the totals.

What you'll read in this blog post is the outcome of this "experiment" I did. So, here it goes!

Probability of getting 6th prize in Mooncake Dice Game

Probability of getting 5th prize in Mooncake Dice Game
The odds are great for the 5th and 6th prizes, but the probabilities drastically drop after this.

Probability of getting 4th prize in Mooncake Dice Game

Probability of getting 3rd prize in Mooncake Dice Game

I did several tries on this, but the outcome indeed points to this conclusion -- it's easier to roll a combination that will merit you the 3rd prize than the 4th prize.

Probability of getting 2nd prize in Mooncake Dice Game


Probability of getting no prizes in Mooncake Dice Game
Okay, I was also surprised that the odds of getting nothing per roll is considerably high, but at least I finally felt a little better. I thought I was just simply cursed.

Fun Facts Probabilities on Pua Tiung Chiu - Mooncake Dice Game

Surprisingly, the odds of rolling 3 consecutive of nothing is somehow equivalent to rolling a 2nd prize. So that's some sort of an achievement in terms of probabilities, but not so much when it comes to prizes. Again, that's 3 rounds of nothing. *sad reacts only*

Anyway, I hope you enjoyed this post. Don't let your friends feel like they are cursed, share this with them. Make them feel a little better. Thanks for dropping by! 



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