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Author Topic: BM + Flag Bearer  (Read 2320 times)

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trivialknot

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BM + Flag Bearer
« on: January 31, 2019, 12:18:33 am »
+12

Geronimoo implemented Rennaissance!  Yay!

I tried some simulations using Flag Bearer.  The conventional wisdom so far, is that getting the flag is great, but if you're the first person to get the flag then you're at a disadvantage.  In the context of a kingdom with only flag bearer, this appears to be mostly correct.

I used a modified version of WinderingWinder's BMU strategy.  The buy rules are as follows:
-Buy Province if $18 in deck
-Buy Duchy if <= 4 Provinces in supply
-Buy Estate if <= 2 Provinces in supply
-Buy Flag Bearer if opponent has Flag
-Buy Gold
-Buy Duchy if <= 6 provinces in supply
-Buy first Flag Bearer
-Silver

This beats an ordinary BMU strategy 97%/2%.  However, there is also a simple counter strategy, which is the same except that it never buys the first Flag Bearer.  This strategy beats Flag Bearer 90%/7%.  It also seems that if either player stops buying Flag Bearers before the pile is out, then that player loses.

Is it never correct to buy the first Flag Bearer?  Well I tried a few things, and it seems that if you buy the first flag bearer after turn 10, this gives you a very modest edge.  We're talking a 50%/42% win percentage (regardless of who's first player ETA: I think first player was randomized).

Using this pair of strategies, I played around with priorities.  It seems that both players should prioritize getting the flag over getting Duchies, and then the win percentage got reduced to 46%/42%.  It does not help to further prioritize the first Flag Bearer.  Basically, you buy the first Flag Bearer during the greening phase if you hit precisely $4, and you always take the Flag from your opponent unless you're buying a Province instead.  I looked at some sample games and it seems that you often get to keep the flag for several turns because your opponent doesn't want to pass on province.

I also tried a strategy that opens Flag Bearer, and tries to snag an extra one so that it keeps the flag when the pile is out.  This helps, but still worse than not opening Flag Bearer.

Conclusions?  Contesting Flag is super good.  The first Flag Bearer is not so good, but can be a tossup even in absence of support.
« Last Edit: February 17, 2019, 11:14:54 am by trivialknot »
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hhelibebcnofnena

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Re: BM + Flag Bearer
« Reply #1 on: April 02, 2019, 11:03:12 pm »
0

Why does buying the first Flag Bearer put you at a disadvantage?
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trivialknot

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Re: BM + Flag Bearer
« Reply #2 on: April 03, 2019, 12:38:24 am »
+2

Why does buying the first Flag Bearer put you at a disadvantage?
Once a bots gets the first Flag Bearer, both bots will keep on getting Flag Bearers until they pile.  So the bot that got flag first does not actually have the flag more often.  And on average, that bot will have more Flag Bearers in their deck (which is bad because of terminal collision).  And finally, once the Flag Bearer pile empties, the bot who got the flag first loses it forever.

Later in the game, when players are greening, getting a Flag Bearer isn't as bad, because the opponent doesn't want to pass up a province just to take the flag away.  (The first bot on the other hand, did not pass up a province, because the rule is that it only buys the first Flag Bearer when it doesn't have enough money for Province.)

You should be cautious about interpreting these results.  They're just bots, and it's just big money.  I think in a real kingdom, first flag bearer is better, because your opponent is often passing up something good to take the flag away from you.
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Awaclus

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Re: BM + Flag Bearer
« Reply #3 on: April 03, 2019, 01:20:45 am »
+4

Why does buying the first Flag Bearer put you at a disadvantage?

What trivialknot said is true, but on a more general level which is applicable to human games too, buying the Flag Bearer when your opponent has the Flag has three effects: removing your opponent's Flag, taking the Flag, and gaining a terminal Silver. Buying the first Flag Bearer only has two of those effects, which means that it's a weaker purchase that enables a stronger purchase for your opponent. Concretely, if both players buy exactly one Flag Bearer and never trash it, the one who bought it first just paid $4 for a terminal Silver and the one who bought it last also still has the Flag.
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ipofanes

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Re: BM + Flag Bearer
« Reply #4 on: April 03, 2019, 06:47:39 am »
0

That raises the question: How would the results differ with 9 or 11 Flag Bearers in the kingdom?
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trivialknot

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Re: BM + Flag Bearer
« Reply #5 on: April 03, 2019, 11:10:44 am »
+1

That raises the question: How would the results differ with 9 or 11 Flag Bearers in the kingdom?
It also seems that if either player stops buying Flag Bearers before the pile is out, then that player loses.
More specifically, if there are 10 flag bearers, then the player who gets first flag loses 7%/90%.  If there are 9 flag bearers, then the player who gets first flag wins 81%/14%.

So yes, the majority of the effect in this case, is who ends up with the flag in the long run.
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aku_chi

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Re: BM + Flag Bearer
« Reply #6 on: April 03, 2019, 01:09:54 pm »
+5

In practice, in the sample of games markus has collected stats for, the Flag Bearer pile empties in only 12% of games in which it appears.  Though, we can't rule out the deterrent effect from taking the first Flag Bearer as a result of the pile size.  Interestingly, this part of the first-mover disadvantage does not exist in 3+ player games.

This might also be a good place to post the stats for the Flag artifact:



The player who gains the Flag first wins very nearly 50% of the time in practice.  Gaining the Flag before turn 3 is negatively associated with winning.
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Holger

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Re: BM + Flag Bearer
« Reply #7 on: April 03, 2019, 04:07:20 pm »
0

That raises the question: How would the results differ with 9 or 11 Flag Bearers in the kingdom?
It also seems that if either player stops buying Flag Bearers before the pile is out, then that player loses.
More specifically, if there are 10 flag bearers, then the player who gets first flag loses 7%/90%.  If there are 9 flag bearers, then the player who gets first flag wins 81%/14%.

So yes, the majority of the effect in this case, is who ends up with the flag in the long run.
Then it seems like an obvious improvement of the strategy to add a rule to buy the LAST flag bearer even if you already have the flag (and maybe even add a penultimate Flag bearer rule?).
The last Flag Bearer is much more important than the first when contested, unless the pile isn't emptied before the very end.
« Last Edit: April 03, 2019, 04:55:56 pm by Holger »
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trivialknot

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Re: BM + Flag Bearer
« Reply #8 on: April 03, 2019, 07:03:43 pm »
0

That raises the question: How would the results differ with 9 or 11 Flag Bearers in the kingdom?
It also seems that if either player stops buying Flag Bearers before the pile is out, then that player loses.
More specifically, if there are 10 flag bearers, then the player who gets first flag loses 7%/90%.  If there are 9 flag bearers, then the player who gets first flag wins 81%/14%.

So yes, the majority of the effect in this case, is who ends up with the flag in the long run.
Then it seems like an obvious improvement of the strategy to add a rule to buy the LAST flag bearer even if you already have the flag (and maybe even add a penultimate Flag bearer rule?).
The last Flag Bearer is much more important than the first when contested, unless the pile isn't emptied before the very end.
Nope, tried that too.
I also tried a strategy that opens Flag Bearer, and tries to snag an extra one so that it keeps the flag when the pile is out.  This helps, but still worse than not opening Flag Bearer.
The best I can do with this strategy is a 15% win rate.
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