Triad Ban Strategy: Game Theory
Ever since I learned about Triad I’ve had a hard time wrapping my head around ban strategy. Yes, sometimes it is extremely easy because all three of your decks have a terrible matchup against one of their decks, so you just ban it. But often enough there is some nuance to it. Before the KFPL Triad qualifier, I put together a spreadsheet to help with my ban strategy. I will share with you what I have learned.
My approach to this problem was to follow a payoff matrix. A payoff matrix is simple a table that gives some numerical value to your strategy. When filling out a payoff matrix you want the rows to represent your potential choices and the columns to represent your opponent’s potential choices.
Here is a basic payoff table for a ban strategy. To fill it in, you will have to go over every one of your ban options and compare it to every one of your opponent’s ban options. You would review what happens when you ban your opponent’s A deck and they ban your 1 deck. Then do the same for A and 2 then A and 3 etc.
The value you put in the space doesn’t really matter, as long as it makes sense and is consistent. For example, you could fill it in with numbers ranging from 0 to 9 or -2 to +2, whatever you feel comfortable with. This method is the purest form of a payoff table for the ban strategy and is also what I described on the timeshapers podcast episode 16. However, I found that in practice, it is extremely difficult to actually get through. It means you need to evaluate your deck against two decks repeatedly. A very time-consuming process that takes more than the allotted time for bans.
Right before the KFPL tournament, I designed this spreadsheet, which I also shared with our Patreon supporters sans an in-depth explanation. What this spreadsheet does is build the payoff table from the individual matchup evaluations.
Instead of filling out the payoff table directly, you only need to evaluate the 9 matchups and fill in the payoff for those. I use -1 for a bad matchup, 0 for an equal matchup, and 1 for a positive matchup. The spreadsheet will do the work for you and tally up the payoffs of each ban.
This is the formula in the cell that overlaps me banning their 1 deck and them banning Countess. It sums up all the payoffs of the decks that remain in play. Then the bottom row in the table shows the worst-case payoff for each of your opponent’s bans based on each of your potential bans. If I ban my opponent’s deck 1 and they ban Falconsight, I have a payoff of 3, if they ban Aquaoxyl I get a payoff of 2 and if they ban Countess I get a payoff of 3. The worst-case scenario here is they ban Aquaoxyl so my worst payoff is 2.
If I go over to the other two columns I can see my worst payoff is 0 and -1, which is obviously worse than 2, so I will definitely ban 1 here. Note that sometimes the worse case in two columns is the same, in which case you can evaluate the highest total, or try to guess which deck they might ban to make your choice.
This is all well and good when playing online, but you’re not likely to start filling out spreadsheets or even tables in a notebook in live events. So I didn’t want to write this article before I found a good Heuristic for the ban strategy. In most cases, I found it sufficient to tally up the total of each of my opponent’s decks and ban the worst payoff one. It is easy to see that if all my decks have a bad matchup against a certain deck I should ban it.
My process is to pick one of their decks, then compare the matchup to my three decks one at a time, and tally the payoffs. This will give me a number ranging between -3 to +3. I will only need to remember one number per deck. Then I will simply ban their deck with the lowest number, my worst matchup overall. If you review this process on the examples in the spreadsheet you can see it works in all cases. The only place this fails is in helping you break ties.
In summary, I presented you with a tool you can use to practice your evaluations and also gave you a heuristic to make it easier once live events roll back around. In the meantime, I am curious if this tool can be used in picking a triad lineup. Take the top lineups from the KFPL season 2 triad league, then compare different lineups you are considering against them and pick the triad lineup that has consistently the highest payoffs. A very interesting exercise. Please do let me know your findings if you choose to do so!