Saturday, May 25, 2013

A Quandary: A Lost Cities Endgame Conclusion

Last month I posed an intriguing decision I faced in a recent game of Lost cities. The decision required making an assumption under great uncertainty while closing the door on an equally palatable option.

Before I get into my proposed solution let me quickly recap the situation and review the details.

I am currently behind with 7 cards to go choosing between the Blue 8 & White 8. By selecting the Blue 8 we lose the opportunity to draw and play the Blue 6 & 7 and similarly by playing the White 8 we lose out on the scoring opportunity of the White 6 & 7, which among other things would score us an eight card bonus in White.

Now there is a distinct possibility that out decision is insignificant here and that our opponent does not have the right cards to exceed our maximum current score of 9 points. But we are facing a competent opponent and in order to improve our position we'll try to make the best decision possible.

I went over this in the initial post in greater detail but essentially the way this game has played out gives us the inclination they hold the White 7 or White 10 as they would have played the White 6 by now as the next natural play. 

Our opponent also played their Blue 10 on turn 8 with 28 cards to go in the game, giving them 11 turns to draw additional blue cards they would currently be holding. Since I didn't draw these cards we can conclude it is a greater likelihood that our opponent drew at least one blue card than the probability that both are sitting in the remaining seven cards of the draw deck.

I give the edge ever so slightly here to playing the Blue 8, as even if only the White 6 is available to draw it would seal the victory. I'm still incredibly conflicted over this choice.

I elected to play the White 8 when this game took place, but I didn't have nearly as much time then to reflect upon it.

In order to get some sort of idea I summarized the situation and put it up in several corners of the internet. The best results (predictably) came from Boardgamegeek.

Judging by the responses I may have been restrictive with the options, but the results are listed below.

The users of Boardgamegeek found playing the White 8 to be superior and there is certainly compelling evidence for that option as well. What do you think? Is there even an optimal choice?