The simulators among you might be wondering why I haven't added the

Penultimate Province Rule feature to my simulator!? Well, it's rare that it applies (<2% for most games) and when it actually does, using it might not have a significant impact on your win rate.

I added some code to my simulator as an experiment:

*if you are behind and a Duchy will put you in the lead, buy Duchy instead of the Penultimate Province*When I let two identical strategies play each other, but one uses the PPR and the other doesn't, there are very few strategies where using the PPR increases the win rate more than 1%.

The only ones I found were very quick games like BM Envoy. The PPR applied in 4% of all games and this was the result (only games where the PPR applied for player 1 are counted here):

**Quick games where you should definetely use the PPR**BM Envoy (ignoring PPR) 40% - BM Envoy 52%

BM Envoy (uses the PPR) 48% - BM Envoy 44%

So the PPR clearly has an impact in this sort of game.

**A slower game involving attacks**BM Mountebank (ignoring PPR) 47% - BM Mountebank 47%

BM Mountebank (uses the PPR) 44% - BM Mountebank 46%

So using the PPR when it applies actually hurts the player in this much slower game! This shouldn't be a surprise because as theory mentioned in the article you should only use the rule if there's a high probability your opponent will be able to buy the last Province in his next turn, which is much more likely in an Envoy game than in a Mountebank game where both player's deck are highly diluted.

All in all, it's cool that the rule exists, but don't let anyone fool you into thinking it will catapult you from spot 5000 to spot 100 on the isotropic leaderboard. Learn all the other stuff first (like good openings, the design of a decent engine,...)!