About Ultimate Sorry

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Ultimate Sorry

Sorry is a great board game. Over the years it has become my go to game for friend and family gatherings. Everyone loves dropping a sarcastic "I'm sorry" and bumping your opponent all the way back to the start.

When playing with my in-laws there is often great debate on what moves are 'optimal' and social factors such as alliances, revenge, or just a desire to stir the pot seem to often decide the winner. I built a Sorry simulator in python that can play thousands of games in a few milliseconds. I explore some of my discoveries below.

I also built a web server to allow a single board position to be analyzed, showing all the possible moves and how each one impacts each player. If you are ever wondering what might be the best move in a Sorry game the move analyzer will help (or confuse) you.

Check out my other projects on my website, WilliamSchaller.com, or check out the code for this project on github.

Some implementation notes: The sorry board state can be captured with a deck and a 4x4 array indicating the position of each of the pawns. During testing, I found it is possible for a player to knock out one of their own pawns by using an 11 card to swap with another pawn that will then slide into the original pawn.


Sorry!

By simulating thousands of sorry games in a few seconds we can answer some interesting questions.

How much of the game is skill vs luck?
To test this we can simulate 100,000 games of Sorry where 3 of the players make random moves. The 4th player uses a simple strategy, chose the move that gets their pawns closest to their home. Out of 100,000 games the 4th player will win 63% of the time, while each of the random strategy players will win 11 to 13% of the time.

How much can an alliance impact the game?
To test this we can simulate games and tell the AI players which players they should try to make win. If we tell all 4 players to make Blue winning their top priority then blue will win 97% of the time! Meanwhile, if all players (including Blue) make Blue losing their top priority then Blue will only win 0.06% of the time. If Blue fights back against the other 3 they can bring their odds all the way up to 20%.

What if you are trying to lose but all 3 other players want you to win? In that case, you will win 50% of games even though you are trying to lose. If 3 players are playing to make themselves win, but one player has a grudge and decides to make it their priority to make Blue lose, then Blue's win chances drop from 25% to 13%. Essentially, grudges and alliances can have a massive impact on the game.

How many turns in Sorry are not valid?
On average, a Sorry game takes 180 turns until someone wins and 60 of those turns are skipped because there is not a legal move. There are around 15 Sorry cards used per game.

Which spots are the most dangerous?
While playing it seemed that sitting just outside another players start zone is a risky move. Just how risky is it? To understand this, I simulated 100,000 games and captured which spots results in the most pawns being knocked back home from Sorrys, slides, or direct landings. The data is extremely clear here.

40% of all pawn knock backs occur on the 4 spots just outside of the player's homes. The next most dangerous spots are located on the slides where each spot is responsible for 2% of knockbacks. The spots outside of home are over 5 times more dangerous than other spots! The safest spots are just before your own slides, because other players are less likely to sorry you as they won't be able to slide directly on that turn.

The spot outside of home is dangerous because:
1) a pawn can be knocked off by a player getting a 1 or 2, and coming out of home.
2) it's at the end of a slide
From there, the numbers are skewed because just outside of home is the most likely spot for a pawn to be! So scenarios #1 and #2 are more likely to occur, plus at the start of the game Sorry cards will be used on pawns in this location. This data did not change if I changed the strategy the players used.

My data is biased. It's skewed by the spots a pawn is most likely to be on in the first place. I need to come back and factor this in to correctly compute which spots on the board or more dangerous than others.

Below is a board where the more red the spot, the more knockbacks occur per game.

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Thank you for reading.