The following are preliminary notes on my interest in the card game Top Trump, why I'm curious about it and how I plan to answer that curiosity.
Top Trumps has to have an optimal strategy that's not just calling the highest number on the card right?
This is actually a topic I want to look into eventually, honestly, by taking decks from different lines and going through the cards. My method, I think, would be to take the stats from each card and see how it measures up to the other cards in the deck, which is to say, if you were to call each statistic, how many cards in the deck would have a lower, higher or equal value, and see if the highest stat of the card is consistently the most likely winning move or not. My guess is that not every stat is similarly weighted, and while the stats mahy have (I believe) the same amplitude, they may not have the same median.)
Of course, this is in a vacuum, and over the course of a Top Trumps game, as more and more cards are revealed and passed around, the likelihood of that statistic would evolve based on availble info of your opponent's deck and your own. Regardless of the initial balancing of each card against every single other card in the deck, a machine perfectly playing the game would likely not choose a card's highest stat at all times in a real game.
My second question, however, would be if this even matters. If, when pitting a perfect player and a 'human' player (ie. The player who instinctually plays the card's highest stat every time), does that cause a significant difference in their respective win/loss ratios? To answer this, I'd have to simulate a number of games between different players. Player A would be a typical human player, calling the highest card stat each time. Player B, if my initial suspicion is correct, would call the stat most likely to win when compared to all other cards in the deck. Player C would call out the stat most likely to win considering which player is in possession of which card.
There are two more player types we could consider. So far, I've worked under the assumption that cards that are won are placed in a separate pile (Let's call it the 'victory pile'), and when a player runs out of cards in their deck, they shuffle their victory pile and continue playing. However, players may just decide to put the cards they have won at the bottom of their deck as soon as they're won. Thus, we could come up, in this confiugration, with yet another player, Player D, who remembers the order the cards were played in and won, and could then know which card, would come next. As soon as the decks start to loop back to the first card played, and choose a winning statistic every time it can. Finally, we could introduce a Player E, whose tactic would simply be to call out stats at random.
Each player would play a significant number of matches against each of the other player, so that at the end, everyone has played against everyone a significant amount of time, and we can tally up the ratio of wins, losses and ties when each strategy is faced with the other.