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Author Topic: Mountain Pass Bidding Strategy  (Read 14470 times)

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jsmarvin

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Mountain Pass Bidding Strategy
« on: June 08, 2016, 02:14:37 pm »
+9

There's been some discussion regarding bidding in the Empires Rulebook thread, but I thought I'd start a separate thread to discuss this topic. I'm not an expert Dominion player, and although I'm familiar with all the cards in Dominion, I don't know them well enough to come up with relevant combinations. So here are some questions regarding bidding that I'd like to see people discuss, some practical, some more of a challenge/theoretical (and possibly some may be the "wrong question", feel free to address what you think the "right question" should have been):

1) If the first Province is bought earlier in the game, what are the factors that will determine bidding strategy and what should that strategy be? 2 player vs. 3-4 player? Colony's available? Dominate available? Alt VP available? My definition of "earlier in the game" for this question would be at a time when the game end is not imminent, so a player would be less likely to bid 40 debt based solely on the fact that they don't think they'll get another turn, or they are willing to play the remainder of the game without buying anything, even though they don't have an alternate gain strategy. How does the fact that not only are you gaining 8 VP but you are denying those VP to your opponent affect your bid?

2) Although it might be difficult to keep accurate track of opponent VP currently, the new "When scoring" Landmarks can make it even more difficult. If both Mountain Pass and a "When scoring" Landmark is present in the game, how does that affect bidding if the first Province was bought late in the game? At what point does bidding 40 become the right thing to do?

3) When, if ever, should the other player pass (giving you 8 VP for 1 debt token) in a 2 player game?  If possible, give an example. Also, although possibly valid, I'm not looking for answers other than "When the other player is already assured of a win and doesn't need the 8VP", i.e. I'm looking for cases where winning the bid and taking any debt tokens will interfere with the players strategy (even if that strategy will deliver more than 8 VP next turn or will be a critical step in generating more VP in later turns, you also have to take into account that they would give 8 VP to you). Even if it has the chance to mess their turn up, should they still gamble and "bid up", i.e. bid something that they hope you'll outbid, but at least not just give the VP away for 1 debt token.

4) If the game has more than 2 players, does that affect the above question?

5) Is there a mid game strategy? What I mean is how might bidding strategy evolve between early and late game (when bidding 40 might be the right answer), or is there more of a knife point transition (e.g. the point where people start buying victory cards rather than treasures or actions) between what you might do prior to an impending game end and what you would do when the game end is imminent?

6) Am I overthinking this? :)

I'd certainly appreciate any real life examples from the play testers or people who have played with it using proxies based on the published Empires rules.



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Orange

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Re: Mountain Pass Bidding Strategy
« Reply #1 on: June 08, 2016, 02:46:52 pm »
+2

Maybe I'm UNDERthinking this, but in a 2-player game, I'm going to simply ask myself 1) how much is my deck generating per turn, and 2) how many lost turns is 8 VP going to be worth to me, then bid accordingly.  I might even go a bit lower if I feel my opponent's deck is not generating much money.
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ephesos

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Re: Mountain Pass Bidding Strategy
« Reply #2 on: June 08, 2016, 02:49:00 pm »
0

I think 3 would be a very rare situation, in which you're running an explosive combo(King's Court Goons Masquerade pin, Goons Watchtower engine, KC Bridge, Villa near-infinite loop) that doesn't care how much VP your opponent has because you're going to beat it by an order of magnitude, if you get the combo rolling before the game ends.
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faust

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Re: Mountain Pass Bidding Strategy
« Reply #3 on: June 08, 2016, 03:05:45 pm »
0

1) I think a factor is how much money your deck can generate. If your deck is built to buy 1 Province/turn, you may have excess money. If you know how much money you generate each turn, I would usually bid at least (that amount)*2-8, so that you cannot buy anything the next turn, but can still buy a Province the turn after. Any alternate source of VP is of course going to affect this; like in a Goons engine, you don't care.

2) I don't know, depends on the Landmark. Bidding 40 is only correct if you can gain Provinces without buying or if you have some other way to score enough VP that you can ignore buying.

3) Mostly if you know you can draw your deck, and know you need that coin to shut your opponent down in whatever way. Or maybe you need to buy the last Colony to win (i.e. your oppoent has a 9VP lead, and you know the have a way to win the next turn).

4) Well, you can assume that other players will bid too, but still there will usually be a price greater than 0 debt that you'd be willing to pay.

5) Buying the first Province early will usually slow your opponent down (if they decide to go for the VP). In conjunction with Tournament, that can be pretty devastating I believe.

6) Yes.
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Re: Mountain Pass Bidding Strategy
« Reply #4 on: June 08, 2016, 03:18:58 pm »
0

If it's the last Province, bid <40>

Otherwise, analyze your opponent. Are they aggressive? Is it a slog and they know getting 9 VP and sacrificing 3-4 turns to pay it off is a good deal? 9 VP chips would probably cost around $10, so bidding <12> to <14> seems reasonable if you're greening.
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Re: Mountain Pass Bidding Strategy
« Reply #5 on: June 08, 2016, 03:19:17 pm »
0

One important factor with all debt, not just Mountain Pass:  if you have strong gaining (Ironworks, Remodel), taking on some debt while still improving your engine isn't nearly as painful. 
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Re: Mountain Pass Bidding Strategy
« Reply #6 on: June 08, 2016, 03:22:19 pm »
+6

If it's the last Province, bid <40>

If it's the last Province, nobody gets to bid.
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XerxesPraelor

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Re: Mountain Pass Bidding Strategy
« Reply #7 on: June 08, 2016, 03:46:06 pm »
+5

If it's the last Province, bid <40>

If it's the last Province, nobody gets to bid.

Salt the Earth
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GendoIkari

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Re: Mountain Pass Bidding Strategy
« Reply #8 on: June 08, 2016, 03:47:56 pm »
0

If it's the last Province, bid <40>

If it's the last Province, nobody gets to bid.

Salt the Earth

Also, if it's the first Province, and you know all the rest of them are about to be gained as well. Or it's the first Province, and 3 other piles were just emptied.
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Re: Mountain Pass Bidding Strategy
« Reply #9 on: June 08, 2016, 03:48:24 pm »
+6

If it's the last Province, bid <40>

If it's the last Province, nobody gets to bid.

Salt the Earth
Even then, the game ends before the "between turn" phase where Mountain Pass does it's thing
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GendoIkari

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Re: Mountain Pass Bidding Strategy
« Reply #10 on: June 08, 2016, 03:51:01 pm »
+2

If it's the last Province, bid <40>

If it's the last Province, nobody gets to bid.

Salt the Earth
Even then, the game ends before the "between turn" phase where Mountain Pass does it's thing

Oh right. That also makes my alternate suggestions wrong.

Ok so edge case of edge cases.... 7 Provinces are salted; then you gain the last one and Ambassador it back to the supply while your opponent has Lighthouse. So it will be the last Province, and the bidding will still happen. BOOM.
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Re: Mountain Pass Bidding Strategy
« Reply #11 on: June 08, 2016, 03:51:46 pm »
0

It's possible to fall into strategies where taking debt will cause extra problems. If you're trying to work with bridge trolls, for example, you might have a lot of cheap kingdom cards to buy but very few coins to pay off any debt first. I'm guessing that you essentially have to just surrender those 8vp if you can plan to score to more points elsewhere.
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Re: Mountain Pass Bidding Strategy
« Reply #12 on: June 08, 2016, 04:02:34 pm »
+1

Purely speculating, but the person gaining the first Province will have the upper-hand.  If I gain it, then even if my opponent doesn't want/need the VP, they will still pretty much have to bid at least something for it, so that I don't get it for free.  And then, I'll have the option of just letting them rack up the debt if I want.  It reminds me of the you-cut-I'll-choose situation -- the cutter's (the one not gaining the first Province) best-case-scenario is they get an even share of the cake, while they chooser's (the one gaining the first Province) worst-case-scenario is they get an even share of the cake and their best-case is they get everything.  Not a 100% comparison, I just thought of it.

"Combos" with Tournament.
« Last Edit: June 08, 2016, 04:09:14 pm by Dingan »
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JW

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Re: Mountain Pass Bidding Strategy
« Reply #13 on: June 08, 2016, 04:13:45 pm »
+6

Maybe I'm UNDERthinking this, but in a 2-player game, I'm going to simply ask myself 1) how much is my deck generating per turn, and 2) how many lost turns is 8 VP going to be worth to me, then bid accordingly.  I might even go a bit lower if I feel my opponent's deck is not generating much money.

Your intuition is correct: you should bid less than your true value if your opponent has a meaningfully lower value for the 8 VP than you do. Long explanation why follows:

Assume two players (P1 and P2) for simplicity, and suppose that their values for the 8 VP are common knowledge among the players. P2’s strategy is simple: bid one more than P1 if they prefer that to P1 winning with their current bid.

Suppose the 8 VP is worth <6> to P1, but <11> to P2 (for simplicity I’ve picked integer values but this probably isn’t the case). Consider P1’s decision. If P1 bids <6>, P2 can get it for <7>, which is “surplus” of <4> to P2. But if P1 bids <10> (so that P2 can’t get any surplus from bidding) P2 will recognize that and let P1 have it, for a surplus of -<4> to P1. So P1 wants to split the difference so that P2 doesn’t have any much better options (this is a “Nash equilibrium” in game theory). If P1 bids <8>, then P2 gets a surplus of <2> from bidding and P1 get a surplus of -<2> if P2 doesn’t bid. Both of these are a better outcome for P1 than if P1 naively bids their value of <6>. And P1 can’t reduce P2 below a surplus of <2> / boost themself above a surplus is -<2> at the same time, so <8> is the best bid.

Now suppose the opposite is true and the 8 VP is worth <11> to P1, but <6> to P2. P1 definitely doesn’t want to bid their value of <11> because then they get zero surplus. But P1 doesn’t want to bid only <6>, P2’s value, either, because then P2 will overbid and get it for <7> and only -<1> surplus.  P1 bidding <8> means that P2 can overbid but has to take a -<3> surplus, or if P2 doesn’t bid P1 gets a <3> surplus. So <8> is also the correct bid here. 

Now, what is 8 VP worth in debt? If it’s time to start greening, +8 VP is more than a Province and it’s an advantage that it doesn’t clog your deck (Tournament games excepted). Also, it’s easier to pay <8> than it is to hit $8 in one turn because you can spread it over multiple turns. So if both players are ready to green by buying Provinces, the winning bid should be more than <8>. If you have the same value as your opponent (let’s say <10.5>), then the strategy as P1 is to bid just less than that value. So P1 bids <10> in this case, and P2 can’t overcall without bidding more than their value.

Purely speculating, but the person gaining the first Province will have the upper-hand.  If I gain it, then even if my opponent doesn't want/need the VP, they will still pretty much have to bid at least something for it, so that I don't get it for free.  And then, I'll have the option of just letting them rack up the debt if I want.  It reminds me of the you-cut-I'll-choose situation -- the cutter's (the one not gaining the first Province) best-case-scenario is they get an even share of the cake, while they chooser's (the one gaining the first Province) worst-case-scenario is they get an even share of the cake and their best-case is they get everything.  Not a 100% comparison, I just thought of it.

You can see from the example above that the person who gains the first Province does not inherently have the upper hand. If values are equal, the first player to bid (the player after the one who bought the Province) does better. Intuitively, that happens because you need to overcall by <1> to win. The key to doing well is to have a higher valuation in debt for the 8 VP than your opponent, which may be related to being able to buy Province first - not the order of bidding.

Why would players have different valuations in debt for the VP? You may be ready to green and your opponent isn’t. For example, you’re playing a money strategy while they’re building an engine that hasn’t built a lot of economy yet and doesn’t have gainers so debt would be crippling. Or they’re playing a strategy that involves a lower money density (such as a Gardens or Silk Roads slog without gainers) and would lose many turns. 

What about 3+ players? The bidding logic outlined above still applicable, but is more complicated. Also, players may prefer that one of their opponents win the bid as opposed to the other.
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trivialknot

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Re: Mountain Pass Bidding Strategy
« Reply #14 on: June 08, 2016, 04:21:07 pm »
+3

The nash equilibrium with two players is simple.  The first player bids such an amount that the second player has two choices that are of approximately equal value.  Second player should pass about 50% of the time.

In theory this gives the first bidder a slight advantage.  Say that both players value 8 VP at 10.5 debt.  Well either the first player gets it for 10, or the second player gets it for 11.

But three players, ouch!  The game theory is too hard.
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trivialknot

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Re: Mountain Pass Bidding Strategy
« Reply #15 on: June 08, 2016, 04:30:15 pm »
0

The game theory is easier if there are enough players that you don't care how the VP/debt affect other players.  First you calculate the value of 8 VP to each player (ie the amount such that if they bid more it would actually hurt them to win).  Then the player who values it the most should bid just enough to beat the player who values it second most.
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Re: Mountain Pass Bidding Strategy
« Reply #16 on: June 08, 2016, 04:39:39 pm »
0

Second player should pass about 50% of the time.

It would be cool if (the new) Dominion online had a way to measure this.  I wonder if it would be higher or lower than 50%.  My guess is that it would be higher, as the majority of online players are probably pretty casual, and just want to "have fun" and bid away at whatever (kind of like how casual online poker players just throw their money around).  Then again, by that logic, the first bidder would do the same.  So maybe less than 50%?
« Last Edit: June 08, 2016, 04:41:09 pm by Dingan »
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Re: Mountain Pass Bidding Strategy
« Reply #17 on: June 08, 2016, 04:47:29 pm »
+2

Second player should pass about 50% of the time.

It would be cool if (the new) Dominion online had a way to measure this.  I wonder if it would be higher or lower than 50%.  My guess is that it would be higher, as the majority of online players are probably pretty casual, and just want to "have fun" and bid away at whatever (kind of like how casual online poker players just throw their money around).  Then again, by that logic, the first bidder would do the same.  So maybe less than 50%?

I'm sure it's around 90-93%.
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Re: Mountain Pass Bidding Strategy
« Reply #18 on: June 08, 2016, 07:49:04 pm »
0

I think most first bids will be at least 10. The 16 VP swing is huge. If you get the first Province and the Mountain Pass bonus, you only need 2 more Provinces for a competitive score: 26-30 if the other player gets all 5 other Provinces, and probably by the time they have bought 5 Provinces you have time for some Duchies too.
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Re: Mountain Pass Bidding Strategy
« Reply #19 on: June 09, 2016, 05:37:14 am »
+37

June 2016inception. Early concern about Mountain Pass bidding strategy arouses
September 201630% of f.ds population is involved in Mountain Pass discussion
November 2016mountainpassbiddingstrategy.com is founded
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Friends, let's be careful with that Mountain Pass bidding strategy!!!

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Re: Mountain Pass Bidding Strategy
« Reply #20 on: June 09, 2016, 07:30:21 am »
+22

This reminds me of my studying of economics:

Bidding in theory works like this,

Step1: Assume perfect information (about gamestate and all possible future gamestates)
Step2: Create an easy to use model and do the math
Step3: Profit

How it works in practice,

Step1: Apply theoretic model, realize you have no idea what you are talking about.
Step2: Bid randomly
Step3: Hope you got it right by chance or that your opponent is even more wrong than you are
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Re: Mountain Pass Bidding Strategy
« Reply #21 on: June 09, 2016, 12:03:52 pm »
+4

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Deadlock39

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Re: Mountain Pass Bidding Strategy
« Reply #22 on: June 09, 2016, 04:32:33 pm »
0

Geronimoo posted about simulating this with a static bid in BMU vs BMU, and has people guessing the results.  I have comments, but thought people might not want their guesses to be influenced, so I am posting them here:

I won't be surprised if in BMU vs BMU the value is quite low. The problem I see is that there is still an even number of Provinces. Losing a turn to pay off the debt may directly cause you to lose you the Province split in BMU, especially from second position. Even if you get an extra Duchy along with these 8 points, it won't get you the 12VP you need to make up for losing the Provinces 3-5. 

I also won't be surprised if I am just dead wrong here.
« Last Edit: June 09, 2016, 04:34:17 pm by Deadlock39 »
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Re: Mountain Pass Bidding Strategy
« Reply #23 on: June 09, 2016, 05:10:15 pm »
0

Geronimoo posted about simulating this with a static bid in BMU vs BMU, and has people guessing the results.  I have comments, but thought people might not want their guesses to be influenced, so I am posting them here:

I won't be surprised if in BMU vs BMU the value is quite low. The problem I see is that there is still an even number of Provinces. Losing a turn to pay off the debt may directly cause you to lose you the Province split in BMU, especially from second position. Even if you get an extra Duchy along with these 8 points, it won't get you the 12VP you need to make up for losing the Provinces 3-5. 

I also won't be surprised if I am just dead wrong here.

I understand your reasoning, but I really don't see anything at or below 8 as a possible right answer. I mean, it's as if they're selling an extra (super-)province, and you want to win the split 5-4. Refusing to pay more than 8 for the most "comfortable" Province can't be the right answer there.
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Deadlock39

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Re: Mountain Pass Bidding Strategy
« Reply #24 on: June 09, 2016, 05:32:18 pm »
0

So yeah, after thinking a bit more, it seems like just a major problem for the player who didn't buy the Province.  It is probably to rudimentary to estimate this way, but if you assume each player will hit $8 every turn after this happens, then that player will lose that split 4-5 every time regardless of bidding strategy. 

I guess it seems like most of the time you need to win this and still get 4 of the Provinces or get 3 more Duchies than your opponent, which seems quite difficult in BMU.  When Geronimoo posts the results, I'd be interested to know how often the player who buys the first Province wins in these, and how it compares to playing without it.
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