How would you model this game?

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In summary, a group of 1000 players are competing to write the lowest non-repeated number in order to win a prize. The game can be approached in two ways: choosing an infinitesimal hyperreal number if any type of number is allowed, or strategically choosing a high number to avoid repetition if only positive integers are allowed. The game involves probability and human psychology, as players must consider what numbers the others may choose. It would be interesting to analyze the distribution of numbers chosen in multiple rounds of the game.
  • #1
kaleidoscope
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a group of 1000 players are asked to write a number greater than 0. the player who writes the lowest non-repeated number wins a prize.

how would you determine which number to pick?
 
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  • #2
case A: if it can be any "type" of number (if the game is not limited to natural numbers- which is what I assume to be the case) just go for an infinitesimal hyperreal infinitely close to 0 (non-standard analysis thingie). not many will think of that one, and besides there is an infinity of such numbers so the chances of 2 people picking the same number are rather low. :P

B: if the game is limited to natural numbers between 0 and 1000... hmmm, that's tricky- I'm not sure.
is there any probabilities and human psychology expert around?

EDIT:
... ooops, I wasn't quite paying attention... 1000 players must choose a positive number... not a number between 0 and 1000... well, I guess case A is a good choice then. :D
 
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  • #3
If we can choose any positive real number, this is basically the same as trying to think of the largest number you possibly can, then take it's reciprocal.

This is interesting only if it is restricted to positive integers. Psychology is definitely involved, since you have to imagine what numbers the other 1000 might choose. I'm thinking I'd choose something fairly high to avoid repeating another's pick. Perhaps 63 or somewhere thereabouts?

It would be interesting to repeat this game a number of times and see what sort of distribution the numbers follow.
 
  • #4
I like to argue that suppose a player chose numbers follow an exponential distribution. Positive skewed exponential mean incline to choose small number but not too small.

The 1000 chosen numbers is certainly an ordered finite set. Use binomial principle I can know the probability of X number of people chose numbers lower than me.
 

1. How do you decide what elements to include in your game model?

The decision of what elements to include in a game model depends on the specific objectives and goals of the game. It also involves considering the target audience and their preferences, as well as the resources and limitations of the game development process.

2. What techniques do you use to create a game model?

There are various techniques that can be used to create a game model, such as flowcharts, UML diagrams, and decision trees. These techniques help to organize and visualize the different components of the game and their relationships, making it easier to understand and modify the model.

3. How do you ensure that your game model is accurate?

To ensure the accuracy of a game model, it is important to conduct thorough testing and validation. This can involve simulating gameplay scenarios and comparing the results to the intended outcomes of the model. Feedback from playtesters and game developers can also help to identify any discrepancies or errors in the model.

4. Can a game model be modified during the development process?

Yes, a game model can be modified during the development process. In fact, it is common for game models to undergo several iterations and revisions as the development team gains a better understanding of the game mechanics and objectives. However, any modifications should be carefully considered and tested to ensure that they align with the overall vision of the game.

5. How do you document a game model?

Documenting a game model is crucial for ensuring that all members of the development team have a clear understanding of the game's design. This can be done through written descriptions, diagrams, and charts, as well as through using standardized notation and terminology. It is also important to regularly update the documentation as the game model evolves throughout the development process.

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