Background
I’ve been a lifelong fan of trading card games.
Ever since the Star Wars CCG (Customizable Card Game) in 1995 and later, Pokémon TCG (Trading Card Game) in 1999 (in the U.S.), I’ve been hooked.
Trading card games are games of skill where two competitors construct decks of cards from those available in the game and play against one another.
One player wins and another loses. (Sometimes, there is a draw.) These games are “zero-sum” in this way.
Working in the gambling industry, as I have, for 10 years now led me to ask: “What if a sportsbook placed betting prices on the outcome of trading card game events like they do for professional sports events?”
Basically: what if you can bet on games like Pokémon and Magic: the Gathering or Yu-Gi-Oh?
What would this take to make work? What are the theoretical concepts than underpin such an endeavor? What kind of profit could the sportsbook expect?
I attempt to answer these and more during the course of this project.
I aim for this project to change and evolve as its proceeds, knowing that the final conclusions I draw may be very different from my starting assumptions.
I hope also to get some comment from readers to help improve what’s being done here.
This project is both a demonstration and also some food for thought.
Objectives
My objectives for this project are:
- Demonstrate how Bayesian Inference can help us construct a predictive model for two-player, winner-take-all events (card games).
- Demonstrate how, given the probabilities assumed by these inferences, odds and betting prices by a fictional sportsbook (“TCGBook”) can be set.
- Model the outcomes of fictional and real matchups in a trading card game tournament setting.
- Model the profit and loss of our fictional sportsbook (“TCGBook”).
- Open these ideas to the public for comment, critique, and improvement.
Limitations
Before starting on this quest to model our TCGBook endeavor, it is important that I acknowledge a few key limitations.
We compare our subject, trading card games, to the tried-and-true professional sports leagues on which our sports betting idea and models are largely based.
Data Availability
The data for card game events can be very hard to come by.
Most of the data sources are compiled by fans of the games and not the hosts or producers of the games themselves. The “big dogs”, as it were, do not wish to disclose their proprietary information. Or at least, not all of it. Maybe they never thought to or they not in a place to do this regularly.
The fans that do this tireless service for us should be acknowledged for their efforts, both for this project, and more importantly, for the fandom and playerbases of these games.
That being said, much of the data that we would like to have is simply unavailable or is, at best, incomplete.
In real sports betting, sportsbooks are able to rely heavily on data aggregators to compile every conceivable bit of data about sports, events, scores, goals, fouls, players, training, coaches, etc. This isn’t the case for trading card games. The interest and size of the market just isn’t the same. It’s much smaller.
We would love to see data on each major tournament, broken down by each round. We would love to see player data reported with unique ID keys to keep variations of a player’s name or misspellings from confusing the data. We’d love to see local, sanctioned tournament data, too. But these are not realities.
We will work within these limitations and show that, at least conceptually, our idea is possible.
We’ll focus only on the widely available data, namely that from major tournaments and the highest ranked players and best known strategies.
Nature of Trading Card Game Events
Trading card game events don’t work like professional sports matches.
In professional sports matches, we know which team will play against which team and on what date. This allows the sportsbook advance knowledge of these events and gives it time to compute odds and set prices. Season schedules for any major sport are announced well ahead of time.
This is not the case for card game tournaments.
At local tournaments, anyone can show up with a deck to sign up to play. At major events, any number of qualified players can show up (or not show up). Add to this the possibility of any given strategy (i.e. deck of cards) being used by any competitor, and the matchups are simply unknowable ahead of time.
In this project we will simply ignore this as a problem. We will make the assumption that the odds are set sometime in advance of the event taking place (maybe just minutes before). Making this assumption allows us to proceed to demonstrate our ideas.
Feasibility of Taking Bets
This project isn’t a serious attempt to find a way to start taking bets on trading card games.
This may or may not be legal in any jurisdiction, and what is proposed in this project is not legal advice nor an inducement to try and make this work outside of the law.
To complicate matters, the participants of many card game events are under the legal age to gamble in many places.
Nowadays, most jurisdictions (at least in the U.S.) allow betting on college sports, where the expectation is that competitors are least 18 years of age.
Whether or not taking bets on such events would fly with gaming regulators is not considered here. This is about proving a concept (and having fun while doing it).
Don’t take anything in this project too seriously as far as making money at gambling on trading card games goes.
This is a big “what if” sort of project.
Assumptions
With our objectives in mind, and our limitations outlined, we’ll make the following assumptions for this project:
- All probabilistic modelling will be based on Bayesian (not Frequentist) inference.
- We will briefly discuss, but largely ignore, the outcome of ties. We care only about win probabilities (and consequently, not win probabilities).
- Win probabilities are expected to describe the win probability of matches; that is, “best two-out-of-three” matches in which the first competitor to win two games, wins the match. (This is the circumstance which often contributes to a draw between players: a time limit for the match it met with neither player having a decisive, tie-breaking win).
- The outcomes we seek are not only probabilistic, but also commercial: this is about setting bet prices for potential bettors. As “the house”, we expect to make money in the long run. Our models, odds, and prices will reflect that desire.
- As mentioned previously, we assume that we know who is playing and which deck they are using before the match. We know the identities of players and the decks they each use beforehand, thus, giving rise to our probabilities for each player to win and the consequent bet prices for each side of the match.
- While I will take time to explain many of the theories and logic behind each step we take in this project, I will assume that readers have some familiarity with the mathematics of probability, statistical inference, the software systems we’ll use, and the games we are speaking about. Feel free to ask in the comments if you’re unsure about something!
Segments
The project is broken down into the following segments, each with its own dedicated page:
- 1.1 Bayesian Inference & Conditional Probability
- 1.2 Modelling Competitor + Strategy Probabilities
- 1.3 Win/Loss Odds & Betting Prices
- 1.4 Building Competitor A Model: Glicko Scores
- 1.5 Building a Strategy Model: Deck Quality and the Metagame
- 1.6 Fine-Tuning the TCG Sportsbook Model
- 1.7 Simulating a TCG World Tournament (1,000 Times!)
- 1.8 TCG Sportsbook Finished White Paper
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