Thursday, January 16, 2014

Handicaps in Puerto Rico

When we first started playing Puerto Rico it quickly became obvious that there was a serious benefit in being the player starting with corn instead of indigo.  The reasons behind this are many - corn can produce earlier and more cheaply, corn can make better use of the Hacienda and also regular plantations because nobody wants a second indigo but the first one is useful, and the corn player is also situated to produce or sell sugar rapidly whereas indigo players are not (except potentially in 5p).  At first we just randomized seating and let the chips fall where they may but it was always frustrating to start the game and before even setting up the pieces to realize that one's chances were much reduced, particularly since PR is such a skill intensive game.  Eventually we settled on a complicated bidding system for seat that involved bidding in 1/2 point increments, though there was always debate on the exact rules for the bidding system.  It was not particularly a satisfactory way to resolve the situation in any case but it was even more silly that we then had to recall our bids at game end to figure out who won.

I did some reading up on this and found that in both games by humans and in games by the best AIs available the win rates in four player went something like 20/20/30/30 with the corn seats getting 30.  This certainly means the indigo players can win but they have a pretty severe handicap, largely because the effect of even a small advantage in the early game is greatly magnified as time goes on.  I can vouch for this as I once played against a couple of mediocre players who let me sell my sugar with a two buck Trader on round 3 one time and my build order went Sm. Sugar, Coffee, Factory, Sm. Indigo, Harbour, Wharf, Customs House, Hospice, City Hall, Office and I had a point total over 90 with my opponents at around 40 each.  They played very badly on the first three turns and then played well but by that time my lead was spiralling out of control.  Nobody should ever get Factory/Harbour/Wharf with 6 rounds left in the game and doing so is really just being a jackass but man it was some fun.

The best solution is not an arbitrary 3 point penalty at endgame but rather something to combat the early game advantage corn players have.  The solution I found was someone who did a bunch of AI testing along with real player testing on games where the players with corn start with -1 dubloon.  This actually sets the corn players back on buildup and in AI testing brought the win percentages right in line with one another in all 3 format sizes.  Players who played ~100 games with this implemented also reported a much more balanced early game experience.  This is a solution I can really get behind because it doesn't require new rules sets and new players don't need to be involved in an auction they have no comprehension of.

This solution only has one drawback that I can see, and that is an issue with the 3 player game because the corn player would start with just 1 dubloon.  They could easily be in a situation where builder is called and they cannot purchase anything but Sm. Indigo if the two Sm. Markets are already taken.  Sm. Indigo for a player that doesn't have indigo isn't disastrous but it has a bad feel to me.  Of course the revision I proposed last week makes this even more problematic because the Sm. Market was recosted to 2.  Regardless of those issues though I very much like the solution.  It is simple, clean, easily understood and administered, and gives the result I want - equalizing the value of each seat in terms of positional advantage at the start of the game.  I hope to use this variant in all my games going forward.

1 comment:

  1. Intriguing.

    I can rarely convince skilled players to play mixed skill games anymore as they worry about bad players letting other people win, so I'm not sure if I'll be able to use this. Better that I just avoid being a corn guy to balance out my experience against newer players.

    But against the good players, this is intriguing.