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[Davio]

That's the question.

I played this game vs. Roger Rabbit: http://dominion.isotropic.org/gamelog/201209/28/game-20120928-023049-913e0c96.html

On turn 16 I had the option to end it with a tie as player 2. Pawn was the only source of +Buy, but none of us bought one.
I actually thought for a bit whether to play it safe or play for the win. I really thought that my deck was a bit better so it might be worth it to grab a Duchy, hope he doesn't buy the last Province or a Duchy himself and get the last Province.

Already, there are a lot of if's and buts and in the end I chose certainty and grabbed the tie.
What would you have done here? Would you have played for the win or taken the tie?

Deck stats:
Opponent: [26 cards] 2 Caravans, 2 Rabbles, 2 Villages, 1 Throne Room, 7 Coppers, 2 Silvers, 3 Golds, 3 Estates, 4 Provinces
Me: [26 cards] 3 Caravans, 2 Rabbles, 2 Throne Rooms, 2 Villages, 1 Adventurer, 1 Mine, 4 Coppers, 1 Silver, 3 Golds, 3 Estates, 3 Provinces

I have an extra Caravan, an extra Throne Room, less Coppers a Mine and an Adventurer which could help against his Rabbles and with my own greening. Both of us are at new clean shuffles at this point. He has just reshuffled and I would do the same after this turn.

In hindsight, we can see he has Rabble collision on Turn 16 and would be hard pressed to grab even a Duchy. My draw was also less than stellar but I could have bought a Duchy. All of this was of course not known when I to make a decision.
Also consider that once I start dipping for Duchies, grabbing the last Province isn't automatic anymore, but I had Mine which could have helped with that.

[Fabian]

No +buy, both have pretty good decks, and to win you need for him to not buy Province and not buy Duchy and you need to buy Province?

Super easy tie situation. Anything else would be a gigantic mistake. Try and put numbers on how often he gets to $8/$5 and how often you get to $8/$5 and it should be pretty clear. In order for Duchy to be better than Province here, you need to get to $8 before he gets to $5 more than 50% of the time, and that's with him "going first". I think 10% seems like a better estimate.

[Davio]

That was my gut feeling too, but I didn't take the time to churn it into numbers and let my opponent wait a couple of extra minutes, I just wanted to ask the community if I was seeing something that wasn't there and it seems I was.

I found that this one is pretty easy to simulate.
Results when I grab the Duchy: I win ~17%, Tie ~22% and lose ~62%.
This means that grabbing the tie is clearly better.

This could be an interesting one for a Tournament situation which awards more points for a clear win than a tie though; I view a tie as a win for both players, but Tournament rules may vary on this.

Let's say a win is 3 points, tie is 2 points and loss is 0 points.
Grabbing the Duchy will give an expected value of 0.17*3 + 0.22*2 = ~1.5 points.
Grabbing the tie gives a value of 2 points, so clearly a tie is better.

How about when the tie gives 1 point?
Duchy: 0.17 * 3 + 0.22 = 0.73
Tie: Still 1

So basically you should always go for the tie here unless you have a compelling reason not to.

[DStu]

Results when I grab the Duchy: I win ~17%, Tie ~22% and lose ~62%.

So basically you should always go for the tie here unless you have a compelling reason not to.

To complete your calculation, you would need points for L:0, T:1, W:x,

where x satisfies 22+17x=100, so x=78/17 which should be about 4.5. 

[Davio]

Results when I grab the Duchy: I win ~17%, Tie ~22% and lose ~62%.

So basically you should always go for the tie here unless you have a compelling reason not to.

To complete your calculation, you would need points for L:0, T:1, W:x,

where x satisfies 22+17x=100, so x=78/17 which should be about 4.5.

I was too lazy to do this. 4.5 points seems a bit much.

Tournament situations are weird anyway. You might need to win this game to go through in a round robin or swiss system.

[Fabian]

Honestly I think 17% win sounds like a huge overestimate. Is that with Roger starting turn 17 given that you bought a Duchy, with 1 Province remaining?

I mean, if it's correctly simulated I guess that's that, but it sounds way high to me.

[Davio]

Honestly I think 17% win sounds like a huge overestimate. Is that with Roger starting turn 17 given that you bought a Duchy, with 1 Province remaining?

I mean, if it's correctly simulated I guess that's that, but it sounds way high to me.

Yeah, I used Geronimoo's simulator and entered the start state as if I had bought the Duchy. I let my opponent begin every time and both players start with a clean shuffle.

I used the "Ultimate Simulation" mode for most significant results.

I used simplified buy rules, just: Province > Duchy > Estate.

[Rabid]

How about without estate buy rules.
I suspect they are a trap, if the game goes on too long you definitely have the advantage.
What was the average turns?

[Rabid]

I have just tried the "same" sim:

And get 5% win rate for you as 2nd player with estates, and with keep player order.

Removing "keep player order" increase your win rate to 18% on quick sim.
Removing estate buy rule drops your win rate to 2%.

Such different results would indicate I am using the sim wrong, but I can't find the error?

Code: [Select]

<player name="A New Strategy 27p"
 author="Anonymous"
 description="No description available">
 <type name="UserCreated"/>
 <type name="TwoPlayer"/>
 <type name="Province"/>
 <type name="Bot"/>
  <start_state>
    <hand contents=""/>
    <discard contents=""/>
    <drawdeck contents="2 Caravan, 2 Rabble, 2 Village, 1 Throne Room, 7 Copper, 2 Silver, 3 Gold, 3 Estate, 4 Province" shuffle="true"/>
  </start_state>
   <buy name="Province"/>
   <buy name="Duchy"/>
   <buy name="Estate"/>
</player>


Code: [Select]

<player name="A New Strategy 24p"
 author="Anonymous"
 description="No description available">
 <type name="UserCreated"/>
 <type name="TwoPlayer"/>
 <type name="Province"/>
 <type name="Bot"/>
  <start_state>
    <hand contents=""/>
    <discard contents=""/>
    <drawdeck contents="3 Caravan, 2 Rabble, 2 Throne Room, 2 Village, 1 Adventurer, 1 Mine, 4 Copper, 1 Silver, 3 Gold, 3 Estate, 3 Province" shuffle="true"/>
  </start_state>
   <buy name="Province"/>
   <buy name="Duchy"/>
   <buy name="Estate"/>
</player>


[Kirian]

Results when I grab the Duchy: I win ~17%, Tie ~22% and lose ~62%.

So basically you should always go for the tie here unless you have a compelling reason not to.

To complete your calculation, you would need points for L:0, T:1, W:x,

where x satisfies 22+17x=100, so x=78/17 which should be about 4.5.

I was too lazy to do this. 4.5 points seems a bit much.

Tournament situations are weird anyway. You might need to win this game to go through in a round robin or swiss system.

Or elimination, depending on the elimination rules.

[Fabian]

You forgot to add the Duchy Davio bought on turn 16, Rabid. With that, Davio wins 16.6% and ties 21.9% on Ultimate simulation, roughly, so the EV of buying Duchy is roughly 0.275 (compared to 0.5 when buying Province).

[Rabid]

Thanks, knew it must be something obvious but couldn't see it.

[Davio]

Even though the answer ends up being pretty dry cut, I hope you still found my little quandary interesting, it doesn't happen often when you can accept a tie and if you don't, your opponent can win on the very next turn.

Maybe some other situations will pop up that share this dilemma which may have more interesting outcomes.