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Author Topic: Ambassador, the card of openning luck?  (Read 4395 times)

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Sparafucile

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Ambassador, the card of openning luck?
« on: November 20, 2013, 02:23:38 am »
+12

So.  Dominion is a game of luck.  We all know this - and this luck aspect makes the game appealing for many people.   Pulling out a victory from certain defeat is a nice nelson "haha" moment.  However, some of us like to believe that through superior playing we can beat even the worst odds.   Just how bad can the odds be anyways?

The issue of opening luck i started thinking about early in my dominion playing.  When hinterlands game out, as with all other expansions, me and my friends started playing through the recommended sets.  We got to the Traveling Circus" set - where for the first time we feature Nomad Camp and Hunting Party.   I thought the nomad camps "place on top of deck" was really cool - so I opened with that on a 4/3 split.  With a little luck, I ended up with a Nomad Camp, Hunting party opening.   After that, I continued to hit 5 coin every turn.  If the nomad camp OR hunting party is in your hand, u will probably hit 5, so it's hard to hit repeated 5s with this combo.  My poor friend struggled around with some silvers a long time before getting his first 5.  By the time he did, I had already scooped up most of the hunting parties.   That game didn't go well for him.  I declared - huh, I think that with that kind of opening luck, you will lose every time.  He didn't believe me.  We recreated the openning sequence - and the exact same thing happened.    Now I doubt we played that set optimally - would probably play it very different today - but we were both relatively noob.   Among us players of roughly equal skill the opening luck   This was my first suspicion that maybe there were some boards where opening luck is the dominating factor in victory.

Let's take a look at some basic luck numbers alone for reference.   

If you play big money vs big money, going first gives:

61.6% win for BigMoney First Player
31.6% win for BigMoney Second Player
6.8% there is a tie.

So we can roughly quantify a 60/30 split on wins as a one turn advantage.   Fortunately, simulators can correct for this bias just by alternating which strategy goes first.  In the following simulations, we will swap who goes first.

Now, if I were to tell you that smithy is on the board - clearly buying a single smithy is better than not.  You won't always win though:

23.8% win for BigMoney
71.7% win for BigMoneySingleSmithy
4.5% there is a tie.

Even with this clearly superior strategy, you only win in a 3:1 ratio.  If you are losing in a 3:1 ratio, you are pretty much losing as poorly has someone who chooses bigmoney vs BigMoneySmithy.  None of this is new to any of you I'm sure.   Most of you have probably seen the thread discussing the possibility of a strategy that will beat big money all the time.  The best we have found is one that wins like 99.98% or something like that.  I wanted to rehash some basic numbers to put in some context for the topic I wanted to discuss - Ambassador.  I've felt for a while that games involving Ambassador are particularly luck prone.   I'm pretty well known among my friends to declare - that's it, game over - after turn 3 or 4.   Am I being pessimistic, or can the odds really be that bad.  Lets find out.

Lets discuss Ambassador tactics.   Always ambassador Estates and coppers.  Return as many copies to the supply as possible.  Don't return estates when the game is ending please. (I've tried variants where we return fewer copies of cards if it improves the buy - and for the most part that tactic makes things worst - a separate post :) )

How does ambassador fair vs BigMoney?  Not great - but a little better than statistical noise:

57.9% win for Ambassador
39.7% win for BigMoney
2.4% there is a tie.

So now lets tip the scales.  We will play ambassador vs ambassador but force the shuffle luck for the first 3 turns.   Each player will always start with a 3/4 split - opening silver + ambassador.    On Turn 3 there will be a lucky player, and an unlucky player.  For example, if a player has 1 ambassador + 4 copper on turn 3, this will force a double copper return.  Lets see some numbers:

1)  Ambassador 2 Copper (unlucky) vs Ambassador 1 Estate. 

36.7% win for Unlucky
61.3% win for Lucky
2% there is a tie.

2)  Ambassador 2 Copper (unlucky) vs Ambassador 2 Estates. 

28.1% win for Unlucky
69.8% win for Lucky
2.1% there is a tie.

3) Ambassador 1 Estate (unlucky) vs Ambassador 2 Estates

42.2% win for Unlucky
53.9% win for Lucky
3.9% there is a tie.

So as long as you get to ambassador on turn 3 or turn 4 things aren't bad.  If you get to return an estate, there's not much effect.  If you have to return a copper though - things start looking little worse.   If your opponent gets to ambassador 2 estates and you just get to ambassador 2 coppers - it's a little worse than going second.  Not great.

Oh, but it gets better, what happens if you miss your ambassador turn because your ambassador is at card 11 or card 12 in the shuffle? Meanwhile, your opponent gets to ambassador on turn 3 or 4.   This will happen to you in about 10% of your ambassador games.  After the opening purchase, lets put an estate as card 11 and ambassador as card 12 in the shuffle and see how our luck fares:  (we also assume our unlucky player does NOT receive a lucky early gold and is forced into a silver silver purchase).

4)  No Ambassador on turn 3/4 (silver silver purchase) vs Ambassador 2 copper
35.1% win for Unlucky
62.4% win for Lucky
2.5% there is a tie.

5)  No Ambassador on turn 3/4 (silver silver purchase) vs Ambassador 1 estate
20.6% win for Unlucky
77.3% win for Lucky
2.1% there is a tie.

6)  No Ambassador on turn 3/4 (silver silver purchase) vs Ambassador 2 estate
15.6% win for Unlucky
82.7% win for Lucky
1.7% there is a tie.

Whoa.  I would put that last one in the solid - you're screwed category.  And if we were playing in real life, you'ld probably hear me rant about it the whole game ;)

What's interesting is if you score an early gold, things may not be as bad:  Lets assume our unlucky player can buy a gold:

7)  No Ambassador on turn 3/4 buys gold (unlucky) vs Ambassador 2 copper
59.2% win for Unlucky
37% win for Lucky
3.8% there is a tie.

8 )  No Ambassador on turn 3/4 buys gold (unlucky) vs Ambassador 1 Estate
48.9% win for Unlucky
48.2% win for Lucky
2.9% there is a tie.

9)  No Ambassador on turn 3/4 buys gold (unlucky) vs Ambassador 2 Estate
38.1% win for Unlucky
56.8% win for Lucky
5.1% there is a tie.

So if you don't get ambassador, but you get an early gold - you may even come out ahead!   However, not even an early gold can not make up for your opponent ambassador 2 estates.  But if you do score an early gold - keep your chin up.  Worst case scenario, you are down one turn. 

While this gives you a pretty good idea of your odds when playing with just big money and ambassador.  Lets take a look at a game involving other cards.  Based off a game I played recently, consider if the following cards are available:

Ambassador, Caravan, Apprentice and Merchant Guild.   

I like this set of test cards, as there is opportunity for purchase at the 3, 4, 5 and 6 level.   (Big money biases our results sometimes, as there is  no benefit to hitting the 4 or 5 in a big money game - and frankly, how many boards are missing 4s and 5s?!)

So the baseline strategy is open Ambassador + Caravan on a 3/4 split.  Purchase up to 5 Caravans, 1 Merchant guild.  Get gold whenever possible and silver otherwise.  How does this fair vs bigmoney (always a good check):

83.9% win for AmbassadorCaravanMerchantGuild
14.8% win for BigMoney
1.3% there is a tie.

Not too bad.

Now let's do a mirror match and throw a little luck in there.  Both players will open ambassador + caravan.  One unfortunate player will get the following sequence:

Turn 3) Copper, Copper, Copper, Copper, Estate,
Turn 4) Caravan, Copper, Copper, Copper, Estate, Estate
Turn 5) Ambassador + 4 Coppers + 1 Silver.

Even with the caravan in play (which misses the reshuffle because it's on turn 4), the ambassador is in position 12 - so no play till turn 5 - and even then no estate.

Compare this to the more fortunate player:

Turn 3) Caravan, Copper, Copper, Copper, Estate, Estate,
Turn 4) Estate, Copper, Copper, Copper, Copper Ambassador

What are you the odds of winning this?

23.1% win for Unlucky
74.8% win for Lucky
2.1% there is a tie.

In this real life scenario - the odds of winning with a little misfortune are actually quite similar to the earlier data.  (Compare with the scenario: Ambassador 1 estate vs no Ambassador).  So I will probably use the above big money data to extrapolate my odds in the future.

What is the value in knowing these numbers?  Well - when you are playing an ambassador opening - it's useful to know where you stand.  If your odds are not great in an equal strategy, mix it up a little.  Play more risky - what have you got to lose?   Defer buying that first province, try something you may otherwise not.

You have noticed that in the above strategy, I did not mention apprentice!   Maybe our unlucky player can add an apprentice to his deck to make a come back:

12.2% win for Unlucky (if buys apprentice)
86.2% win for Lucky
1.6% there is a tie.

Actually - purchasing apprentice makes things worse.  This was a counter intuitive result for myself.   In fact, I've tried adding many variants to this strategy - and adding the apprentice seems to almost always makes things worse.  In fact, if your unlucky player skips apprentice and the lucky player buys apprentice:

35.8% win for Unlucky (skip apprentice)
61.4% win for Lucky (buys an apprentice)
2.8% there is a tie.

Of course simulators don't play perfect - and probably play apprentice poorly in the late game.  The takeaway though is that all it took was for the "lucky" player to make one bad call among otherwise equal strategies - buying the apprentice - and a 2 turn advantage was reduced to a one turn advantage.   So With 10 cards on the table - be vigilant.  If you make just a couple calls better than your opponent you may be able to make up even the worst of ambassador luck.    If you have an unfortunate opening with ambassador, you are like going to be practicing more sportsmanship than dominion skills if your opponent is relatively close to you in skill.

(In case you are curious, here's that last example showing how one sets shuffle luck in Dominulator)
Code: [Select]
        var player1 = Strategies.AmbassadorCaravanApprenticeMerchantGuild.PlayerCustom(playerName: "Unlucky", shouldApprentice:false);
            var player2 = Strategies.AmbassadorCaravanApprenticeMerchantGuild.PlayerCustom(playerName: "Lucky", shouldApprentice: true);                                   
           

            var builder = new GameConfigBuilder();
           
            builder.SetShuffleLuckPerPlayer( new CardCountPair[][] {                                 
                new CardCountPair[] { new CardCountPair(Cards.Copper, 4), new CardCountPair(Cards.Estate, 1),
                                      new CardCountPair(Cards.Copper, 3), new CardCountPair(Cards.Estate, 2),                                                                           
                                      new CardCountPair(Cards.Copper, 4), new CardCountPair(Cards.Estate, 1),
                                      new CardCountPair(Cards.Caravan, 1), new CardCountPair(Cards.Copper, 3), new CardCountPair(Cards.Estate, 2),
                                      new CardCountPair(Cards.Ambassador, 1), new CardCountPair(Cards.Silver, 1), new CardCountPair(Cards.Copper, 4),
                },               

                new CardCountPair[] { new CardCountPair(Cards.Copper, 4), new CardCountPair(Cards.Estate, 1),
                                      new CardCountPair(Cards.Copper, 3), new CardCountPair(Cards.Estate, 2),                                     
                                      new CardCountPair(Cards.Caravan, 1), new CardCountPair(Cards.Copper, 3), new CardCountPair(Cards.Estate, 2),
                                      new CardCountPair(Cards.Ambassador, 1), new CardCountPair(Cards.Copper, 4), new CardCountPair(Cards.Estate, 1),
                },
            });
           
            PlayerAction.SetKingdomCards(builder, player1, player2);

            ComparePlayers(
                player1,
                player2,
                builder.ToGameConfig(),
                firstPlayerAdvantage:false,
                createHtmlReport: true,
                numberOfGames: 1000,
                shouldParallel: false);
« Last Edit: November 20, 2013, 02:28:59 am by Sparafucile »
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2.71828.....

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Re: Ambassador, the card of openning luck?
« Reply #1 on: November 20, 2013, 08:53:17 am »
+1

Lets discuss Ambassador tactics.   Always ambassador Estates and coppers.  Return as many copies to the supply as possible.  Don't return estates when the game is ending please. (I've tried variants where we return fewer copies of cards if it improves the buy - and for the most part that tactic makes things worst - a separate post :) )
Nice article, although I want to add one thing about ambassador tactics.  In most ambassador games, I really like to go A/A, or maybe A/S/A.  In his article and ensuing discussion, WW and others go into much greater length about all the different strategies surrounding ambassador, and I realize this is difficult if not impossible to simulate.  However, you can probably do something with "perfect shuffle luck" to get ambassador with two estates then two coppers t3/t4, and I would be interested to see how this fares against the A/S perfect shuffle luck.
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florrat

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Re: Ambassador, the card of openning luck?
« Reply #2 on: November 20, 2013, 01:19:17 pm »
+2

Hmm... Interesting results. I haven't read everything yet (but I certainly will), but here are some preliminary comments:

- Often you want to go Double Ambassador, have you tried to compare that (there getting unlucky is even more likely, because I think the odds are roughly 50/50 whether you can ambassador once or twice on T3/T4 (ignoring the very small chance to miss both Ambassadors))?
- Your analysis seems to suggest that returning 2 Coppers is worse than returning 1 Estate. In the usual Ambassador heuristics (that I know) you prefer returning 2 Coppers over 1 Estate. Maybe this is different in Single Ambassador vs Double Ambassador, because in the latter you're really committed to obtain a very slim deck.
- In the puzzle forum, in the lucky chancellor thread (and part 2), there are solutions which beat lucky chancellor even with worst possible shuffle luck. These strategies are certainly able to beat Big Money 100% (without rounding) of the time.
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Sparafucile

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Re: Ambassador, the card of openning luck?
« Reply #3 on: November 20, 2013, 01:44:17 pm »
0

Quote
you can probably do something with "perfect shuffle luck" to get ambassador with two estates then two coppers t3/t4, and I would be interested to see how this fares against the A/S perfect shuffle luck.

I assumed that by A/S perfect shuffle luck, you mean the player ambassadors 2 estates, and also hits silver with 4 coppers, enabling an early gold.   

58.13% win for SingleAmbassador  (Open ambassador/silver. Turn 3 ambassador 2 estates, Turn 4 buy Gold)
39.22% win for DoubleAmbassador (open ambassador/ambassador.  Turn 3 ambassador 2 estates, Turn 4 Ambassador 2 copper)
2.65% there is a tie.

For completeness sake, here's single ambassador vs double ambassador in BigMoney situation. (using tactics mentioned above)
52.51% win for SingleAmbassador
45.66% win for DoubleAmbassador
1.83% there is a tie.

Thank you for the article link above.  One of the topics discussed is whether it's better to return 2 coppers or 1 estate. This is a little bit deviating from the original topic of Ambassador luck, lets see what the simulators can tell us about ambassador tactics in big money.   

I have written 3 different Ambassador tactics. 
   1)  AmbassadorAlwaysReturnBestTrash - Always return the card with the highest Trash Priority.  (estates over copper). 
   2)  AmbassadorReturnIfNotDisruptPurchase - Similar to 1, except becareful when returning copper.  Never return so many coppers on the current hand that it changes what you would buy this turn.   In BigMoney, this translates to ambassador + 4 copper would return 1 copper still enabling purchase of a  silver.  Ambassador + 3 copper would return nothing, as that would disrupt a silver purchase.
   3) AmbassadorMaxReturn - Always prefer to trash 2 of a card - even if you could return 1 of a card of a lower trash priority.  In otherwords.  Prefer 2 estates over 2 coppers.  Prefer 2 coppers over 1 estate.  etc ...

And here's the round robin results using BigMoney, and a single ambassador:

35.39% win for AmbassadorMaxReturn
61.84% win for AmbassadorReturnIfNotDisruptPurchase
2.77% there is a tie.

44.57% win for AmbassadorAlwaysReturnBestTrash
52.38% win for AmbassadorReturnIfNotDisruptPurchase
3.05% there is a tie.

39.57% win for AmbassadorMaxReturn
57.48% win for AmbassadorAlwaysReturnBestTrash
2.95% there is a tie.

Maybe these results are skewed because it's bigmoney.  Let's add Caravan and Laboratory into the mix to see if that changes the rankings:

26.27% win for AmbassadorMaxReturn
72.12% win for AmbassadorReturnIfNotDisruptPurchase
1.61% there is a tie.

45.49% win for AmbassadorAlwaysReturnBestTrash
52.19% win for AmbassadorReturnIfNotDisruptPurchase
2.32% there is a tie.

31.52% win for AmbassadorMaxReturn
66.76% win for AmbassadorAlwaysReturnBestTrash
1.72% there is a tie.

From these simulator guided results, the conclusion seems to be that returning 2 coppers over 1 estate is a bad idea.  (This also matches my intuition personally).  It also appears that even though the temptation is great to ambassador as many coppers as possible, it seems like you should NOT disrupt your current purchase order to ambassador an extra copper away...

Of course, please keep in context that these are simulator results - and it would not be surprising to find that the very best dominion players can outwit these odds through human ingenuity.  However, I'm not of the very best players, and to my intermediate dominion playing skills these numbers reflect my experience.

For reference, here's the 3 tactics

Code: [Select]
    public class AmbassadorAlwaysReturnBestTrash
      : UnimplementedPlayerAction
    {
        private readonly PlayerAction playerAction;

        public AmbassadorAlwaysReturnBestTrash(PlayerAction playerAction)
        {
            this.playerAction = playerAction;
        }

        public override Card GetCardFromHandToReveal(GameState gameState, CardPredicate acceptableCard)
        {
            Card cardToReturn = playerAction.trashOrder.GetPreferredCard(gameState, card => gameState.Self.Hand.HasCard(card) && acceptableCard(card));           
            return cardToReturn;
        }

        public override int GetCountToReturnToSupply(Card cardToReturn, GameState gameState)
        {           
            return 2;           
        }
    }

    public class AmbassadorReturnIfNotDisruptPurchase
      : UnimplementedPlayerAction
    {
        private readonly PlayerAction playerAction;

        public AmbassadorReturnIfNotDisruptPurchase(PlayerAction playerAction)
        {
            this.playerAction = playerAction;
        }

        public override Card GetCardFromHandToReveal(GameState gameState, CardPredicate acceptableCard)
        {
            Card cardToReturn = playerAction.trashOrder.GetPreferredCard(gameState, card => gameState.Self.Hand.HasCard(card) && acceptableCard(card));
            if (cardToReturn == null)
                return null;
           
            PlayerState self = gameState.Self;
            int currentCoin = self.ExpectedCoinValueAtEndOfTurn;
            int coinCountIfReturn = currentCoin - cardToReturn.plusCoin;

           
            if (currentCoin < Dominion.Cards.Gold.DefaultCoinCost)
                return cardToReturn;
           
            Card cardWithAllCoin = playerAction.GetCardFromSupplyToBuy(gameState, card => card.CurrentCoinCost(self) <= currentCoin);
            Card cardWithReturnedCard = playerAction.GetCardFromSupplyToBuy(gameState, card => card.CurrentCoinCost(self) <= coinCountIfReturn);

            if (cardWithAllCoin != cardWithReturnedCard)
                return null;

            return cardToReturn;
        }

        public override int GetCountToReturnToSupply(Card cardToReturn, GameState gameState)
        {
           
            PlayerState self = gameState.Self;
            int currentCoin = self.ExpectedCoinValueAtEndOfTurn - cardToReturn.plusCoin;
            int coinCountIfReturn = currentCoin - cardToReturn.plusCoin;


            if (currentCoin < Dominion.Cards.Gold.DefaultCoinCost)
                return 2;
           
            Card cardWithAllCoin = playerAction.GetCardFromSupplyToBuy(gameState, card => card.CurrentCoinCost(self) <= currentCoin);
            Card cardWithReturnedCard = playerAction.GetCardFromSupplyToBuy(gameState, card => card.CurrentCoinCost(self) <= coinCountIfReturn);

            if (cardWithAllCoin != cardWithReturnedCard)
                return 1;
           
            return 2;
        }
    }

    public class AmbassadorMaxReturn
      : UnimplementedPlayerAction
    {
        private readonly PlayerAction playerAction;

        public AmbassadorMaxReturn(PlayerAction playerAction)
        {
            this.playerAction = playerAction;
        }

        public override Card GetCardFromHandToReveal(GameState gameState, CardPredicate acceptableCard)
        {
            int maxCount = 0;
            // find out which card that is wanted to be trashed you have most of in hand.
            foreach (Card card in playerAction.trashOrder.GetNeededCards())
            {
                maxCount = Math.Max(maxCount, gameState.Self.Hand.CountOf(card));
            }

            if (maxCount > 2)
                maxCount = 2;

            Card cardToReturn = playerAction.trashOrder.GetPreferredCard(gameState, card => gameState.Self.Hand.CountOf(card) >= maxCount && acceptableCard(card));
            return cardToReturn;
        }

        public override int GetCountToReturnToSupply(Card cardToReturn, GameState gameState)
        {
            return 2;
        }
    }

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ftl

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Re: Ambassador, the card of openning luck?
« Reply #4 on: November 20, 2013, 02:11:43 pm »
+7

I think the 2 coppers/1 estate thing comes from the fact that in a game where amb is good, you're likely competing in an ambassador war with another player, and likely building an engine afterwards. It's the same reason that you would play chapel and trash all four coppers if you opened chapel and drew Ch-C-C-C-C on turn 3.

This might not be coming out in your simulations because you don't have a particularly good payload for the engine (and were even testing Ambassador + Big Money, which just isn't really a practical thing). For example, a reasonable thing to do would be IF you get your engine going first, draw your whole deck, and keep playing 2 ambassadors per turn for the rest of the game to make sure your opponent *never* slims their deck down and gets their deck going. Winning the ambassador war can mean giving your opponent all 10 curses.
« Last Edit: November 20, 2013, 02:13:04 pm by ftl »
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Re: Ambassador, the card of openning luck?
« Reply #5 on: November 20, 2013, 03:20:25 pm »
+1

Of course, please keep in context that these are simulator results - and it would not be surprising to find that the very best dominion players can outwit these odds through human ingenuity.  However, I'm not of the very best players, and to my intermediate dominion playing skills these numbers reflect my experience.
Thanks for the results on A/A.  As you mention here, these are simulator results and ambassador really doesn't work well with simulations because there are so many contributing factors into how to appropriately play ambassador. From his article:
Few decks can beat ambassador when it has all its toys, but when its missing something, there are a number that can. And this is more of a sliding scale thing - the more things the amb deck is missing, the less strong the counter has to be.
A simulator can't take into account "ambassador with all its toys" or its lack of "toys."  Your results are using an ambassador + BM strategy as ftl points out, which is the same as Ambassador with no toys at all.  So the opposing strategy doesn't need a much help.  However, when I see ambassador I have learned the value of the card, even with just a tiny bit of support.  And like you said, the numbers reflect your experience, and this article is a great warning of how difficult it is to correctly play ambassador and that it can be very hard for a newer player to win using it.  In fact, ambassador is one of those cards that I doubt anyone can claim they have "mastered" because of all the intricacies involved with the card usage from early in the game to late game usage.
« Last Edit: November 20, 2013, 03:22:39 pm by 2.71828..... »
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eHalcyon

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Re: Ambassador, the card of openning luck?
« Reply #6 on: November 20, 2013, 03:25:03 pm »
0

Ambassador is really best for engines because it trims and speeds up your deck while slowing down opponents.  Simulations are far less useful when it comes to engine strategies; simply adding Lab and Caravan to the simulation doesn't really help with that.
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Sparafucile

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Re: Ambassador, the card of openning luck?
« Reply #7 on: November 20, 2013, 04:14:23 pm »
0

Quote
simply adding Lab and Caravan to the simulation doesn't really help with that

Agreed that these do not make an engine.  My goal in adding them was so that there would be interesting cards at the 4 and 5 purchase price point - cards that also are good for ambassador, as they assist in draw.

Quote
Simulations are far less useful when it comes to engine strategies

That's an interesting statement.  Why?  Do you have an example engine strategy, preferably involving ambassador, that you would like to see some simulator stats on?   If you have a link to an example game on goko that's even better.   If someone posts a good one, I'll even try to show the effect of luck on the engine in a mirror match up.   If there is a set of cards with 2 competing engines, also involving ambassador - even better.   I have been able to simulate every engine I have tried to simulate to date, so I'm not sure what you mean.

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eHalcyon

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Re: Ambassador, the card of openning luck?
« Reply #8 on: November 20, 2013, 05:26:43 pm »
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Simulations are far less useful when it comes to engine strategies

That's an interesting statement.  Why?  Do you have an example engine strategy, preferably involving ambassador, that you would like to see some simulator stats on?   If you have a link to an example game on goko that's even better.   If someone posts a good one, I'll even try to show the effect of luck on the engine in a mirror match up.   If there is a set of cards with 2 competing engines, also involving ambassador - even better.   I have been able to simulate every engine I have tried to simulate to date, so I'm not sure what you mean.

Engine building is very intricate and more reactive to the opponent's strategy as well as the luck each player experiences.  What order do you buy cards in?  What do you fall back on if you can't buy what you want?  When do you stop building the engine and start greening?  You can simulate it, but it's much more difficult to optimize an engine strategy than it is to optimize a Big Money strategy.  I mean, BM has to answer those questions too, but there are fewer variables you need to consider.  I'd also expect optimization to have a much bigger impact on engines than on BM.
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Polk5440

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Re: Ambassador, the card of openning luck?
« Reply #9 on: November 21, 2013, 04:17:39 pm »
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When building an ambassador engine and checking the MaxReturn strategy, you have to check one very important condition: don't return 2 coppers if that leaves you with less than $3 in your deck (unless you have a good reason for only needing $2).
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yed

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Re: Ambassador, the card of openning luck?
« Reply #10 on: November 21, 2013, 05:09:16 pm »
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When building an ambassador engine and checking the MaxReturn strategy, you have to check one very important condition: don't return 2 coppers if that leaves you with less than $3 in your deck (unless you have a good reason for only needing $2).
Same thing happend to me in game against Stef. It is not good idea to count on that he will return copper.
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WanderingWinder

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Re: Ambassador, the card of openning luck?
« Reply #11 on: December 08, 2013, 11:30:00 am »
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So, I got to
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If you play big money vs big money, going first gives:

61.6% win for BigMoney First Player
31.6% win for BigMoney Second Player
6.8% there is a tie.
And basically stopped there. How are you coming to this? Everything I've ever found shows it as basically 50/40/10.

Okay, skimming further, you're doing this all with big money. Big Money is not at all what you want to do with Ambassador. If you're going to play BM, you are probably better off going with some other card rather than Ambassador. You really really want to be building an engine with Ambassador.

Why are simulators bad at engines? Well, just because nobody has gone through the trouble of programming one up that plays them really well yet. I'm sure it's possible, but it would take some work.
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