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Predictability and bluff


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#21 TemplateRex

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Posted 27 August 2018 - 08:48 PM

Just for fun, and because I like math, I computed the equilibrium of a simplified game. I gave blue 2 strategies: "hit" or "run away" with the colo, and I gave red 2 strategies "bluff with cap" or "chase with gen". In poker terms: blue has "fold" or "call", red has "bluff" or "value bet". 

 

For better or worse, I took piece value from Vincent de Boer's thesis. This has the rough guideline that (with the high ranks still on the board) rank R is worth the same as rank R-1 + R-3 combined (marsh ~ gen + major), slightly more than 2 pieces of R-2 (marsh >= 2 colos) and about the same as 3 pieces of rank R (marsh ~ 3 majors). Info on piece of rank R is worth about a R-3 piece (major for marsh info, cap for gen info). So I took as points an unkown gen = 90, known gen = 62, known colo = 42, unknown cap = 29, sarge = 14. 

 

Then I plugged these strategies and payoffs into the open source tool Gambit.

 

KVfwjxC.jpg

 

The equilibrium is for red to come out with the cap 25% of the time, and 75% of the time with a gen. For blue, the equilibrium is to run away 75% of the time, and to hit 25% of the time. The net value for red is less than 4 points (about a 1/4 of a sergeant).

 

So if you can convincingly represent the chasing piece as a gen (in this case, it came from D3, so it was believable) this mixed strategy is a slightly +EV gamble. If you only do this 25% of the time with a cap, you are indifferent whether blue calls or folds with his colo.

 

I ran the same analysis for chasing a known gen with either a major or a marsh (either unknown) when there is a captain present for the major to pick up if it doesn't get hit. In this case, there is also a small +EV gamble to bluff a major 22% of the time, and for the gen to call this 33% of the time. The EV is about 1/4 a captain here, not a very high reward for such a risk.

 

Conclusion: regardless whether these numbers are 100% accurate, in cases where you have a mid-level piece on a believable general starting place, you can make a very small gain (about 1/4 of the time you succeed in gaining the sergeant) by sometimes bluff-chasing the colo, for a pretty big risk (a captain down, vs a known colo up minus gen info). 

 

 


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#22 GaryLShelton

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Posted 29 August 2018 - 12:41 AM

and because I like math

 

Really?  :D


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#23 Wogomite

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Posted 29 August 2018 - 02:01 AM

TemplateRex, as much as you THINK you understand this game, when will you join a tournament with us? :)

#24 TemplateRex

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Posted 29 August 2018 - 11:40 AM

TemplateRex, as much as you THINK you understand this game, when will you join a tournament with us? :)

 

Oh I don't think I understand this game at all, yet  ;) All I did was use some analysis to confirm the basic intuition of Fks and others that certain types of bluffs are very risky, even if borderline +EV. 

 

I was trying to understand the nature of bluffing in Stratego. If you compare Stratego to poker, the nature of a "bet" is very different. In the example of my OP, the "pot" was the sergeant at A7. Blue's "hand" was a colonel, and I tried to "bluf" him out of the pot by representing a gen, while holding a cap. In poker terms, this was a massive overbet, since I committed more than twice the pot (valueing a cap to at least twice a sarge). It was slightly +EV, but with a huge variance (lose cap, gain colo for gen info). 

 

There are many of such borderline "bets", like capturing a known piece of rank R with your unkown piece of rank R+1 or R+2 (taking with R+3 seems excessive, already giving up about as much info value as the piece value being captured), that can be defended with rank R+2 or R+3. Depending on how you value different ranks, hitting such known pieces are more or less neutral, maybe slightly -EV even. The higher R, the lower the EV probably (don't think hitting a known and covered colo with an unknown gen is worth it, in general). 

 

So that leads to Nortrom's concept of chain trades, where you have 2 or 3 "pots" with at least a major or a colonel at stake, which in isolation are all -EV, but they are negatively correlated, so a colo taking a major and being recaptured by the marsh, raises the expectation of the other bet(s). So effectively the chain trades are like playing multiple poker pots with hands from the same deck! Or more accurately, it's like multiple poker pots with each player choosing hands from his own deck. Someone revealing aces in one pot, will likely lose the other pots.

 

But yeah, I am practising games as well, pretty badly so far (with the occasional games that go just right).


Edited by TemplateRex, 29 August 2018 - 11:44 AM.

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#25 Dobby125

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Posted 30 August 2018 - 04:24 AM

I was looking through my archive games and actually found a captain bluff charge of a colonel.  The player really wanted to call my bluff at the 50 second mark.  I almost blew it by moving too fast.  It's fascinating watching how players react.  

 

https://www.youtube....eature=youtu.be


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