## 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.

## Poverty and distributions

No, this post is not about the distribution of poverty. This is a rather technical post about probability distributions. Just that it has something to add to the poverty debate. And like the previous post, this is a departure from the normal RQ-type posts – there will be no graphs, no tables. Just theorizing.

So in the last week or two a lot of op-ed space in India has been consumed by what is described as the “poverty debate”. A recent survey by the National Sample Survey Organization (NSSO) has revealed that poverty levels in India have declined sharply in the last couple of years. And it only accelerates a sharp decline that started after a similar survey in 2004-05. Now, you have the “growthists” and the “distributionists”. The former claim that it is high economic growth in this time period that has led to the fall in poverty. The latter think it is due to redistributionist policies such as the National Rural Employment Guarantee Act (NREGA). Both sides have their merits. However, I’m not going to step into that debate now.

I ask a more fundamental question – how well can we trust the numbers that the NSSO has put out? My concern is this – that the poverty numbers have been gleaned out of a survey. I don’t have a problem with surveying – in fact surveying is a rather well-studied science, and I’m sure people at the NSSO are well-versed with it. My concern is that in this particular survey, the results may not have been properly extrapolated.

Most surveys rely on what is known as the “law of large numbers” and the “central limit theorem” and assume that the quantity being surveyed (people’s consumption expenditure as per this survey) follows a normal distribution. Except that we know that incomes (at least at the upper side of the scale) don’t follow a normal distribution. Instead, it has been shown that they follow what is called as a Power Law distribution.

While I don’t doubt the general quality of scholarship at the NSSO, I want to ask if they have actually studied the real distribution of incomes and used the appropriate one, rather than using a normal distribution. It could be that incomes at the lower end of the scale actually do follow a normal distribution, in which case standard sampling techniques might be used. If not, however, I expect and hope that the NSSO has used a sampling and extrapolation technique appropriate to the distribution incomes actually follow.

Let me illustrate the issue with an extreme example. Let’s say that one of the names drawn as part of the NSSO’s “random sample” for Mumbai is one Mr. Mukesh D Ambani. Assume that there are 99 other persons in Mumbai who are drawn in the same sample, and each of them has an annual household income of Rs. 1 lakh. What will be the mean income of the group? Assuming Mr. Ambani earns Rs. 10 Crore a year (number pulled out of thin air), the mean income of the group of 100 will come out to be close to Rs. 11 lakh!

This is the problem with estimating incomes using surveys and standard extrapolation techniques. While the above example might have been extreme, even in smaller groups of population, there will be “local Mukesh Ambanis” – people whose incomes are much higher than their peer group. Inclusion or exclusion of such people in a standard survey can make a massive difference.

I will end with an example and a request. I remember reading that any family in India that earns over Rs. 12 lakh a year (i.e. Rs. 1 lakh a month) is in the top 1% of all families in India! My family (wife and I) earn more than Rs. 12 lakh. But do we consider ourselves rich? By no means! Why? Because people who are richer than us are much richer than us! That is the problem with quantities that follow a power law distribution.

Now for the request. Can someone instruct me on the easiest way to get the raw data out of the NSSO? Thanks.