The Shape of Card Games

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Ninety-Eight: Basic Statistics

on Feb 6, 2019

With the basic Ninety-Eight coded in RECYCLE, it is time to run many simulations in CardStock with both random and AI players. To gather statistics for this and the next post on heuristics, we ran 100 games with all random players, 100 games with one AI and the rest random players, and 100 games with all AI players. We did these simulations for 2, 3, 4, and 5 players. Let’s see if we can answer some basic questions about the game.

Are there sufficient choices for players?

Ninety-Eight, like Pairs is very consistent in the number of choices a player has on their turn: always 4. A player can play any of their four cards, and then draw a new card from the STOCK location.

How does game length vary with the number of players?

Even though the choices are limited on each turn for a player, the length of the game is undetermined. So, how long is an average game of Ninety-Eight? We’ll again eschew real time estimates, since we are working with simulated games. Instead we’ll look at the average number of calls to a choice block for a player decision, since these should be well-correlated.

We can see in the image below that the game will last between 10 and 14 turns on average. This is pretty consistent no matter how many players are in the game.

Ninety-Eight Length

Unlike Pairs, we don’t see evidence that the AI players make the game longer or shorter. I would have thought that the AI would be more adept at playing Kings to get to 98 faster, but perhaps this is offset by the other AI players knowing how to respond with a Ten, Jack, or Queen. We’ll see some hints of the AI strategies in the lead histories

Can players be strategic in Ninety-Eight?

Yes! The AI players are very likely to do well in Ninety-Eight! The goal is again to not lose, so we compare the success of an AI player versus other random players to the expected non-loss rate. While not as striking as in Pairs, the non-loss rate is quickly approaching 1.

Pairs Markov Gain

Up Next

Next post, we’ll see how Ninety-Eight measures up with our heuristics and look at the overall gameplay experience with all AI players. What else would you like to see analyzed about Ninety-Eight? Let me know in the comments below, and I’ll see if I can incorporate them in future posts. Thanks for reading!

(Image courtesy of https://www.publicdomainpictures.net/en/view-image.php?image=24744&picture=playing-cards](https://boardgamegeek.com/image/3667931/pairs))