Odds of winning Orchard Game? I recently started playing the Orchard Game with my sons.  It is a simple children's game but I cannot figure out how to calculate the probability that you win.  Here are the setup/rules:


*

*There are 4 pieces of 4 different fruits (4 plums (blue), 4 green apples (green), 4 red apples (red) and 4 pears (yellow)).

*There is a bird

*There is a basket 

*All the fruit starts outside the basket

*There are no teams, you rotate rolling the dice but everyone is on the same team

*On the dice there are 4 colors - one for each fruit - a basket and a bird

*If you roll a color of the fruit, you place one piece of that fruit in the basket.  If all four pieces of that fruit are in the basket, nothing happens

*If you roll the basket you can pick any one piece of any fruit you want and put it into the basket

*If you roll the bird the bird moves forward one space


Win/loss
You win if you get all the pieces of fruit into the basket before the bird moves 5 spaces.  If the bird moves 5 spaces before you get all the fruit into the basket you lose.
What are the odds that you win?  The basket along with rolling a color when there is nothing of that color left complicates the calculation and it is beyond abilities.
Thanks!

I recently started playing this game with my son, and had the same question! I ended up writing a story about it which ends by showcasing win probabilities for a few different strategies, and for different variations of the game.
Here are the parameters I end up adjusting:


*

*The number of fruits per color (4 in First Orchard, 10 in Orchard Game)

*The number of raven rolls required for a loss (5 in First Orchard, 9 in Orchard Game)

*The number of fruit you can remove when you roll the fruit basket (1 in First Orchard, 2 in Orchard Game)

*The number of fruit colors (4 in both games).


Fortunately, I was able to duplicate the probabilities that tehtmi reported. 
Here's the link if you're curious. Enjoy! https://mattlane.us/stories/harvesting-wins/
