Erictaveren
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- Joined
- Jan 9, 2024
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Hello and thanks in advance for looking at this. I just talked with an AP Stats teach and had her head spinning. Here we go…
I’m designing a card and dice based game to help kids learn chemistry. Their goal will be to collect element cards (Oxygen, Hydrogen, etc) in order to combine them and create compounds (NaCl, AgNO3, etc). The element cards will come from two separate decks, one for gaseous elements, one from solids. To get cards, they’ll roll an eight sided die. Five sides will net them a gas, two a solid, and the last a card that isn’t applicable to my dilemma. What I’m trying to figure out is multiple things. How many times will then need to roll the dice (I’ve arbitrarily chose six as how many they roll a turn, but that’ll be one of the variables to adjust), in order to create a specific compound. This is to determine the difficulty and this how many points to award. Another question is how many rolls will it take to make anything, as opposed to a specific thing. I want to make sure they’ve got something to do hopefully every other roll or so. I know the solids are the limiting factors for most of the compounds, so having an appropriate distribution of card accrual is a factor as well. Not everything need to be equal, but I’m hoping to see a spread that is both predictable and reasonable.
I’ve got an excel sheet where I’ve all the compounds listed as well as all the elements. The elements have arbitrary points assigned currently based on frequency of appearance in the compounds, and the compounds have point totals shown based on that. I have columns to indicate % of gas or solid in a given compound. It won’t impact this equation, but it’s to help show trends on the compounds in case I need to adjust the die results. Each deck (gas and solid) each has 165 cards, and the breakdowns of each element within are listed. From there, I have the odds of gas/solid based on die roll, the odds of the card based on how many times it’s in the deck, followed by an odds of being drawn (multiplying those together). There’s a die roll cell to be updated as needed based on results.
There are two columns I imagine will need replacing (or junking entirely). One is Odds per Roll, and the other is Required Rolls. The Odds per roll was created by multiplying the odds of each instance of element and then by the number of dice. The Required Rolls was 1/odds per, to see how many rolls to get to 100%. This is faulty because it doesn’t take into account accrued cards of previous rolls. I don’t know how to do that math. I can approximate with some of the simpler ones by dividing the odds of a compound by the odds of the highest element in that compound on the assuming I’ll have drawn that one at some point, but going beyond a two atom compound I’m at a loss.
Looks like I can only attach pictures (spreadsheet would have been nicer), but here a shot of the excel sheet. The list goes 41 compounds down.
My ultimate goal with this is to create a statistically balanced game where I can assign fair points based on compound difficulty and variety. There are modifier cards that’ll exist, but that‘s a wrench in the plans for another day.
Hopefully that all made sense and hopefully you can follow my math on the sheet.
Thanks again.
I’m designing a card and dice based game to help kids learn chemistry. Their goal will be to collect element cards (Oxygen, Hydrogen, etc) in order to combine them and create compounds (NaCl, AgNO3, etc). The element cards will come from two separate decks, one for gaseous elements, one from solids. To get cards, they’ll roll an eight sided die. Five sides will net them a gas, two a solid, and the last a card that isn’t applicable to my dilemma. What I’m trying to figure out is multiple things. How many times will then need to roll the dice (I’ve arbitrarily chose six as how many they roll a turn, but that’ll be one of the variables to adjust), in order to create a specific compound. This is to determine the difficulty and this how many points to award. Another question is how many rolls will it take to make anything, as opposed to a specific thing. I want to make sure they’ve got something to do hopefully every other roll or so. I know the solids are the limiting factors for most of the compounds, so having an appropriate distribution of card accrual is a factor as well. Not everything need to be equal, but I’m hoping to see a spread that is both predictable and reasonable.
I’ve got an excel sheet where I’ve all the compounds listed as well as all the elements. The elements have arbitrary points assigned currently based on frequency of appearance in the compounds, and the compounds have point totals shown based on that. I have columns to indicate % of gas or solid in a given compound. It won’t impact this equation, but it’s to help show trends on the compounds in case I need to adjust the die results. Each deck (gas and solid) each has 165 cards, and the breakdowns of each element within are listed. From there, I have the odds of gas/solid based on die roll, the odds of the card based on how many times it’s in the deck, followed by an odds of being drawn (multiplying those together). There’s a die roll cell to be updated as needed based on results.
There are two columns I imagine will need replacing (or junking entirely). One is Odds per Roll, and the other is Required Rolls. The Odds per roll was created by multiplying the odds of each instance of element and then by the number of dice. The Required Rolls was 1/odds per, to see how many rolls to get to 100%. This is faulty because it doesn’t take into account accrued cards of previous rolls. I don’t know how to do that math. I can approximate with some of the simpler ones by dividing the odds of a compound by the odds of the highest element in that compound on the assuming I’ll have drawn that one at some point, but going beyond a two atom compound I’m at a loss.
Looks like I can only attach pictures (spreadsheet would have been nicer), but here a shot of the excel sheet. The list goes 41 compounds down.
My ultimate goal with this is to create a statistically balanced game where I can assign fair points based on compound difficulty and variety. There are modifier cards that’ll exist, but that‘s a wrench in the plans for another day.
Hopefully that all made sense and hopefully you can follow my math on the sheet.
Thanks again.
