Top Trumps is a card game for children. The mind can wander when playing such games with kids… typically, I start thinking: what is the best strategy for this game? But also, as the game drags on: what is the quickest way to lose?
Since Top Trumps is based on numerical values with simple outcomes, it seemed straightforward to analyse the cards and to simulate different scenarios to look at these questions.
Many Top Trumps variants exist, but the pack I’ll focus on is Marvel Universe “Who’s Your Hero?” made by Winning Moves (cat. No.: 3399736). Note though that the approach can probably be adapted to handle any other Top Trumps set.
There are 30 cards featuring Marvel characters. Each card has six categories:
- Top Trumps Rating.
What is the best card and which one is the worst?
In order to determine this I pulled in all the data and compared each value to every other card’s value, and repeated this per category (code is here, the data are here). The scaling is different between category, but that’s OK, because the game only uses within field comparisons. This technique allowed me to add up how many cards have a lower value for a certain field for a given card, i.e. how many cards would that card beat. These victories could then be summed across all six fields to determine the “winningest card”.
The cumulative victories can be used to rank the cards and a category plot illustrates how “winningness” is distributed throughout the deck.
The best card in the deck is Iron Man. What is interesting is that Spider-Man has the designation Top Trump (see card), but he’s actually second in terms of wins over all other cards. Head-to-head, Spider-Man beats Iron Man in Skill and Mystique. They draw on Top Trumps Rating. But Iron Man beats Spider-Man on the three remaining fields. So if Iron Man comes up in your hand, you are most likely to defeat your opponent.
At the other end of the “winningest card” plot, the worst card, is Wasp. Followed by Ant Man and Bucky Barnes. There needs to be a terrible card in every Top Trump deck, and Wasp is it. She has pitiful scores in most fields. And can collectively only win 9 out of (6 * 29) = 174 contests. If this card comes up, you are pretty much screwed.
What about draws? It’s true that a draw doesn’t mean losing and the active player gets another turn, so a draw does have some value. To make sure I wasn’t overlooking this with my system of counting victories, I recalculated the values using a Football League points system (3 points for a win, 1 point for a draw and 0 for a loss). The result is the same, with only some minor changes in the ranking.
I went with the first evaluation system in order to simulate the games.
I wrote a first version of the code that would printout what was happening so I could check that the simulation ran OK. Once that was done, it was possible to call the function that runs the game, do this multiple (1 x 10^6) times and record who won (player 1 or player 2) and for how many rounds each game lasted.
A typical printout of a game (first 9 rounds) is shown here. So now I could test out different strategies: What is the best way to win and what is the best way to lose?
If you knew which category was the most likely to win, you could pick that one and just win every game? Well, not quite. If both players take this strategy, then the player that goes first has a slight advantage and wins 57.8% of the time. The games can go on and on, the longest is over 500 rounds. I timed a few rounds and it worked out around 15 s per round. So the longest game would take just over 2 hours.
Strategy 2: pick one category and stick with it
This one requires very little brainpower and suits the disengaged adult: just keep picking the same category. In this scenario, Player 1 just picks strength every time while Player 2 picks their best category. This is a great way to lose. Just 0.02% of games are won using this strategy.
Strategy 3: pick categories at random
The next scenario was to just pick random categories. I set up Player 1 to do this and play against Player 2 picking their best category. This means 0.2% of wins for Player 1. The games are over fairly quickly with the longest of 1 x 10^6 games stretching to 200 rounds.
If both players take this strategy, it results in much longer games (almost 2000 rounds for the longest). The player-goes-first advantage disappears and the wins are split 49.9 to 50.1%.
Strategy 4: pick your worst category
How does all of this compare with selecting the worst category? To look at this I made Player 2 take this strategy, while Player 1 picked the best category. The result was definitive, it is simply not possible for Player 2 to win. Player 1 wins 100% of all 1 x 10^6 games. The games are over in less than 60 rounds, with most being wrapped up in less than 35 rounds. Of course this would require almost as much knowledge of the deck as the winning strategy, but if you are determined to lose then it is the best strategy.
The hand you’re dealt
Head-to-head, the best strategy is to pick your best category (no surprise there), but whether you win or lose depends on the cards you are dealt. I looked at which player is dealt the worst card Wasp and at the outcome. The split of wins for player 1 (58% of games) are with 54% of those, Player 2 stated with Wasp. Being dealt this card is a disadvantage but it is not the kiss of death. This analysis could be extended to look at the outcome if the n worst cards end up in your hand. I’d predict that this would influence the outcome further than just having Wasp.
So there you have it: every last drop of fun squeezed out of a children’s game by computational analysis. At quantixed, we aim to please.
The post title is taken from “Weak Superhero” by Rocket From The Crypt off their debut LP “Paint As A Fragrance” on Headhunter Records