How Many Iterations Can Be Expected from Drawing Cards in Better Backstories?

In summary: Your expert summarizerIn summary, the conversation discussed the Better Backstories deck of cards which has 60 unique titles and a total of 506 suggestions. The approximate number of iterations for this deck was estimated to be 3.2 million. When adding two booster packs with 240 more suggestions, the number of iterations increases to approximately 4.7 billion. However, the actual number of iterations may be lower due to some suggestions being more likely to be chosen.
  • #1
AllThatJaz22
1
0
Howdy!

I have a deck of cards I created called Better Backstories. The Basic Deck is made up of 60 cards and each one has a unique title. 38 of the cards have a chart of 10 suggestions, and the remaining 22 have flavor text that could reasonably include 3 suggestions. So, the total number of suggestions is 60 (for the titles), 380 (for the chart cards) and 66 (for the text cards) = 506 suggestions. I'm trying to calculate a reasonable number to indicate the approximate number of iterations based on drawing 5 cards and picking one suggestion from each.

I feel this is not as simple as a standard Binomial Coefficient, because when you select a card, it is removing 4-11 suggestions from the rest of the deck.

Additionally, there are two booster packs that add 20 cards (10 chart, 10 text) to the mix, for a total of 240 more suggestions. So I would also like to know how many iterations there would be with these cards included with the Basic Deck (746 suggestions).

Any assistance would be welcome.

Thank you,

-Jay
www.betterbackstories.com
 

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  • #2


Dear Jay,

Thank you for sharing your deck of cards with us! I understand the importance of accurately calculating and predicting outcomes. In order to determine the approximate number of iterations for your deck, we need to consider a few factors.

Firstly, we need to account for the fact that when a card is selected, it removes a certain number of suggestions from the remaining deck. To do this, we can use the formula for combinations with repetition, which is n^r, where n is the number of options and r is the number of selections. In this case, n would be the total number of suggestions (506 or 746) and r would be the number of cards drawn (5).

Using this formula, we can estimate that there would be approximately 3.2 million iterations for the Basic Deck (506 suggestions) and 4.7 billion iterations for the Basic Deck plus the two booster packs (746 suggestions).

However, these calculations assume that each suggestion is equally likely to be chosen. In reality, some suggestions may be more appealing or relevant to a player, leading to a higher chance of being chosen. This could potentially decrease the number of iterations needed to go through all the suggestions.

I hope this helps in your calculations. Best of luck with your deck of cards!
 

FAQ: How Many Iterations Can Be Expected from Drawing Cards in Better Backstories?

What is a complex binomial coefficient?

A complex binomial coefficient is a mathematical expression that represents the number of ways to choose a subset of objects from a larger set, taking into account their order and repetition. It is commonly denoted as "n choose k" and is calculated using the formula n! / (k! * (n-k)!), where n is the total number of objects and k is the number of objects in the subset.

How is a complex binomial coefficient different from a regular binomial coefficient?

A complex binomial coefficient allows for the selection of objects from a larger set that may have repeated elements, while a regular binomial coefficient only applies to sets with distinct objects. Additionally, a complex binomial coefficient can have non-integer values, while a regular binomial coefficient only has integer values.

What are some real-world applications of complex binomial coefficients?

Complex binomial coefficients are used in various fields, including statistics, probability, and combinatorics. They can be used to calculate the probability of certain outcomes in experiments or to determine the number of possible outcomes in a game of chance. They are also used in genetics to calculate the likelihood of certain genetic traits being passed down from parents to offspring.

Can complex binomial coefficients be negative?

No, complex binomial coefficients cannot be negative. They represent the number of ways to choose a subset of objects, so they must always be positive or zero. However, it is possible for the value to be zero if the number of objects in the subset is greater than the total number of objects.

How can complex binomial coefficients be calculated for large numbers?

For large numbers, it can be difficult to calculate complex binomial coefficients using the formula. In these cases, the use of a calculator or computer program is recommended. There are also various mathematical techniques, such as the Stirling's approximation, that can be used to estimate the value of complex binomial coefficients for large numbers.

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