A Response to Jorbs, regarding Poker and the Tragedy of the Commons

Last night I saw that Jorbs (the Slay the Spire Streamer and former pro-poker player) posted a video discussing tournament hold ’em and the tragedy of the commons. While Tao isn’t a huge poker player, I’m not entirely without skills. And mixing game theory, poker, and policy design? The kind of catnip topic I haven’t seen in years!

To summarize the video:

1. In tournament poker (unlike in cash games) not all chips are equal value (the Independent Chip Model)
2. In the final table of a tournament (for example) this model leads to optimal play often being to wait for you and him to fight. “Going to war” (with random hands) on net costs both players expected value. (I don’t really think you — the average Tao reader, gifted with math knowledge far above average — needs that link. Nor does Jorbs. But maybe I’ll catch some traffic that does).
3. Jorbs provides the example of a 6 handed table folded to the small blind. In this situation, the SB may just shove all in much more often than optimal (in a cash game), because the clever BB — even if he knows that he SB is bullying — is stuck. Calling with more than the “correct” set of hands (whatever that may be) is just destroying his expected value.
4. This is a tragedy of the commons, a known problem (Jorbs uses the “picking up trash in a public park” example). (It’s kind of a two player prisoner’s dilemma, with a small blind/big blind, but because it can be repeated with multiple actors, it extends. There are some assumptions buried in there, but for a 20 minute video or a blog post, I think its fine to handwave this).
5. But — here is the crux of Jorbs’s frustration — Pro Poker players are some of the most strategic thinkers on the earth (in their domain at least) … So, why have they not come up with a solution to this problem via some enforcement strategy?
6. More frustratingly for Jorbs is that apparently poker players do not apparently acknowledge this problem.

I have many thoughts….

Let’s You and Him Fight

First, this problem is a typical “multi-player wargame” issue. This is the reason 3+ player (non-team) Chess doesn’t work. If A and B trade pawns, C is better off. There’s a reason that Titan is a classic: If A and B fight, C may be the big loser (because fighting has gains and losses …. the fight’s winner can gain points, a recruit, an angel, possibly legion tokens).

In fact, I think Jorb’s simplified model over-stated how negative the EV was of going to war. He just assumed payouts of 6,5,4,3,2,1. But typical tournament payout would be something like 300,150,75,40,25,10 … the values would depend on entries, but winning is ~40% …. Running a full EV calculation is harder then, but my gut feeling is that it lessens the impact of going all, but it would still be a negative EV play. (The calculation is harder b/c the person who doubles up now has a 40% chance of winning the tournament, but also improved chances of 2nd, and reduced chances of 5th, etc. This calculation may be solved, but I don’t know the solution and don’t care to do it now. Perhaps one of my readers knows the answer).

As any bridge player has heard, Matchpoints isn’t real bridge. (See my review of Matchpoints by Kit Woolsey). So, Jorbs feeling that tournament poker has these annoying corner cases makes total sense. You have taken an open-ended cash game (like Bridge, originally) and turned it into a format that can take an arbitrary number of entries and produce a winner in a relatively fixed time frame. Why would you expect that to be a perfect translation?

Perhaps the TL;DR of this essay is “Given that this is a known problem in tons of domains, why would you think Poker is immune?” Again — hardly satisfying. So let’s dive into it in more detail

Enforcers != Enforcement

Jorbs brings up the idea that people should enforce it. Let’s define that. An optimal player in the Big Blind will know the range of hands to calldown with if the Small Blind is playing optimally (even if I don’t). This is likely solved. If the small blind is “stealing” (betting or shoving all in on more hands than is optimal) then the Big Blind can call more aggressively and still be playing optimally (assuming he has a good estimate of how much the small blind is cheating).

We’re still in game theory. But what if the Big Blind decides to change from “optimal” play to an enforcer? Now they will not only call when it is optimal, they will call sometimes when it is sub-optimal, just to hope to catch the small blind and punish them. Something I have said professionally (but not on this blog, apparently) is

“Security is paying a small cost to impose a large cost on your adversary.”

(Me)

So, an enforcer expands their range of plays (possibly to the point of just always calling anyone who appears to be consistently stealing). If all the seats agree to do this, then you have solved the tragedy of the commons, or so the argument goes. Because players see that you are willing to punish defectors

Let’s posit that some players at the final table are just lucky and not up to game theory.

If we go back to our park example. An optimal person will pick up some trash and keep the park clean for everyone (“cooperate” in the prisoner’s dilemma). If they see a defector (someone who walks past a piece of trash without picking it up or even worse tosses some trash on the ground), they will not do anything. But an enforcer will punish the defector. Call them out, shame them, fine them, something. The enforcer takes an additional cost to make things right.

So now our enforcer rushes over to the guy who tossed a soda cup on the ground, harangues them, and then gets their reputation destroyed on social media, gets fired from their job and the litter bug’s Go Fund Me explodes … (Now might be a good time to mention the “Central Park Karen” — I haven’t followed that particular story enough to know who is actually the bad guy here, but this is not a hypothetical).

The obviously true fact is at the poker table, there’s a lot of variance. “Punishing” the defector is probably taking away a couple percent from them in the long run, but in the short run you’ll double them up a fair amount of the time.

And what do the other players see? A way to tilt the enforcer (should they ever be sitting to his right). Because “Enforcer” is another way of saying “Not playing optimally.”

Enforcement may incentivize the behavior you are trying to stop. Particularly for an opponent who recognizes he’s outclassed. (This is another aspect of Matchpoints. When you are inferior to the field you should absolutely not use the exact same bidding system as the field. Why get to the average contract and let the result be decided by technical perfection when the other players are better at it? Better to flip a coin, even if you know the coin is slightly biased against you).

It would be one thing if when you tossed some trash on the ground, enforcers (cops or otherwise) magically appeared and gave you a $50 fine. But if they magically appear and give you a fine 52% of the time and give you a $50 gift card 48% of the time, you are “losing” EV, but it might take a while to catch on.

People play lotteries voluntarily and plenty of criminals risk decades (or life) of jail time because enforcement is haphazard at best, and that’s with paid enforcers.

A minor but related point — If your village has 100 people, the park is probably small but nice. Everyone knows everyone, and if Giselle doesn’t pick up the trash because she thinks its beneath her, people will talk. If your commons are Manhattan’s Central Park …. well, there’s a lot of anonymity in the big city (except for Karen) anyway. Even if you discount the bad incentives and knew that everyone would see what you are doing and react accordingly, it matters if you are playing against the same crowd over and over again (where they will learn you are enforcing) versus some people you’ll likely never see again. (Yes, this might very well be the definition of Tragedy of the Commons, but I wanted to make it explicitly).

The Elephant in the Card Room

One aspect that Jorbs touches on …. there is an enforcer. The Casino. As he mentions, there are rules against collusion. The Casino cares about that, because if word got out that a gang (etc) were colluding in their card room the game (and their sweet, sweet rakes) would dry up. The tournament rules (like raising stakes) also exist for the Casino’s benefit, because they don’t rake each hand (only the fees), so they have incentives to make it fast enough to be profitable, but long enough that players want to play.

And the Casino is a notoriously ruthless enforcer. If I became desperate enough to resort to stealing, I’d go for a waitresses tips before trying to steal chips from an area where all the players had went to the bathroom. Even for non-crime, rules of the game enforcements, casinos are tough to beat. I’ve been called out for string raising because I didn’t know the exact rules of that particular card room (for example), even though I’m usually careful to not string-raise. The dealer is often very sympathetic to me, while rigidly enforcing the rules.

A story I read in a poker book. In one of the early tournaments, a small stack pushed all in under-the-gun. The next person (a medium stack, with several big stacks behind him) pushed all in and flipped over his pair of aces. The logic was impeccable, he was likely to bust out the small stack, but a big stack might think he was also cheating and try to bust him out, and even if he had a hand, ICM theory said it might be right to call. The ace-holder might very well grab a bunch of chips, but it was at a risk and by advertising he was making the safe solid play.

This is another weird Matchpoint-esque situation. Playing for cash you’d be happy to have a bunch of callers.

Now casinos ban players from showing their cards.

Of course, there’s a whole bunch of reasons why Casinos don’t say “No cheating in the final table, tragedy of the commons situation.” How to tell and enforce? Casinos want a bright line rule. But from the Casino’s POV, this is a legitimate angle/shot, all part of the game, and not something that (most) players care about. If players did care, Casinos might try to enforce it, but mostly it takes care of itself. Chip stacks are rarely even and the blinds will increase fast enough that other issues come to the fore.

Part of my wonders if one reason that Pros (in general) don’t care isn’t a lack of awareness, its just that its a small minor corner cases that they get over (“Matchpoints”). And against that small benefit, if they ever decided to band and somehow not have it backfire, they are worried about the casino.

Because if you (and the rest of the Pros) stood up and loudly proclaimed “We will punish defectors” some Average Joe somewhere is going to go to the Casino and say “Aren’t they colluding?” (I don’t really think this is an issue, but its an interesting angle).

Some random other thoughts / Conclusion

I keep thinking back to Hirschman’s Exit, Voice and Loyalty. For any problem inside an organization or system some people accept it (Loyalty), some complain but try to work within the system (Voice) and some just give up and walk away (Exit). This is obviously a butchering and gross simplification of Hirschman’s book, which I doubt I remember enough to treat well …. Thankfully poker isn’t nearly as important as most tragedies of the commons.

My main response to Jorbs is that I think he’s correct, and I can see why it bother him, but … well, I play a lot of Matchpoints these days. What he’s describing is true, and has no solution that I can see. If it really bothered me, well, I’d be an exit-guy as well. I’m sympathetic. Whaddya going to do? It’s the rules of the game.

PS — For a great article discussing capitalism, evolution, and various tragedies including the prisoner’s dilemma, paperclip maximizers and the race to the bottom — with a stop in Las Vegas — I suggest Scott Alexander’s (very long) essay Meditations on Moloch.

I will now jump from boring game theory stuff to what might be the closest thing to a mystical experience I’ve ever had.

Like all good mystical experiences, it happened in Vegas. I was standing on top of one of their many tall buildings, looking down at the city below, all lit up in the dark. If you’ve never been to Vegas, it is really impressive. Skyscrapers and lights in every variety strange and beautiful all clustered together. And I had two thoughts, crystal clear:

It is glorious that we can create something like this.

It is shameful that we did.

Scott Alexander, Meditations on Moloch

Pandánte

Courtesy of a Mr. A____ R____ I heard good things about Pandánte. The fact that Sirlin’s new card game makes a good cash game caught my attention, so I picked up a copy. Initial testing (with the Taoling) indicates that the gentleman’s opinion was not mistaken.

The rules aren’t difficult. This really is Texas Hold’Em mixed with Coup, and a bit of “Dragon Poker” special effects. As always, small changes have organic consequences.

There are three rounds of betting with fixed bet amounts. You either bet or fold. The first round of betting is post-flop, and you can’t fold until the turn (or river). The twist — your bet also declares your minimum hand type. You can never lower your bet, so why bet high? The reason is that after the flop (and turn), players can drawing a card and then discard it or replace one of their original hole cards.

This is never bad, since at worst you’ve seen one card. But only the player(s) who claimed the best hand get this option (called “Snacks”) for free. The rest pay $2 for each level difference between their hand and the claimed best. (A pair is level 1, a straight flush is level 10). Two pair isn’t a level, so if you have that you can safely claim a pair (level 1), but maybe you want to claim a full house (level 4) to jack up the price for everyone who just claimed a pair. After all, if other players can replace their cards, they may get a Floosh (4 card flush — Level 5) or Flush. [The deck has 6 suits, flushes are rarer that normal poker, hence higher than full house].

But if you do this you may miss your Full House, Floosh, or whatever. Once you get past the river then each hand can use their hole cards special abilities (or any special abilities, by claiming to have them as hole cards) and then bet again (to raise their hand type).

At that point, If you have the highest hand players can challenge or not. If anyone challenges and you don’t have the hand you claimed; you fold. (And any challenge for high hand, or having cards in abilities, results in a direct side payment between challenged and challenger).

Let me quote an example hand posted by the Gentleman on a mailing list (this example assumes $1 ante).

So, let’s take a typical 4-player hand:

One player buy new cards ($2), everybody antes and bets first round ($12)

$2 goes in for draw-1-discard-1 option, one person folds, rest bets ($6)

$2 goes in for draw-1-discard-1 option, all bet ($6)

Orange/Green (Hand improvement) Abilities are called, a player successfully calls bluff (no pot effect).

Red Ability is used (all other players fold or add $5), 1 player folds, other player adds $5 to pot

Black (stealing) ability is used (no pot effect).

One player adds $2 to the pot to increase his final hand declaration.  He now is claiming the highest hand.

One player calls his bluff, and is correct, the player did not have the declared hand (no pot effect).

There is only one player remaining, he takes down the pot.

As the example implies if the highest hand gets challenged and was bluffing, then the next highest hand gets a shot. But only active (un-folded) players can call a bluff, so if everything else gets challenged away the lowest hand wins automatically, without having to reveal. Clever.

Now, the side bets. There are two types — if you claim an ability, everyone can challenge. If you were bluffing you pay each challenger $5 and can’t use your power. If you had the cards, you reveal the suit(s) of your card(s), challengers pay you $5, and you take the actions. For the full hand, if you are challenged and bluffing, you pay each challenger $5 and don’t reveal your hand. If you were telling the truth, each challenger pays you $5 per player that started the hand.

So a double bluff can take down a huge amount if you can convince everyone to challenge you. (In the extreme case, for a six player game, where everyone thinks you are bluffing, that’s $150 + the pot).

Just to make it more dangerous. If you win before the showdown (or during it, when you could have been challenged) and were bluffing you can grab a special ability (“Panda Lord”) to use in the next hand(s). So is that massive hand call out of nowhere a bluff to get the pot and a the panda lord (maybe risking a few extra $5 bets), or a sucker player to try to get a bunch of big payouts?

Combine all of this and you can imagine that while Hold ’em has bluffs and setup plays, Pandánte is filthy with them. For example, I can claim a Red/Black hand for abilities, and then claim a flush (which requires me to have say, Red/Red). Or I can claim a red/red ability, get called on it pay out $5 per challenger then claim a flush requiring Red/Red. If people challenge me on it and I have it, now they’d have to pay me $10-30 each (depending on how many players started the hand), and I’d only have to pay $5 a challenger if I’m bluffing. So did I actually have Red/Red and paid that off to set up the obvious challenge?

That’s just one example, the rules make Pandánte an action game:

• Being forced to play at least to the river means that terrible hands can hit.
• If you don’t win, you can keep your hand (unless you successfully stole money with a special ability). Since some suits protect you, others build pots, do you keep? But your opponents may have gotten a read on you. Changing hands isn’t free (except for the winner, which it is free and mandatory)
• Snacks provide more information, and let you shape your hand. Sometimes you split a pair to go for a straight (or rainbow straight) or floosh. These decisions can be tricky.

And then there’s the joker.

Let’s face it, in poker the joker is a terrible idea. When I heard Pandánte had one, I was skeptical. But despite being an immensely powerful card, it has drawbacks. First and foremost, you can use the joker as any suit, which means you can use all the abilities. But if you reveal it, nobody has to pay a side bet for being wrong. And that applies during a showdown AND you only get half the pot. So if you flash the joker during the ability phase, everyone knows its a free challenge.

In what other poker game would you ever consider throwing away a joker mid-hand.

Even playing Heads up with the Taoling revealed interesting decisions every hand.

• Folding early with nothing?
• Do you split your hole card pair for a flush draw?
• How high should I push my declared value to force others to pay more for snacks? Should I (after abilities) raise my bet to go first?
• Sometimes you don’t want to have the highest (declared) hand, particularly if you didn’t make. And then you definitely don’t want to flash the joker, as everyone will challenge you and get paid out for your bluff.
• Do I keep my (losing) hand or chuck it for a fee?
• How do I string people into calling my (made) hand?
• If I have a tie (for a floosh, say) what exact value do I declare for my hand? (Remember, hands are challenged in order).
• When should I push a bluff hard to win a Panda Lord?

Remember, all bets (and side bets) are fixed, so you don’t bluff by throwing lots of money at it, you think (and act) correctly. This isn’t No Limit Hold’em “all in” bludgeon. Pandante is fought with rapiers.

Gaming on the Cruise

Just got back from a vacation cruise. Now let’s be clear — I hate cruises. So I spend a bunch of time in the casino, ‘gaming’ (The gambling industry’s attempt to sound respectable). Thankfully the cruise had a poker table, and surprisingly … it was automated.

So I figured I’d review it.

The table was a PokerPro, by PokerTek. Here’s how it works. There’s a main screen built into the center of the table. It shows each players stack (as a numeric value) the amount of chips in the pot (and rake), who still has cards, the dealer button, whose turn it is to act and (when the hand is done) displays the winning hand, moves the money around and redeals. Just to be clear, the players you are playing are sitting at the same table with you. (I assume the table could handle remote players, but the game is set up as “Face to Face, but computer moderated.”

Each player has their own touchscreen. This shows the table (and gives you the first names of everyone), acts as your menu (Check/Call, Bet/Raise, Fold) and your cards. Your cards are face down, unless you touch them, at which point they curl up. You’ll want to cup your hands around them so that others can’t peek (just like real cards).

From my standpoint, there is a lot to like. No arguments about string bets. No folding out of turn. The rules are enforced by code. Presumably no mistakes in reading the winner or splitting chips, making change, and the like (I never saw any obvious ones). The table I was on only did no-limit hold-em, but even then the time savings were pretty significant (the computer pauses at the end of the hand to let you see the cards, but it still only takes about 10 seconds between one hand ending and the next hand’s deal. You can review the prior hands results on your personal screen). In a game like Omaha Hi/Low, the time saved on split pots would be fairly significant.

Mechanically, the table seems rugged … I witnessed two drinks spilled on the main LCD (and quickly wiped up … no problems). The touchscreens are hard to operate with fingers, but the corner of your ID card works well. You have to double-tap a selection to bet/raise/fold, so accidental bets aren’t a major problem. But it can occur. A player who was trying to ‘clean’ his screen by rubbing it with the corner of the card went all in once, and I witnessed several new players run out of time trying to enter the right bet amount, via a calculator interface. There are ‘hot-key’ standard bets (minimum, 2x blind, 4x blind, pot, all-in). There are a few places the GUI could be cleaner, but once our group had figured out the basics, almost no problems.

The rake was a bit higher than I remember (10%, going by 50 cent intervals, capped at $6), but I normally play limit and it may be configurable. I’m used to $1 increments capped at $4 or $5. On the other hand, with no dealer to tip that saves you the extra dollar (assuming you normally tip). The casino director indicated that they didn’t buy the equipment … PokerTek provided it in exchange for part of the rake.

Showing all of the players first names is a good idea, too. I imagine that cruise poker is more social than casino poker (since you play most the same people over the course of a week), but it’s just nice to have the table act as introducer. Having an opponent named “Hung” is good for roughly 10 hours of jokes, FYI.

I was disappointed that there weren’t multiple tables and I never got to see how the PokerPro ran a tournament. (The casino had plenty of blackjack/slot/bingo ‘tournaments’ I’d imagine a $20 or $50 fixed tournament would be a big way to get non-gamblers to pony up… but with only one table it was probably easier to just leave it set as a money game). I imagine you’d see real time savings there, as it automatically monitors tables (and breaks up smaller tables), adjusts blind structure, colors up, moves people around, etc. I find the claims of 30% speedup in tournaments easy to believe.

Casinos must love it — faster throughput (so, more money raked), no dealers to pay (and keep a close eye on, to prevent theft), automatic accounting (and real time reporting). Most everyone seemed wary at the start, but quickly got over it. I suppose the programmers could have put in backdoors for when they play, but I suspect I’m less likely to get jobbed than with a random dealer (who may have a friend or two). I do wonder what happens during a power outage, and how often (and redundantly) each player’s balance is updated.

The cruise also didn’t have the kiosk where you swipe your card to get on the waiting list and the software handles the wait list. It was handled by the players themselves, which works fine for a small group, but would be another big benefit for a large casino.

About the only downside is that players need cards (with a PIN) and buyin away from the table. That’s usually only a five minute process, but it is easier to just walk up to a table and drop your money onto it. From the casino’s POV, that’s a feature, as they don’t have to collect (and monitor) money from each table. The money is tied to an account, not a card, so if you lose your card you just cancel it (presumably by showing proof of ID), assuming that whoever got your card hasn’t played it and lost all your money to their card … but even if they did, I suspect they could trace it.

Probably those of you who go to Vegas more often have already seen these … I’m told they’ve just started appearing on cruise ships in the last 6-12 months. These babies really are impressive, and I’d love to see them handling gaming in our sense of the word. Sadly there’s not much money to be made there, as compared to poker. But they do show what could be done …

Update: And, just so you know (since it came up earlier), my comment spam filter blocks the word “Poker.” So call it P*ker or “The Great Game” or “The Curse” or what have you. Calling it “MILFs” or some such may get the filter pissed off at you, though.

Adventures in Low Limit Hold’em

My business trip had unexpected Casinos. [Unexpected in the sense that I don’t really know where to expect them, beyond Vegas, Atlantic City, and a few other cities that I’ve found one]. So I played a bit of poker. I got on the waiting list, ate dinner, watched some baseball, then played for perhaps 2.5 hours. (I was in the Casino for under four hours total).

I suspect that 75% (or more) of the players were locals, with the prototypical passive-loose play. People who see almost every flop, look for excuses to stay in the hand, and then throw it away when the last card shows they’ve got nothing.

You know what? I’m not sure playing that counts as enjoyment anymore. I get to play ‘real money’ poker so rarely (and I prefer a structured game like Hold’Em, Stud, etc, over the free-wheeling dealers choice types). The issue is that (barring a few places), the casinos are only dealing out the lowest limits, and nobody feels the monetary pinch. I don’t feel a glow from winning. It’s grinding. I simply play <50% of the hands, and that gives me a huge edge. In fact, I had an atrocious run of cards and still made money. I saw a single pair in my time (3s), and only had three hands with two high cards (AJs and KQo twice). [Not that pairs are great hands against many players].

I could have made more money, but once I was safely ahead I started playing mediocre hands (still not the crap that the table played). I missed several pots where I folded Q2o and the board hit QQx. In 50+ hands, you get excellent flops a few times, but on most of those hands you should have folder earlier).

But anyway, that win was less interesting than my No Limit loss from January, simply because the play is less interesting. Most of the players are just gambling (and the casino encouraged this with a huge bad beat jackpot, as well as a “busted aces” payout, which I’d never seen before. (If you hold AA and lose, then you get $40. We literally had that happen four times in a hour, which was high, but given how people play, I’m surprised the Casino has that deal. Aces 221:1 against (I believe), so with a full table you’ll probably see them once every 22 deals, and they’ll probably lose over half the time (given how everyone sees the flop), so they’ll probably pay out every 44, and a poker table only earns $4/hand. I guess those little jackpoints keep people coming.

The real issue is that most of my opponents just aren’t interesting. Gaming snobbery. I should stick to tournaments, but I probably won’t, so I do this so rarely.

Another interesting idea — Alien Problems

I saw this poker article and thought “That’s a generally applicable idea.”

You would’ve called there, right, Matt? …

My response to this question is, yes; if I had somehow found myself in that situation, I would’ve called. But the only way I could’ve ended up in that situation is if I had fallen out of a spaceship and been flung into my seat

…

I call problems like [that] “alien problems.”

Games rarely so clean cut, but it’s still a good idea: Is your current situation the result of a poor decision earlier? Focus your strategy thoughts where they matter.

[Hat Tip: Fourth Checkraise]