[Do] Mathy folks, I have a doozy of a probability experiment for you.

Any mathematically oriented people out there want to help me out with a probability experiment? This is in regards to the system I’m using for Do: Pilgrims of the Flying Temple. I think I’ve come across a pretty elegant pacing mechanic. I tried running these experiments manually and writing down the results, but I think I’ll need some serious math to get any kind of reliable results. I’d appreciate any help you can offer.

—————–

There are four players: Adam, Beth, Charlie, Donna.

There is a bag filled with eight black stones and eight white stones.

Each turn, a player draws three stones from the bag, resulting in any of the following possible outcomes:
○ ○ ○
● ○ ○
● ● ○
● ● ●

After drawing, the player has a choice to either keep the black stones or keep the white stones.
For example: Adam drew ●○○ and chooses to keep the ○○.

The stones she does not keep are put back into the bag.
For example: Because Adam did not choose ●, it goes back into the bag.

After the stones are put into the bag, the turn ends.

When there are 2 or fewer stones in the bag at after a player draws their stones, the game is over.

—————–

EXPERIMENT 1
Adam and Beth will always choose to keep the highest number of stones.

Charlie and Donna always choose to keep the lowest number of stones. (That includes keeping zero stones, in the case of drawing three-of-a-kind.)

—————–

EXPERIMENT 2

Players are now allowed the option of removing stones from their reserve, to add to their draw. Restriction: Players may only spend their black or white stones from their reserve, not a mixture of both. Any spent stones are placed in the bag along with the rest of the stones that a player did not choose to keep.
For example: Beth drew ●○○ and chooses to keep the ○○. She also has ●●●○○ in reserve. She spends all her black stones, thus putting ●●●● back in the bag. She now has ○○ in reserve at the end of her turn.

In addition to the color-restriction, players may only spend up to 3 stones from their reserve.
For example: If Charlie had ○○○○● in his reserve, he could only spend at most ○○○.

Adam will always keep the highest number of stones possible. Also, he will always spend the maximum number of black stones he has in his reserve.

Beth will always keep the highest number of stones possible. Also, she will always spend the maximum number of white stones she has in her reserve.

Charlie will always keep the lowest number of stones possible. Also, he will always spend the maximum number of black stones he has in his reserve.

Donna will always keep the lowest number stones as possible. Also, she will always spend the maximum number of white stones she has in her reserve.

—————–

QUESTIONS
– How many turns are in an average game?
Hypothesis: 10-15 turns.

– How likely is it to draw three-of-a-kind? (That is, ○○○ or ●●●)
Hypothesis: 4 occurrences of three-of-a-kind per game.

– What is the likelihood of drawing three-of-a-kind in each turn as the game progresses?
Hypothesis: Highly unlikely in the first round, but with such increasing likelihood in each subsequent turn that there is never a complete round of turns after the first.

– How many turns are there between occurrences of a three-of-a-kind as the game progresses?
Hypothesis: About five turns before the first occurrence. Less than three turns before the second. Less than two before the third. Almost 0 before the fourth.

—–

Once again, I thank anyone who is willing to run these experiments. 🙂