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Author Topic: Design the board with the largest P1 advantage  (Read 14737 times)

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JW

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Design the board with the largest P1 advantage
« on: November 30, 2016, 03:01:59 pm »
+3

What board would you design to give P1 the highest chance of victory?  Let's assume that there is a 2 event/landmark limit.

I'll start off with Ferry, Travelling Fair, Squire, Gardens, 8 villages. Hope for a 3-4 split so you can Ferry Squire turn 1, topdeck 3 squires on turn 2, and gain all the remaining Squires on turn 3! All credit to gamesou for this discovery.

IRL game with Gardens, Squire, Travelling Fair & Ferry. Gain all the Squires by turn 3 and you feel like Celestial Chameleon.
(perhaps the most favourable board for P1 I've ever seen).
« Last Edit: November 30, 2016, 11:03:26 pm by JW »
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faust

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Re: Design the board with the largest P1 advantage
« Reply #1 on: December 01, 2016, 02:21:56 am »
+1

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JW

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Re: Design the board with the largest P1 advantage
« Reply #2 on: December 01, 2016, 02:36:13 am »
+1

This one?

First, it has more than 2 events/landmarks. Also, if you don't draw the turn 1 win (only a 42% chance you'll draw it), can you do anything to stop your opponent from pulling it off (if they have the 42% hand themselves)?

A game where you're almost certain to win a key split by being first player may offer substantially better odds. I'm not sure if the Squire-Gardens example above qualifies, it depends how many Squires Player 1 can assure themselves of on a start beside 3/4.

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majiponi

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Re: Design the board with the largest P1 advantage
« Reply #3 on: December 01, 2016, 03:07:38 am »
0

Courtyard, Fool's Gold, Village, City, Fortress, Mining Village, Port, Walled Village, Worker's Village, Border Village
Donate, Travelling Fair
Now you see what I am saying.
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Holger

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Re: Design the board with the largest P1 advantage
« Reply #4 on: December 01, 2016, 11:55:52 am »
+1

I'll start off with Ferry, Travelling Fair, Squire, Gardens, 8 villages. Hope for a 3-4 split so you can Ferry Squire turn 1, topdeck 3 squires on turn 2, and gain all the remaining Squires on turn 3! All credit to gamesou for this discovery.

A game where you're almost certain to win a key split by being first player may offer substantially better odds. I'm not sure if the Squire-Gardens example above qualifies, it depends how many Squires Player 1 can assure themselves of on a start beside 3/4.

If Player 2 didn't buy any, Player 1 could gain a total of 9-10 Squires by the end of T3 with a 3/4 or 5/2 start, and 6-7 Squires with 4/3 or 2/5. But player 2 can also buy 2-4 Squires on their first two turns (2.6 on average). So player 1 will always win the split at least 6:4, but usually 7:3 and occasionally (P=25%) 8:2.
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mith

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Re: Design the board with the largest P1 advantage
« Reply #5 on: December 01, 2016, 12:17:29 pm »
+3

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).
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JW

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Re: Design the board with the largest P1 advantage
« Reply #6 on: December 01, 2016, 04:16:18 pm »
0

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).

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%.
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mith

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Re: Design the board with the largest P1 advantage
« Reply #7 on: December 02, 2016, 12:42:18 pm »
+2

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.
« Last Edit: December 02, 2016, 12:45:57 pm by mith »
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luser

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Re: Design the board with the largest P1 advantage
« Reply #8 on: December 03, 2016, 12:58:46 pm »
+2

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.
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ephesos

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Re: Design the board with the largest P1 advantage
« Reply #9 on: December 05, 2016, 12:12:10 am »
+1

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.

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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ephesos

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Re: Design the board with the largest P1 advantage
« Reply #10 on: December 05, 2016, 12:20:28 am »
0

Code: [Select]
<player name="Delve/Donate"
 author="Ephesos"
 description="Delve -> Donate -> Masterpiece -> Feodum">
 <type name="Province"/>
 <type name="UserCreated"/>
 <type name="Bot"/>
 <type name="TwoPlayer"/>
  <board contents="Baker, Masterpiece, Feodum, Donate, Delve" bane="" Mountain_Pass_Bid="0" Obelisk_Choice=""/>
   <buy name="Delve">
      <condition>
         <left type="countTurns"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Delve">
      <condition>
         <left type="countTurns"/>
         <operator type="equalTo" />
         <right type="constant" attribute="3.0"/>
      </condition>
      <condition>
         <left type="countCardsInDeck" attribute="Silver"/>
         <operator type="equalTo" />
         <right type="constant" attribute="4.0"/>
      </condition>
   </buy>
   <buy name="Donate">
      <condition>
         <left type="countTurns"/>
         <operator type="equalTo" />
         <right type="constant" attribute="3.0"/>
      </condition>
   </buy>
   <buy name="Masterpiece">
      <condition>
         <left type="countAvailableMoney"/>
         <operator type="greaterOrEqualThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
      <condition>
         <left type="countCardsInSupply" attribute="Silver"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
   <buy name="Delve">
      <condition>
         <left type="countCardsInSupply" attribute="Silver"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
   <buy name="Feodum"/>
   <buy name="Province"/>
</player>

And it is done. 79.45% P1 win, 12.88% P2 win, 7.67% ties
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mith

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Re: Design the board with the largest P1 advantage
« Reply #11 on: December 06, 2016, 04:03:47 pm »
+2

I believe there is a way to turn the turn 1 solution into a turn 2 solution by adding Death Cart and removing Shelters. Death Cart gets around the possibility of opponent buying a Villa on turn 1 (only need 5 buys to empty the Ruins, instead of 10 for Patrician/Emporium; the remaining buys can gain Border Village/Duchy for points), and also gives you a way to be sure your turn 2 hand gets to 5.

With 2 or 3 on turn 1, just buy Travelling Fair + Ruin - this sets up turn 2 to have at least the Ruin and 3 Coppers, and then the turn 1 solution follows.
With 4 or 5 on turn 1, buy Borrow + Travelling Fair + Death Cart (use Baker token if needed) - this gives you a Ruin in hand and $5 from Death Cart (trashes itself or the other Ruin, either way), so you don't need the Baker token.

Unless I'm missing something, this is 100% for player 1, though of course we are still well over the Event limit.
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luser

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Re: Design the board with the largest P1 advantage
« Reply #12 on: December 07, 2016, 04:45:20 pm »
+1

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.

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.
Even better you could delve+donate on turn 2 which with baker token leads to 4 silver deck for both 5/2 and 3/4. Not sure if p2 3 delve+donate on turn 1 helps.


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mith

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Re: Design the board with the largest P1 advantage
« Reply #13 on: December 07, 2016, 05:27:13 pm »
0

I think using Raid instead of Masterpiece is better in most cases, too - best case is SSSSS which is 7 Silver with Masterpiece and 7 Silver with Delve+Delve+Raid (plus the -1 Card effect). If both players are buying Raid every turn, both max out at $9 for Borrow+Delve+Delve+Raid (so 6 Silvers per turn); might as well Borrow as long as the Raids are happening.

5/2 might look like:

T1: Delve+Delve+Delve+Donate (keep two Coppers)
T2: $8 - Pay debt
T3: $8 - Borrow+Delve+Delve+Raid (and you have a deck of 9 Silver, 2 Copper; so you'll only get 5 Silvers per turn sometimes from this point)

That seems awfully strong, I don't see an obvious way to prevent P2 having an advantage if he gets 5/2 and P1 doesn't.
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ephesos

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Re: Design the board with the largest P1 advantage
« Reply #14 on: December 07, 2016, 07:34:17 pm »
+1

Even better you could delve+donate on turn 2 which with baker token leads to 4 silver deck for both 5/2 and 3/4. Not sure if p2 3 delve+donate on turn 1 helps.

Redid the sim with T2 donate, leads to 98.07% P1 win, 1.93% P2 win, 0% ties, and ever so slightly beats out T3 Donate in both start orders.

I think the next best thing would have to be 100% at this point.

EDIT: With the P2 3 delve+donate, it's back down to 96.92% P1 win, 2.86% P2 win, 0.22% ties.

Slight nuance I just noticed though; the sim doesn't keep any Copper from Donate, and goes down to 4 Silver every time.
« Last Edit: December 07, 2016, 07:40:58 pm by ephesos »
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JW

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Re: Design the board with the largest P1 advantage
« Reply #15 on: December 07, 2016, 07:46:54 pm »
+2

Even better you could delve+donate on turn 2 which with baker token leads to 4 silver deck for both 5/2 and 3/4. Not sure if p2 3 delve+donate on turn 1 helps.

Redid the sim with T2 donate, leads to 98.07% P1 win, 1.93% P2 win, 0% ties, and ever so slightly beats out T3 Donate in both start orders.

I think the next best thing would have to be 100% at this point.

EDIT: With the P2 3 delve+donate, it's back down to 96.92% P1 win, 2.86% P2 win, 0.22% ties.

Slight nuance I just noticed though; the sim doesn't keep any Copper from Donate, and goes down to 4 Silver every time.

If you will Donate on turn 2, then except on a 2-5 start shouldn't you buy Feodum on turn 1? You keep a coin token on 5-2 while still having 4 Silvers after turn 2 and on a 3-4 or 4-3 start you end up with 5 Silvers after turn 2.
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luser

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Re: Design the board with the largest P1 advantage
« Reply #16 on: December 08, 2016, 09:17:24 am »
+1

Even better you could delve+donate on turn 2 which with baker token leads to 4 silver deck for both 5/2 and 3/4. Not sure if p2 3 delve+donate on turn 1 helps.

Redid the sim with T2 donate, leads to 98.07% P1 win, 1.93% P2 win, 0% ties, and ever so slightly beats out T3 Donate in both start orders.

I think the next best thing would have to be 100% at this point.

EDIT: With the P2 3 delve+donate, it's back down to 96.92% P1 win, 2.86% P2 win, 0.22% ties.

Slight nuance I just noticed though; the sim doesn't keep any Copper from Donate, and goes down to 4 Silver every time.

If you will Donate on turn 2, then except on a 2-5 start shouldn't you buy Feodum on turn 1? You keep a coin token on 5-2 while still having 4 Silvers after turn 2 and on a 3-4 or 4-3 start you end up with 5 Silvers after turn 2.

Thats a problem. It gives counter to second player. If he buys it when first player doesn't then at end p1 must choose between winning silver split but losing feodum one 4-3 or winning feodum split and losing silver one which gives smaller advantage. Then there could be problem that silver will split evenly instead p1 winning split if they get more silver in turn 1/2, one must check that or invoke rule that you could play with any number of silver. Second possibility to fix this would be 3 player game, but I didn't analyze that yet.
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ephesos

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Re: Design the board with the largest P1 advantage
« Reply #17 on: December 08, 2016, 04:28:22 pm »
0

Some math on Feodum/Silver

Losing the split means you need to earn more Silver, but how much more? With 3/4 of the Feodums, you need to have 4/3 as many Silvers, approximately.

So that's 4/7*40, which rounds up to 24 Silvers.

And we can see that at 24 Silvers, you get 8*3=24 points, and your opponent gets 5*4=20 points.

At 23 Silvers, you get 7*3=21 points, and your opponent still gets 20 points. But at 22 Silvers, your opponent's Feodums go up, so you lose 21 to 24.

So to give up the Feodum split, you need to win Silver split by 6 or more
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ephesos

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Re: Design the board with the largest P1 advantage
« Reply #18 on: December 08, 2016, 05:18:42 pm »
+2

Sadly the simulator is stupid and doesn't trash Feodum. Maybe after the quarter is over, I'll make a fork and see if I can get it running.
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JW

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Re: Design the board with the largest P1 advantage
« Reply #19 on: December 08, 2016, 05:22:18 pm »
0

Some math on Feodum/Silver

Losing the split means you need to earn more Silver, but how much more? With 3/4 of the Feodums, you need to have 4/3 as many Silvers, approximately.

So that's 4/7*40, which rounds up to 24 Silvers.

And we can see that at 24 Silvers, you get 8*3=24 points, and your opponent gets 5*4=20 points.

At 23 Silvers, you get 7*3=21 points, and your opponent still gets 20 points. But at 22 Silvers, your opponent's Feodums go up, so you lose 21 to 24.

So to give up the Feodum split, you need to win Silver split by 6 or more

Additionally, if one player has more Feoda and less Silver and the other player has more Silver and fewer Feoda, but both have equal points from their Feoda, the player with more Silver has the advantage because they have better money density.
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ephesos

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Re: Design the board with the largest P1 advantage
« Reply #20 on: December 08, 2016, 06:24:39 pm »
0

True, I didn't actually account for the post-Feodum game. If you're even close to tied, I think Silver lead wins just by getting more Provinces.
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mith

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Re: Design the board with the largest P1 advantage
« Reply #21 on: December 09, 2016, 06:41:46 pm »
0

Not 100% win though; Silver leader could have worse draws (SSSFF only buys Duchy) while the other player's Feodum's spread out.
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luser

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Re: Design the board with the largest P1 advantage
« Reply #22 on: December 10, 2016, 06:06:56 am »
0

One of possible fixes of my strategy would be add alms, trav.fair and borrow so you could on turn 1 get buy from baker+borrow using tfair. With first buy alms a feodum, with second donate. Opponent would need to mirror it or be turn behind. I hope that silver would split unevenly here.
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faust

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Re: Design the board with the largest P1 advantage
« Reply #23 on: December 10, 2016, 05:04:22 pm »
0

One of possible fixes of my strategy would be add alms, trav.fair and borrow so you could on turn 1 get buy from baker+borrow using tfair. With first buy alms a feodum, with second donate. Opponent would need to mirror it or be turn behind. I hope that silver would split unevenly here.
That's more than 2 events though.
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Holger

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Re: Design the board with the largest P1 advantage
« Reply #24 on: December 11, 2016, 02:34:42 pm »
0

Quote from: JW link=topic=16589.msg659913#ms
  g659913 date=1481158014
Even better you could delve+donate on turn 2 which with baker token leads to 4 silver deck for both 5/2 and 3/4. Not sure if p2 3 delve+donate on turn 1 helps.

Redid the sim with T2 donate, leads to 98.07% P1 win, 1.93% P2 win, 0% ties, and ever so slightly beats out T3 Donate in both start orders.

I think the next best thing would have to be 100% at this point.

EDIT: With the P2 3 delve+donate, it's back down to 96.92% P1 win, 2.86% P2 win, 0.22% ties.

Slight nuance I just noticed though; the sim doesn't keep any Copper from Donate, and goes down to 4 Silver every time.

If you will Donate on turn 2, then except on a 2-5 start shouldn't you buy Feodum on turn 1? You keep a coin token on 5-2 while still having 4 Silvers after turn 2 and on a 3-4 or 4-3 start you end up with 5 Silvers after turn 2.
Agreed. You can also use the token to have 5 Silvers after turn 2 with 5-2.
I really don't see how you get a  90+% win for P1 on this board. If both players Donate T2 for a 5 Silver deck, they'll usually split the Silvers 20-20 on T5 and then also split Feoda and Provinces evenly, resulting in a perfect tie.
« Last Edit: December 11, 2016, 03:02:15 pm by Holger »
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