[legitster]

Richard Garfield (mathematician and designer of Magic the Gathering and others) used to give a talk about randomness in games.

He talked about the history of chess, and how there used to be a lot more variants of the game (some even being a 4 player game with dice!), and over time competitive players naturally will want to remove random elements from the game.

But on the other hand, some amount of wild unpredictability is important to attract players - there's a softening of skill gaps.

[mod]

In some of my own pursuits, I've seen things that make me agree.

Pool has little randomness, and therefore it is very difficult to beat a player who is better than you. The best players want to eliminate the possibility of that happening by making longer races, racking their own balls, winner breaks, things like that. Pool is dying for it.

Meanwhile poker has a large amount of short term variance (luck) and it keeps bad players interested for years and years. The worst player in the world can sit and beat the best players in the world at any given moment. Poker is still going as strong as ever-- maybe more strongly than ever at this point. People are coming out of the woodwork this year itching to play.

I think most of the greatest, longest- lived games in the modern era will need a high amount of randomness, because of computers doing analysis. Even more, with the absent of solvers and the like, many poker variants cannot be solved in real time and all-encompassing strategies cannot be developed. More computational power could change that in the future, I guess.

[tialaramex]

The machine doesn't care about randomness. Poker variants people actually play get tackled by machines.

Cepheus http://poker.srv.ualberta.ca/about is an approximately perfectly strategy for Heads Up Limit Hold Em. That is, the two player game of Texas Hold Em poker with fixed bet sizes. There are almost certainly other approximately perfect strategies, which would break even against Cepheus over the long term, but you can't beat it. The best an opponent could hope for is to merely get lucky briefly, for which you might just as well play Roulette.

In principle if you could memorise Cepheus you could play the same strategy, but it's basically a vast number of fractions/ percentages so you're not going to -- and it's important to note that while the strategy is unbeatable it is not the best way to extract money from weaker players. If you want to grind money playing poker you need to focus on taking $1000 from that holidaymaker playing $5/$10 before anybody else realises they're soft, not on trying to break even with a machine.

Heads Up No Limit which was still being played a fair amount not so many years back, is crushed by AI. Pluribus beat the best players in the world, comprehensively. Unlike Cepheus, Pluribus doesn't have an incredibly boring yet precise strategy mapped out that you could copy, it's a result of AI learning. Its bet sizing feels a bit weird to humans, but it ends up taking their money, so, whatever.

[mod]

You've picked two of the easier games to solve--heads up games. More specifically, heads up games with specific stack depth

There is no AI that can play well, for instance, in a 9-handed game with varying stack sizes, while itself and some competent players are 600BB deep and some other players are 40bb deep.

It takes a specific, narrow ruleset to tailor an AI to be able to play it at such a high level. Or more compute than we currently have in real-time.

Pluribus' matches against pros had each hand reset to 100BB.

Also, notably, the bot can still lose in the short term to terrible players, which was the thrust of my post. In fact, given its bluffing frequency, it might actually do worse against weaker players than it did against pros. Additionally, no human can realistically implement an AI strategy, meaning the AI is not a big detriment to the actual game of poker, as it's currently played.

[bskrobisz]

>Also, notably, the bot can still lose in the short term to terrible players, which was the thrust of my post. In fact, given its bluffing frequency, it might actually do worse against weaker players than it did against pros.

To be clear about why this might be true for someone who doesn't know much of poker strategy--the AI is (I presume) going to optimize for strategies that can't be beaten by changing one's own distribution of plays (for (simplified) example, if the AI raises a given hand 20% of the time and folds 80%, it's doing so because even if opponent were to call 100%, fold 100%, or something in-between; it wouldn't change the overall expected value of that hand with that distribution of plays). Professional human players, on the other hand, will absolutely cotton onto a player whose distribution of plays is not optimal and can therefore be exploited for profit.

[mod]

Yes, and bluffing bad players generally doesn't work out as well as bluffing good players.

The AI notoriously bluffs a lot, which many bad player types accidentally counter by calling too often.

Good human players will also specifically exploit bad players, as you note, while the AI attempts instead to itself be unexploitable.

[tialaramex]

Cepheus doesn't care about "stack depth". It's just brutal statistics, this strategy beats your strategy unless your strategy is also approximately perfect regardless of what strategy you have. Good, bad, newbie, pro - it doesn't matter.

Yes, if it's very chip poor, Cepheus could run out of chips before it stops being unlucky and takes your money, but that's unavoidably true anyway in Poker due to it being a game of chance as well as skill.

Cepheus is actually a good Rorschach test for players who say "GTO" a lot. If you actually grasp what game theory optimality is about, you see Cepheus and you're like "OK, I'm done playing Heads Up Limit" (and indeed although it was once somewhat common you won't find any professionals playing this for some years now). But if you're the sort of person for whom it's just another phrase to sling around, like complaining you had a "bad beat" when you were never better than evens, chances are you see Cepheus and you think "I could beat that". Oh dear.

> Also, notably, the bot can still lose in the short term to terrible players, which was the thrust of my post.

This is exactly the useless observation I'm complaining about. Poker is a game of chance so of course anybody might get lucky in the very short term. If what you value is the fact you could win despite being terrible at it, just play roulette and save everybody else the trouble.

> In fact, given its bluffing frequency, it might actually do worse against weaker players than it did against pros.

It isn't about "doing worse" here and that's yet more of the mindset that got you into trouble here. The machine doesn't care about "doing worse" it just wins statistically over time. A grinder needs to make rent and buy groceries, so for them being up $50 after a full day feels like losing, it is losing. But the machine doesn't need money.

Again, if it's just about being able to get lucky and get some sort of temporary "High" from that, I'd commend roulette over poker, or, if you like cards, try blackjack.

No, there aren't any academics showing off bots that play full ring. Of course, there weren't any academics showing off that they could count Blackjack. At least not until after they were run out of Vegas with a fortune of the casino's money... Grinding online full ring with AI is not academically interesting, but it would be profitable. The former would cause you to publish (like Cepheus) the latter not so much.

[YeGoblynQueenne]

Good to note that Pluribus is trained with Counterfactual Regret Minimization rather than deep learning, same as Libratus, the first AI player to beat professional players in Heads up no limit Texas Hold' em.

I'm not sure about the relation between Pluribus and Libratus- I think Pluribus is a newer version of Libratus, essentially?

[mcguire]

Greg Costikyan's book Uncertainty in Games is another good source.

And this topic frequently comes up in wargaming circles (frequently enough to be annoying :-)). Some feel that nondeterminism is a crutch for the low-skilled while others feel that it is the only reasonable way to handle a low-fidelity model of reality or that it teaches the valuable skill of how to deal with the bag of rotten lemons that the universe periodically hands you.

[da_chicken]

You can see his lecture on YouTube:

https://youtu.be/dSg408i-eKw

You can tell he's going a little from memory, but the points are all still there. His arguments that skill and luck are not opposite sides of the same spectrum is quite good.

[joshuaissac]

> some even being a 4 player game with dice!

Charutaji: https://en.wikipedia.org/wiki/Chaturaji

[mikepurvis]

In many games, it's pretty clearly part of the design that the random elements are there to provide rubber-banding— particularly in games with more than 2 players, where sometimes you try to win without looking too much like it, so you avoid getting ganged up on (think: the robber in Settlers).

[floren]

This is why I really like cribbage. There's a major element of randomness based on the cards you're dealt, but lots of opportunities for strategy in how you play them. New players have a chance but more experienced players tend to make better choices with what they have.

[Andrew_nenakhov]

Yeah, add health to pieces and use dice to determine what happens when pawn takes the queen: roll 5 and your queen wins, but with 1/3 health.

That would really suck.