For my first explore math project, I wanted to do something with the trending trivia app “HQ”. Essentially, the game has a live host who asks 12 questions ranging from easy to hard. The player has 10 seconds to pick from 3 possible answers. The winner(s) win/split the prize, which ranges from 1,500$ to 20,000$. Most games have about 300,000-600,000 players to start, and about 1-100 people win. I wanted to evaluate my chances of winning.

Evaluation 1: The chances of winning with 1 phone, and by guessing every question.

(No data for this evaluation, because it is in general):

Because there are 12 questions, and 3 possible answers per question, by guessing every question, the chances of winning are:

3*3*3*3*3*3*3*3*3*3*3*3

=

531441→ 1/531,441 chances of winning

Evaluation 2: My chances of winning with 1 phone, and only me person guessing.

•Of the 5 games that I recorded data from (when there was only 1 phone and I was the only one guessing):

So, if I subtract 12 by 3.8, I get 8.2, so I would need to guess 8.2 questions to win:

3*3*3*3*3*3*3*3*1.2

=

7873.2 → 1/7873.2 chances of winning

Evaluation 3: My chances of winning with 3 phones, and when 7 people are guessing.

•I did these trials over winter break, so my brother, me, and my uncle were all playing HQ on our phones. We also had my mom, my dad, my aunt, and my grandma guessing. The chances are of winning on any phone, so I recorded the highest question that we got up to on any phone.

So if I subtract 12 by 6.6, I get 5.4, so I would need to guess 5.4 questions to win:

3*3*3*3*3*1.4

=

340.2→ 1/340.2 chances of winning

Unlike others conclusions I’ve made in the past, this conclusion really helps me understand something I enjoy doing. I now know that it would take about year to win if I played ones of the games each day, with 3 phones and 7 of my family members. Knowing that the prize of most games is usually split into about 5-50 dollars per winner, investing that much time into the game isn’t practical. But then again, I can always get lucky.

While my answers ended up being very reasonable, my project did have multiple areas of discrepancy. For one, my data didn’t take into account “educated guesses”. Also, answering questions “confidently” is not quantifiable. I’m certain that there were multiple questions that I answered “confidently” but still got wrong.

Evaluation 1: The chances of winning with 1 phone, and by guessing every question.

(No data for this evaluation, because it is in general):

Because there are 12 questions, and 3 possible answers per question, by guessing every question, the chances of winning are:

3*3*3*3*3*3*3*3*3*3*3*3

=

531441→ 1/531,441 chances of winning

Evaluation 2: My chances of winning with 1 phone, and only me person guessing.

•Of the 5 games that I recorded data from (when there was only 1 phone and I was the only one guessing):

- Game 1: I got up to question 4, and I answered the first 3 questions confidently
- Game 2: I got up to question 7, and I answered the first 5 questions confidently
- Game 3: I got up to question 3, and I answered the first 2 questions confidently
- Game 4: I got up to question 6, and I answered the first 5 questions confidently
- Game 5: I got up to question 5, and I answered the first 4 questions confidently

So, if I subtract 12 by 3.8, I get 8.2, so I would need to guess 8.2 questions to win:

3*3*3*3*3*3*3*3*1.2

=

7873.2 → 1/7873.2 chances of winning

Evaluation 3: My chances of winning with 3 phones, and when 7 people are guessing.

•I did these trials over winter break, so my brother, me, and my uncle were all playing HQ on our phones. We also had my mom, my dad, my aunt, and my grandma guessing. The chances are of winning on any phone, so I recorded the highest question that we got up to on any phone.

- Game 1: We got up to question 6, and we answered the first 4 questions confidently
- Game 2: We got up to question 11 (!!!!), and we answered the first 9 questions confidently
- Game 3: We got up to question 6, and we answered the first 5 questions confidently
- Game 4: We got up to question 8, and we answered the first 7 questions confidently
- Game 5; We got up to question 10, and we answered the first 8 questions confidently

So if I subtract 12 by 6.6, I get 5.4, so I would need to guess 5.4 questions to win:

3*3*3*3*3*1.4

=

340.2→ 1/340.2 chances of winning

Unlike others conclusions I’ve made in the past, this conclusion really helps me understand something I enjoy doing. I now know that it would take about year to win if I played ones of the games each day, with 3 phones and 7 of my family members. Knowing that the prize of most games is usually split into about 5-50 dollars per winner, investing that much time into the game isn’t practical. But then again, I can always get lucky.

While my answers ended up being very reasonable, my project did have multiple areas of discrepancy. For one, my data didn’t take into account “educated guesses”. Also, answering questions “confidently” is not quantifiable. I’m certain that there were multiple questions that I answered “confidently” but still got wrong.