Draw Probability Calculator

A draw probability calculator customized for card games like Magic the Gathering.

https://savanaben.github.io/Draw-Probability-Calculator/

This tool applies hypergeometric and monte carlo methods of calculation to determine probabilities. For magic, this tool also supports london mulligans. Probably the most unique aspect of this tool is the monte carlo calculation, which can factor card attributes and overlap (something that the hypergeometric method can't do). Parts of this tool are more confirmed mathematically than others, which are outlined below.

Mathematical accuracy

• hypergeometric and multivatiate math is confirmed
• mulligan math is mostly confirmed, though not in complex situations with linked (multivariate) groups.
• Monte carlo advanced simulation

Notes/to do

• Fix category name method so it's index-based, and does not require unique text names.
• Figure our accurate london mulligan method for multivariate calculations.
• Extend linking logic so it's not capped at 4 categories.
• Extend mulligan support (maybe go up to like 5/6 mulligans).
• Support adding more turns.
• support advanced mana probability calculations

Known Accessibility to-do

• Contents within the monte accordion (Advanced mana and...) need to not be in the tab index when the accordion is closed.
• Focus needs to move to "cancel simulation" when the simulation modal opens. This is partially fixed but the focus visual state is not showing??
• screen reader
  • For some reason, the custom groups title label is not connecting to the input in step 2. Not sure why, as the mana inputs are.
  • In step 2, the mana labels need to be better (not "W", "plans"). Need to be careful not to mess with this as that value ("W") is used in the simulation too.
  • more info popovers need toggle/open/closed declaration.
  • I think the mana and custom cards need sub-grouping. like, a parent focus state that says "custom group name", and then you arrow or tab into that group. I can imagine screen readers would have some trouble connecting/grouping.
  • when a user clicks "add custom group" or "add mana group", I think either focus should move to that new group, or an alert should be read out so the screen reader person knows to kind of backtrack and look for that group. Maybe both needs to happen.
  • "click to copy email" in FAQs should prolly have an alert, like "email copied to clipboard".
  • The probabilities output area feels functional to me, but it could be better. Maybe a table layout would be more understandable. Or focus group each row so it's easier to jump around.

Nice to haves

• fancier link/multivariate logic, such as OR operator (what are the chances I draw a plains and an island, OR a dual land).
• Group linked cards in the output visual in some way (connector line, within a box, include link name, even just adjacent)
• Support variable draws per turn? (what if I have a lot of cantrips, scry, early-game draw, etc). I'm imagining a dropdown next to each "draw x" output, which could let you increase that value by 1-3. Consider if scry can be supported in a similar way (assume you always pitch a card to the bottom if it's not a desired card?)
• support shuffling on any turn (fetch lands, etc, would change probabilities with london mulligan as the cards placed on the bottom sort of "re-enter" the random pool).
• Some kind of integration with moxfield tags... (I imagine the groupings ppl use on moxfield might also be the groupings they'd want to know probabilities for.. (what are the chances I get x card from "creatures" or "removal")).
• I had considered supporting "enter tapped" flags and logic for the mana probabilities, but I am less convinced on how helpful this would be. For example, the tool could be expanded to say what the percent change is that you get 1,2,3, etc enter tapped lands. But often enter-tapped lands come with more consideration (can you play them in a way that still allows you to play what you want on a certain turn). Additionally, I think most people avoid tapped lands whenever possible, so a tool that somehow considered their impact might not be too helpful.

Mulligan challenge

The London mulligan calculations were the most challenging part of this project! I believe the calculations are correct given my outputs match Michael Moore's guiding exemplar, as well as Kelvin Liu-Huang's mtg combo calc.

There are two open aspects:

• My mulligan outputs are sometimes ~0.5% off from Kelvin's. Not sure if there's some rounding aspect that's causing this minor difference. It does not seem to ever reach significance.
• Kelvin's tool does not support calculations with more than 1 desired card (ex - I have a 10 card group, and I want to get 2 of them). Because of this, I can't confirm that aspect of my calculations are correct.

The "london" aspect of the london mulligan (placing x cards on the bottom of your deck, where x = number of mulligans) adds some assumptions and considerations:

• It's always assumed the desired card(s) are not in your hand, drawn, or placed on the bottom of the deck.
• For calculation simplicity I assume it does not matter (between your hand or the bottom of the deck) where these london mulliganed cards go, as in either location, they should not really be factored into the hypergeometric calculation. The calculations assume the cards are still in your hand. My key assumption is that practically, this leads to the same probabilities because if the cards were on the bottom of the deck, they'd be known to be the furthest away.