Dominion > Puzzles and Challenges

Design the board with the largest P1 advantage

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mith:
I get 5 Squires after two turns with a 5/2:

Turn 1: Travelling Fair, Ferry, Squire (top deck)
Turn 2: Play Squire (+2 Buys), Travelling Fair, Squire x4

Still, that's a 11/12 chance of winning the split, usually 7:3 or better. Of course, you still have to prove a win with this advantage, though I'd be surprised if there weren't a way to do that, given the slots available; and if you can win these about 83% of the time you're already better off than the turn 1 solution (even ignoring the Event restriction).

JW:

--- Quote from: mith on December 01, 2016, 12:17:29 pm ---Still, that's a 11/12 chance of winning the split, usually 7:3 or better. Of course, you still have to prove a win with this advantage, though I'd be surprised if there weren't a way to do that, given the slots available; and if you can win these about 83% of the time you're already better off than the turn 1 solution (even ignoring the Event restriction).

--- End quote ---

Where do you get the 83% number from? To approximate the turn 1 kingdom, a kingdom where we alternate having 41.7% chances of winning on our turns, and I go first, only yields a 63.2% chance of victory for the first player. For those interested, the formula is 1 / (2-p), where p is the chance each of us wins on each turn.

In the 11/12 (91.7%) of the time the first player wins the Squire split, they won't need anything close to an 83% average win % to have an overall chance of winning above 63%. On the assumption that P2 wins half of games when they get 5-2 and can tie the split, the required percentage to equal the turn 1 solution is only 64.4%.

mith:
I had started to write something about this earlier, and then forgot I didn't post it, so it does look like I pulled that number out of nowhere.

In the turn 1 kingdom, I'm pretty sure the first player can always win on turn 2 if neither player wins on turn 1; the setup of the Mission turn is simply a topdecked Fortress, which can be done for $2 with Travelling Fair + Alms (so, always). The one potential hangup I see is that the second player gain multiple Villas somehow and keep you from having enough Buys, but on the other hand turn 2 has the advantage of being able to buy cards normally, so you can likely get around that somehow.

So the probability of winning is 5/12 + 7/12*7/12 (win first turn + don't win first turn and neither does P2) = 109/144 > 75%. (And then divide by 11/12, 109/132 is about 82.6%.)

The 83% is still too high though; I didn't account for the 1/12 case of P2 having a 5/2 and splitting the Squires evenly. P2 might have a slight advantage here (except in the case where P1 also got a 5/2), but it's certainly not a lost cause for P1. So, somewhere between 78% (if 5/2 is 50-50) and 83% (if it were always a P2 win), but closer to the lower end of that.

luser:
What about donate,  delve, masterpiece, feodum, baker. Strategy there should be exact minor. 2 silvers in t1/2 with masterpiece for 6 and delve on 5/2. p2 could likely win with lucky 5/2 hand mostly reversing player order.
Then donate on t3 keep 4 silvers, pay debt on turns 4, from turn 5 overpay masterpieces.  On turn 6 p1 does final overpay and win silver split which likely wins a game.

ephesos:

--- Quote from: luser on December 03, 2016, 12:58:46 pm ---What about donate,  delve, masterpiece, feodum, baker. Strategy there should be exact minor. 2 silvers in t1/2 with masterpiece for 6 and delve on 5/2. p2 could likely win with lucky 5/2 hand mostly reversing player order.
Then donate on t3 keep 4 silvers, pay debt on turns 4, from turn 5 overpay masterpieces.  On turn 6 p1 does final overpay and win silver split which likely wins a game.

--- End quote ---

Why would you Masterpiece for 6 when you could Delve 3 times instead? Your average $ with 4 Silver is above 1, so you're diluting it by getting a Masterpiece Copper, which means your Debt might be 1 higher.

Also, T3 you can Delve + Donate for that extra Silver to keep and guarantee $10 on the next hand. Not sure if Delving 2+ times before Donate is worth doing though. Possibly equivalent to doing it the next turn, though there's something with Masterpiece and Debt totals where there's an optimal play at each amount.

Feels like this should go into a simulator.

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