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It's interesting to watch the videos they link of deepmind playing against the top-level Stratego masters [0]. I usually find Stratego to be a bit of a dull game (less elegant and more drawn out than Go and chess), but I'm a sucker for watching top-level AIs play.

Its skills for bluffing are both fascinating and a bit scary.

[0] https://www.youtube.com/watch?v=HaUdWoSMjSY https://www.youtube.com/watch?v=L-9ZXmyNKgs https://www.youtube.com/watch?v=EOalLpAfDSs https://www.youtube.com/watch?v=MhNoYl_g8mo



FWIW one of the big things poker AI taught humans is massive overbets (eg. going all in for $200 over a $15 pot).

This is scary to do well in practice, because the mathematically optimal bluff frequency approaches 50% as you increase the overbet size.


Wow, that's crazy.

It seems like it would be easier for AI to do, since it doesn't have any tells (it's easier to have a poker face when you don't have a face at all).

I remember playing poker as a kid, and experimenting with pretending like my cards were good/bad with body language. I don't think that any professional players use that approach (they just have sunglasses and a straight face), but I wonder if AI could beat humans even more consistently if it developed a way to convey tells and fake tells?


All Poker AIs developped as yet approaches Nash Equilibrium -- it's just a "perfect" strategy that wins by default because it makes no mistakes. Since you make mistakes against the AI strategy, and the sum of the game of poker is 0, you lose by default.

No poker bots yet I know of have developed "exploitative" strategies, where they deviate from the Nash Equilibrium strategy to exploit opponent mistakes.

Back when I played professionally (2012-2016, poker AIs being relevant in 2015/16) the standard was to use a bot to study the best default strategies and use expert human judgement to deviate from it against bad opponents.


Nash equilibriums exist when bluffing is involved?

It seems like it would introduce a level of predictability that would make it easier to know when the opponent is bluffing.


They absolutely do. Since it's world cup time I'll use a contrived soccer example.

A penalty kick where the kicker can kick left or kick right. The goalie has to jump one direction, if they jump the wrong direction a goal is scored. Both people know that this kicker is great at kicking to the left side of the goal but rather "meh" at kicking to the right, so if the kicker kicks to the left and the goalie jumps left, there's still a 20% chance of scoring, but if the kicker kicks to the right and the goalie jumps right, there's only a 5% chance of scoring.

There is a Nash equilibrium for the kicker, and it can't be "always kick left" because then the goalie would "always jump left" which would give the kicker an advantage if it kicked right.

Similarly the Nash equilibrium for poker can't be to always fold a weak hand, because that's leaving money on the table because then the opponents will always fold against a raise, which would mean the player could get easy money by raising with a weak hand.


> Nash equilibriums exist when bluffing is involved?

In some sense that's the whole point of Nash equilibria.


A strategy can involve probability, like bluff 30% of time.


Bluffing isn’t really something one needs to compensate for. Bluffing as a game rule simply means that all hands or values may be max or min values, but the idea is that if you are making bets based on the mathematics of your hand itself this isn’t so pertinent.


There is a new player in the professional poker scene that people call "Casino Eric". He combines reverse tells with insults and jabs at the opponent. This helps him make up for a lack of pure technical skills when compared to top online players like Linus Love. This is a meta game that people have played for a long time, but "Casino Eric" is known in professional circles as someone who is naturally trying to perfect this.


Unless it's completely random, you're just giving away information. i.e. do the opposite of their body language, only exhibits body language when it's really bad or really good, voluntary vs involuntary body language.

You only use the "tell" when you believe there to be a pattern.

Otherwise, if it is truly random, I realize I can't get any info there and I ignore it, which then leads to me just having a straight face.


Is that heads-up only? Early massive overbets are nearly a coin toss in heads-up, so you break even in on a call and win on a fold, which is an equilibrium.

However at a large table, you are going to get called only by the person who thinks they have the best hand, which is a lot better than the average hand of a typical opponent.


This is mostly done at the river where you've ended heads-up even when starting the hand with 6-10 players


Its more common in heads up, yes.

In multiplayer you see it where ranges are narrowed, like 3bet pots or on turn/river

It matters less than you'd think because overbets imply you have a polarized range (nuts or air). You generally pick the bluffs to be hands that have cards blocking the best calling hand combinations.


Okay, that makes sense. I think it matters some still because if someone else has nuts, then they automatically know you are bluffing, and the more players still in the pot the more likely one of them has nuts.


Fascinating games. But I played a lot of Stratego as a kid, and I remember 1 was the strongest piece and 9 was the weakest. In these videos it seems 10 is strongest and 2 is weakest and that's making it confusing to watch. Did the pieces change sometime in the past 40 years or am I imagining things?


I've just watched a video https://www.youtube.com/watch?v=HYQbGHgaWbM that talks about "original" Stratego, a game created in 1947 by Jacques Johan Mogendorff. It might be nostalgic for you.

Searching to find out whether "original" is the current version, I've noticed that https://en.wikipedia.org/wiki/Stratego#Versions answers your question

"European versions of the game give the Marshal the highest number (10), while the initial American versions give the Marshal the lowest number (1) to show the highest value (i.e. it is the #1 or most powerful tile). More recent American versions of the game, which adopted the European system, caused considerable complaint among American players who grew up in the 1960s and 1970s."


I guess that makes me one of those complaining Americans. If I ever get back into the game, I'll have to get used to the new numbers.


I just checked my UK eighties version and the Marshal is 1 on the board


Watched some of the first game. I'd bet stratego favors defence, advantage to the AI that has no/minimal concept of the value of time.


Yeah this is one of the reasons why I find it more dull than chess.

There is an incentive to just not move your pieces, so that the other player thinks they're bombs. As a result, players only activate 2-3 pieces at a time.

In chess, on the other hand, you are constantly moving your pawns to the other side to promotion, or otherwise trying to activate/coordinate all of your pieces for an attack.

It makes me think that if deepmind for Stratego was trained to not lose instead of win, then the top strategy might be shuffling pieces and letting the enemy come to attack. No human would ever have the patience to play that way though.


> It makes me think that if deepmind for Stratego was trained to not lose instead of win, then the top strategy might be shuffling pieces and letting the enemy come to attack. No human would ever have the patience to play that way though.

Tournament Stratego uses a clock, which reduces some of the issue there. It's not hard to beat a player that does what you suggest; just send some middling pieces after each piece that moves. You'll take the weak pieces and reveal the strong pieces.

It is much more defensive than chess in general though, as moving a piece and capturing with a piece both give the other player information.


> It's not hard to beat a player that does what you suggest; just send some middling pieces after each piece that moves. You'll take the weak pieces and reveal the strong pieces.

But taking a strong piece means revealing a stronger piece of you own. That’s why I think the best strategy is to put almost all your weak pieces up front.,and wait for your enemy to reveal their pieces. Scouts, especially, are canon fodder that you sacrifice to find out information about the enemy and that you need to get rid of so that you get room to maneuver.


Having scouts in the mid/late game is important to make them play more cautiously with their spy, since a scout can take out a spy from any straight-line path.


If you know know where the enemy’s spy is he either is dead or served his purpose by killing your marshall.

So, the idea is to, in midgame, make educated guesses as to the positions of the spy (e.g. the piece that stays close to the enemy general, or that moves towards your marshall), and sacrifice scouts, hoping to kill the spy?

Interesting tactic (and if that’s their common usage, why are they called scouts? ‘Assassin’ might be a better name)


That is one of several uses for scouts. When the opponent has scouts, it's safer to keep your spy behind one of the lakes, since they will occasionally fly across the map just to reveal a piece; you don't want your spy getting "accidentally" killed by a scout either. If the opponent sacrifices all of their scouts early you can move the spy around more easily.

Since killing the opponents Marshall with the spy is such a huge advantage, losing your spy is a big disadvantage.


> When the opponent has scouts, it's safer to keep your spy behind one of the lakes

I don’t know anybody who plays the game that way, but reading the rules (https://www.hasbro.com/common/instruct/Stratego.PDF), that wouldn’t fully help. The rules say

“scouts are the only pieces allowed to both move and attack in the same turn. A scout can move any number of open squares forward, backward or sideways into an attack position. Once in position, it can then attack”

That doesn’t say in any way that that attack has to be in the direction of movement. So, you could move a scout 3 squares forward and then attack leftwards.


Different editions of Stratego have different wordings for scouts. Some rules are silent on moving and attacking in the same turn (implying that scouts can't move & attack in the same turn), some rules specifically state that the scout cannot move and attack in the same turn. Some rules say they can move and attack in a straight line, and some use the wording you quote.

The ISF rule is that the attack must be in-line with the move[1].

1: https://isfstratego.kleier.net/docs/rulreg/isfgamerules.pdf Section 5.3


Chess has the 50 moves rule https://en.wikipedia.org/wiki/Fifty-move_rule about

A "player can claim a draw if no capture has been made and no pawn has been moved in the last fifty moves"


A common variation of the game is to let the aggressor win battles where both pieces have the same value. The default is a draw. This promotes aggression.


I was hoping they'd have examples of this variant in the testing data, because I think it MASSIVELY alters how you have to play


The other variant that would be interesting here is where only the attacker (or alternatively the defender) reveal their rank.


why would you make a move that would place your piece next to an opponent if it just gave them the potential advantage in a battle? Wouldn't it increase wariness?


Are these games against stratego masters? I'm watching the first one, but it doesn't say who they're playing against


The player in the first game had an advantage and didn't trade 10's, then for some crazy reason left his 10 out there to the only piece approaching the 10. I played a ton of stratego as a young adult, and i would never have thought that was close to an optimal strategy.


Dont think the player pool is very deep, doubt there are many masters around..


What makes you think that? The article says that one of the coauthors used to be a world champion, which suggests to me that there is some kind of competitive organized league.


How many people study Stratego as much as an International Master studies chess?


I think there are probably very much diminishing returns.

A small scene is probably pretty damn good at the top. Having hundreds of thousands of competitive players helps, but even with a small sample you are probably likely to get at least some very, very strong players.

It's hard to think of a relevant real world example, but a fun corollary I'm familiar with is Fedex (Federico Perez Ponsa). He is a full chess Grandmaster, #461 in the world in chess amongst ~300k active FIDE players. By your "International Masters study hard" logic, when you drop him into Age of Empires 2, a game with ~500 competitive tournament players, his work ethic should dominate. But it turns out that the top ~100 AoE2 players are really damn good and practice a ton (easily chess IM amounts), and Fedex tops out around ~#50 in the world.

https://ratings.fide.com/profile/117927 https://liquipedia.net/ageofempires/Fedex


Love the real life example.

No matter how good the top players are relative to the competition tho, I feel like a large playerbase still raises the skill bar to a huge degree. There's a ratchet effect where someone figures something out, other people copy, and it breaks into public consciousness through influencers and popularizers. Then on the tail end, regular people regurgitate it for years like it's new information. (Getting sick of hearing about cognitive biases and product-market fit and dunning kruger, ffs). I've seen it with dota over the last 10 years. Pro players were always good, but now bad players are good and pro players are better. Not to mention the motivation that comes from seeing other people work hard.

When it comes to stratego, watching the linked games (from an armchair!), the human players looked relatively sloppy. Overusing scouts in the early game, too eager to trade, noticed a piece being forgotten about once. Not to say I'd be better, but it definitely looks like the scene is "for fun" and not so serious.


I completely without knowledge on the topic would imagine the "for fun" aspect is probably a pretty dominant factor.

I play disc golf pretty regularly. Over the last 10 years, it has exploded in popularity.

I'm not sure that the explosion of popularity has resulted in better people performing in tournaments.

But what has changed, is how much money can be won by competing in disc golf, and how much money is available across the sport as a whole.

The increased prize money has dramatically changed the number of people and level of competition for people playing the game seriously as well as how seriously everyone involved in top level play takes the sport. This then has a trickle down effect in the number of people and seriousness of things like training clinics, professional teachers, professional and more intelligent course construction and analysis. It pays for more analysis into all aspects of gameplay to increase the competitive edge of performers at the top.

The increased player base, in turn, pays for most of this, as it increases the potential market for the same services as all of the above. And the more seriously top level play is, and the higher the winning prize pool money goes, the more respectable the sport has become in the public eye, which in turn creates a catch-22 effect whereby players appear more willing to spend more money on the sport on those services.

All of which increases the level of play at the top. And you can see it in the quality of new young athletes that are coming up in this new environment, and how much better they are and how much more they are able to learn from the more widely accessible resources than their equivalent counter-parts were 10 years ago.

Its been fascinating to watch, and very exciting. Particularly over the pandemic, the sport has come from being called "frolf" on a golf course or in your local park, to "disc golf" with multi-million dollar professional contracts, dedicated disc golf resorts and private courses, training clinics, and dedicated PPV channels. Very cool : D

A counter-example might be the various competitive communities around different forms of boardgames, which tend to be very small, but often very competitively driven and taken very seriously by a very dedicated community, but I don't know enough about the topic to discuss : )


That type of logic is unsafe - we don't know that Ponsa is playing AoE with the same intensity as chess.

In fact, the idea that someone can train with sufficient intensity to be a high ranking chess master then break in to the top 50 of AoE at the same time suggests a lower skill saturation in the AoE world.


And the top 5 AoE2 players are significantly better than the top 20 who are significantly better than the top 100.


I don't know. How many?


yep, top anonymized players




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