Games of luck and skill

My good friend Anuroop has two hobbies – poker and wildlife photography. And when we invited him to NED Talks some 5 years ago, he decided to combine these two topics into the talk, by speaking about “why wildlife photography is like poker” (or the other way round, I’ve forgotten).

I neither do wildlife photography nor play poker so I hadn’t been able to appreciate his talk in full when he delivered it. However, our trip to Jungle Lodges River Tern Resort (at Bhadra Wildlife Sanctuary) earlier this year demonstrated to me why poker and wildlife photography are similar – they are both “games of luck AND skill”.

One debate that keeps coming up in Indian legal circles is whether a particular card game (poker, rummy, etc.) is a “game of luck” or a “game of skill”. While this might sound esoteric, it is a rather important matter – games of skill don’t need any permission from any authority, while games of luck are banned to different extents by different states (they are seen as being similar to “gambling”, and the moralistic Indian states don’t want to permit that).

Many times in the recent past, courts in India have declared poker and rummy to be “games of skill“, which means “authorities” cannot disrupt any such games. Still, for different reasons, they remain effectively illegal in certain states.

In any case, what makes games like poker interesting is that they combine skill and luck. This is also what makes games like this addictive. That there is skill involved means that you get constantly better over time, and the more you play, the greater the likelihood that you will win (ok it doesn’t increase at the same rate for everyone, and there is occasional regression as well).

If it were a pure game of skill, then things would get boring, since in a game of skill the better player wins every single time. So unless you get a “sparring partner” of approximately your own level, nobody will want to play with you (this is one difficulty with games like chess).

With luck involved, however, the odds change. It is possible to beat someone much better (on average) than you, or lose to someone much worse (on average). In other words, if you are designing an Elo rating system for a game like poker, you need to change players’ ratings by very little after each game (compared to a game of pure skill such as chess).

Because there is luck involved, there is “greater information content” in the result of each game (remember from information theory that a perfectly fair coin has the most information content (1 bit) among all coins). And this makes the game more fun to play. And the better player is seen as better only when lots of games are played. And so people want to play more.

It is the same with wildlife photography. It is a game of skill because as you do more and more of it, you know where to look for the tigers and leopards (and ospreys and wild dogs). You know where and how long you should wait to maximise your chances of a “sighting”. The more you do it, the better you become at photography as well.

And it is a game of luck because despite your best laid plans, there is a huge amount of luck involved. Just on the day you set up, the tiger might decide to take another path to the river. The osprey might decide on a siesta that is a little bit longer than usual.

At the entrance of JLR River Tern Lodge, there is a board that shows what animals were “sighted” during each safari in the preceding one week. Each day, the resort organises two safaris, one each in the morning and afternoon, and some of them are by boat and some by jeep.

I remember trying to study the boards and try and divine patterns to decide when we should go by boat and when by jeep (on the second day of our stay there, we were the “longest staying guests” and thus given the choice of safari). One the first evening, in our jeep safari, we saw a herd of elephants. And a herd of gaur. And lots of birds. And a dead deer.

That we had “missed out” on tigers and leopards meant that we wanted to do it again. If what we saw depended solely on the skill of the naturalist and the driver who accompanied us, we would not have been excited to go into the forest again.

However, the element of luck meant that we wanted to just keep going, and going.

Games of pure luck or pure skill can get boring after a while. However, when both luck and skill get involved, they can really really get addictive. Now I fully appreciate Anuroop’s NED Talk.

 

Lessons from poker party

In the past I’ve drawn lessons from contract bridge on this blog – notably, I’d described a strategy called “queen of hearts” in order to maximise chances of winning in a game that is terribly uncertain. Now it’s been years since I played bridge, or any card game for that matter. So when I got invited for a poker party over the weekend, I jumped at the invitation.

This was only the second time ever that I’d played poker in a room – I’ve mostly played online where there are no monetary stakes and you see people go all in on every hand with weak cards. And it was a large table, with at least 10 players being involved in each hand.

A couple of pertinent observations (reasonable return for the £10 I lost that night).

Firstly a windfall can make you complacent. I’m usually a conservative player, bidding aggressively only when I know that I have good chances of winning. I haven’t played enough to have mugged up all the probabilities – that probably offers an edge to my opponents. But I have a reasonable idea of what constitutes a good hand and bid accordingly.

My big drawdown happened in the hand immediately after I’d won big. After an hour or so of bleeding money, I’d suddenly more than broken even. That meant that in my next hand, I bid a bit more aggressively than I would have for what I had. For a while I managed to stay rational (after the flop I knew I had a 1/6 chance of winning big, and having mugged up the Kelly Criterion on my way to the party, bid accordingly).

And when the turn wasn’t to my liking I should’ve just gotten out – the (approx) percentages didn’t make sense any more. But I simply kept at it, falling for the sunk cost fallacy (what I’d put in thus far in the hand). I lost some 30 chips in that one hand, of which at least 21 came at the turn and the river. Without the high of having won the previous hand, I would’ve played more rationally and lost only 9. After all the lectures I’ve given on logic, correlation-causation and the sunk cost fallacy, I’m sad I lost so badly because of the last one.

The second big insight is that poverty leads to suboptimal decisions. Now, this is a well-studied topic in economics but I got to experience it first hand during the session. This was later on in the night, as I was bleeding money (and was down to about 20 chips).

I got pocket aces (a pair of aces in hand) – something I should’ve bid aggressively with. But with the first 3 open cards falling far away from the face cards and being uncorrelated, I wasn’t sure of the total strength of my hand (mugging up probabilities would’ve helped for sure!). So when I had to put in 10 chips to stay in the hand, I baulked, and folded.

Given the play on the table thus far, it was definitely a risk worth taking, and with more in the bank, I would have. But poverty and the Kelly Criterion meant that the number of chips that I was able to invest in the arguably strong hand was limited, and that limited my opportunity to profit from the game.

It is no surprise that the rest of the night petered out for me as my funds dwindled and my ability to play diminished. Maybe I should’ve bought in more when I was down to 20 chips – but then given my ability relative to the rest of the table, that would’ve been good money after bad.