games – Pertinent Observations

Warming the house

Midway through my housewarming function on Sunday, I had a “Lawrence of Arabia” moment. In the movie, Lawrence, a reluctant soldier has to execute a guy named Gasim in the Arab army he is leading. Lawrence shoots Gasim, and then finds that he actually enjoys killing people. This is probably one of the pivotal moments in the story.

My day had begun badly, as the priests who were supposed to turn up by 5, did not make their appearance until a full hour later. What was interesting was that the photographer, who had been asked to turn up at 630 came in a full hour earlier. With the priests not coming in till it was close to 6, I was going bonkers, and declaring war on the priest community, and regretting that I had agreed for a religious ceremony at all.

They arrived soon, however, and off I went to change into a silk panche (not a great idea for summer). And I heard clapping and shouting outside. Three eunuchs had invaded the house and were refusing to leave until they had been paid Rs. 1100. I must mention this was the first time I had been so harassed. And these people were refusing to negotiate or bow to threats. Finally the demanded sum was paid and off they went. This transaction has been recorded in my housewarming ceremony income and expenses statement.

My official family priest, who was unable to make it thanks to an earlier booking, had mentioned that the complexities of handling a housewarming meant that we had to employ four priests. Any doubts of any value that multiple priests added were dispelled in the first few minutes of the ceremony beginning. One priest with a good voice chanting mantras can occasionally be pleasing to hear. But four priests singing in tandem, not all of them at the perfect pitch – which created a nice effect – and not all of them singing simultaneously, was phenomenal. Their chants reverberated off the walls of the empty house (not too many people want to turn up for a ceremony at 7 am on a Sunday, so we had spared most guests the moral agony and had invited them only for lunch), and when it was accompanied by the ringing of bells, as it was occasionally, it was absolutely mindblowing.

It was around this time that I had the Lawrence of Arabia moment. After all my protestations against religious ceremonies and suchlike, I discovered that I was actually enjoying the process. The sound was fantastic. With significant hand-holding from the priest what I had to do was also enjoyable – throw flowers into one area at irregular intervals. I could construct my own little games (not unlike Pee-ball) and it was a lot of fun.

After a short break for coffee and a longer one for breakfast (technically you are supposed to fast during such events but such rules have become flexible nowadays), it was time for the “homa” or throwing things into the ritual fire as an offering to the fire god Agni and his wife Swaha. I didn’t start the fire. It was initially lit using burning camphor by two aunts. It was fueled mostly by the priests (another time when multiple priests came in handy – two chanted the mantras while the other two kindled the fire).

My role here was to occasionally pour in ghee using the small wooden ladle, and then later put in “modaks” (fried momos filled with coconut and sugar) into the fire. Again I invented my own little games. How do you throw the modak such that it immediately catches fire? How do you ensure the modak doesn’t bounce outside of the fire pot? Can you create patterns with the burning modaks?

Midway through this ritual I started imagining doing a barbecue on this ritual fire (this thought was fueled by a particular modak, which on partial burning, started looking like a piece of grilled chicken). A couple of days earlier I had imagined what would happen if illegal weeds were to be procured and added to the ritual fire. The wife and I had then thought that the original intended purpose of such rituals was communal bakery.

We had planned to finish the ceremonies by 9:30, so that we could prepare to receive guests who would arrive around 11. The problem is that if you are the only person(s) who know certain guests, they can get lost and bored if you are stuck in rituals. Hence we had planned the rituals such that we could be ready to receive guests by the time they arrived. We had built in an hour an a half of slack (9:30 to 11), and it came of good use as the rituals ceased at 10:30 (the hour’s delay being a function of the delay in priests’ arrival).

Guests came, saw, ate and went. Around 5 in the evening the wife started cleaning the house. By 8, there were no traces of a ceremony having happened there. And we went out.

Tradition demands you spend a night in the new house even if you don’t intend to move in immediately. We went to bed at 12, after having opened the presents. Initially sleep was good. Then we got woken up at 430 by a pack of dogs that were prowling the streets and fighting. Then we tried to get back to sleep, but were again woken up by the nearby mosque’s azaan. I hope this isn’t a sign of things to come once we move.

Duckworth Lewis and Sprinting a Marathon

How would you like it if you were running a marathon and someone were to set you targets for every 100 meters? “Run the first 100m in 25 seconds. The second in 24 seconds” and so on? It is very likely that you would hate the idea. You would argue that the idea of the marathon would be to finish the 42-odd km within the target time you have set for yourself and you don’t care about any internal targets. You are also likely to argue that different runners have different running patterns and imposing targets for small distances is unfair to just about everyone.

Yet, this is exactly what cricketers are asked to do in games that likely to be affected by rain. The Duckworth Lewis method, which has been in use to adjust targets in rain affected matches since 1999 assumes an average “scoring curve”. The formula assumes a certain “curve” according to which a team scores runs during its innings. It’s basically an extension of the old thumb-rule that a team is likely to score as many runs in the last 20 overs as it does in the first 30 – but D/L also takes into accounts wickets lost (this is the major innovation of D/L. Earlier rain-rules such as run-rate or highest-scoring-overs didn’t take into consideration wickets lost).

The basic innovation of D/L is that it is based on “resources”. With 50 overs to go and 10 wickets in hand, a team has 100% of its resource. As a team utilizes overs and loses wickets, the resources are correspondingly depleted. D/L extrapolates based on the resources left at the end of the innings. Suppose, for example, that a team scores 100 in 20 overs for the loss of 1 wicket, and the match has to be curtailed right then. What would the team have scored at the end of 50 overs? According to the 2002 version of the D/L table (the first that came up when I googled), after 20 overs and the loss of 1 wicket, a team still has 71.8% of resources left. Essentially the team has scored 100 runs using 28.2% (100 – 71.8) % of its resources. So at the end of the innings the team would be expected to score 100 * 100 / 28.2 = 354.

How have D/L arrived at these values for resource depletion? By simple regression, based on historical games. To simplify, they look at all historical games where the team had lost 1 wicket at the end of 20 overs, and look at the ratio of the final score to the 20 over score in those games, and use that to arrive at the “resource score”.

To understand why this is inherently unfair, let us take into consideration the champions of the first two World Cups that I watched. In 1992, Pakistan followed the principle of laying a solid foundation and then exploding in the latter part of the innings. A score of 100 in 30 overs was considered acceptable, as long as the team hadn’t lost too many wickets. And with hard hitters such as Inzamam-ul-haq and Imran Khan in the lower order they would have more than doubled that score by the end of the innings. In fact, most teams followed a similar strategy in that World Cup (New Zealand was a notable exception, using Mark Greatbatch as a pinch-hitter. India also tried that approach in two games – sending Kapil Dev to open).

Four years later in the subcontinent the story was entirely different. Again, while there were teams that followed the approach of a slow build up and late acceleration, but the winners Sri Lanka turned around that formula on its head. Test opener Roshan Mahanama batted at seven, with the equally dour Hashan Tillekeratne preceding him. At the top were the explosive pair of Sanath Jayasuriya and Romesh Kaluwitharana. The idea was to exploit the field restrictions of the first 15 overs, and then bat on at a steady pace. It wasn’t unlikely in that setup that more runs would be scored in the first 25 overs than the last 25.

Duckworth-Lewis treats both strategies alike. The D/L regression contains matches from both the 1992 and 1996 world cups. They have matches where pinch hitters have dominated, and matches with a slow build up and a late slog. And the “average scoring curve” that they have arrived at probably doesn’t represent either – since it is an average based on all games played. 100/2 after 30 overs would have been an excellent score for Pakistan in 1992, but for Sri Lanka in 1996 the same score would have represented a spectacular failure. D/L, however, treats them equally.

So now you have the situation that if you know that a match is likely to be affected by rain, you (the team) have to abandon your natural game and instead play according to the curve. D/L expects you to score 5 runs in the first over? Okay, send in batsmen who are capable of doing that. You find it tough to score off Sunil Narine, and want to simply play him out? Can’t do, for you need to score at least 4 in each of his overs to keep up with the D/L target.

The much-touted strength of the D/L is that it allows you to account for multiple rain interruptions and mid-innings breaks. At a more philosophical level, though, this is also its downfall. Because now you have a formula that micromanages and tells you what you should be ideally doing on every ball (as Kieron Pollard and the West Indies found out recently, simply going by over-by-over targets will not do), you are now bound to play by the formula rather than how you want to play the game.

There are a few other shortcomings with D/L, which is a result of it being a product of regression. It doesn’t take into account who has bowled, or who has batted. Suppose you are the fielding captain and you know given the conditions and forecasts that there is likely to be a long rain delay after 25 overs of batting – after which the match is likely to be curtailed. You have three excellent seam bowlers who can take good advantage of the overcast conditions. Their backup is not so strong. So you now play for the rain break and choose to bowl out your best bowlers before that! Similarly, D/L doesn’t take into account the impact of power play overs. So if you are the batting captain, you want to take the batting powerplay ASAP, before the rain comes down!

The D/L is a good system no doubt, else it would have not survived for 14 years. However, it creates a game that is unfair to both teams, and forces them to play according to a formula. We can think of alternatives that overcome some of the shortcomings (for example, I’ve developed a Monte Carlo simulation based system which can take into account power plays and bowling out strongest bowlers). Nevertheless, as long as we have a system that can extrapolate after every ball, we will always have an unfair game, where teams have to play according to a curve. D/L encourages short-termism, at the cost of planning for the full quota of overs. This cannot be good for the game. It is like setting 100m targets for a marathon runner.

PS: The same arguments I’ve made here against the D/L apply to its competitor the VJD Method (pioneered by V Jayadevan of Thrissur) also.

On Schooling

Usually I’m quick to defend the school where I studied between 1986 and 1998. I made lots of good friends there and generally had a good time. Of late, however, in discussions on schooling, I find myself mention teachers from that school who I considered particularly horrible, mostly for their method of teaching.

Yesterday I was chatting with a classmate from this school who now works in the education sector, and she happened to mention that she considered her schooling to be mostly “a waste” and that she didn’t learn too much there. And I quickly concurred with her, saying all that I had learnt was at home, and school didn’t teach me much. So what explains my love for the school even though they might not have done a great teaching job?

From 1998 to 2000, I went to another school, where again they didn’t teach much, and instead assumed all of us went to JEE factories which would teach us anyway. What made things bad there, though, was that they didn’t treat us well. That school had a strict disciplinary code which was enforced more in letter than in spirit. Teachers there had a habit of loading us with homework, calling us for Saturday classes and having surprise tests. The problem with School 2 was that not only did they not teach well, but they also made life miserable in several other ways. The only redeeming factor for that school was the truckload of interesting people I got to meet during my two years there.

So what explains my love for School 1 despite the fact that they didn’t do a great job of teaching? The fact that they treated us well, and left us alone. The uniform wasn’t very strictly enforced, as long as you wore blue and grey. The school had an explicit “no homework” policy. Exams happened only according to schedule and there were few assignments. Even in class 10, we had three “periods” a week dedicated to “games” where we played volleyball or basketball rather than wasting our time in “PT”. Teachers were mostly very friendly and the atmosphere on the whole was collaborative and not so competitive.

My friend might think she “wasted” her 10 years in the school because she didn’t learn much there, but I argue that it was better than her going to another school where she wouldn’t be treated as well and where her life wouldn’t have been as peaceful.

Ranji Trophy and the Ultimatum Game

The Ultimatum Game is a commonly used research tool in behavioural economics. It is a “game” played between two players (say A and B) where A is given a sum of money which he has to split among himself and B. If B “accepts” the split, both of them get the money as per A’s proposal. If, however, B rejects it, both A and B get nothing.

This setup has been useful for behavioural economists to prove that people are not always necessarily rational. If everyone were to be rational, B would accept the split as long as he was given any amount greater than zero. However, real-life experiments have shown that B players frequently reject the deal when they think the split is “unfair”.

A version of this is being played out in this year’s Ranji Trophy thanks to some strange rules regarding points split in drawn games. A win fetches five points while a loss fetches none. In case of a drawn game, if the first innings of both sides has been completed, the team that has scored higher in the first innings gets three points, while the other team gets one. The rules, however, get interesting if not even one innings for each side has been completed. If the match has been rain affected and overs have been lost, both sides get two points each. Otherwise, both sides get zero points each!

I don’t know about the rationale of this strange points system, but I guess it is there to act as a deterrent against teams preparing featherbeds, batting for most of the four days and not even trying to win the match. In general, I haven’t been a fan at all of the Ranji Trophy’s points scoring system, and think it’s quite irrational and so refuse to comment on this rule. What I will comment about, however, is about the “ultimatum” opportunity this throws up.

In the first round of matches, Saurashtra batted first against Orissa and piled up a mammoth 545 in a little under two days. The magnitude of the score and the time left in the match meant that Orissa had been shut out of the game, and the best they could’ve done was to overtake Saurashtra on first innings score and get themselves three points. However, they batted slowly and steadily, with Natraj Behera scoring a patient double century, and with a few minutes to go in the game, they were still over 50 runs adrift of Saurashtra’s score, with three wickets in hand.

At that time, they had the chance to declare their innings, still some runs adrift of Saurashtra’s score, and collect one point, and handing over three points to Saurashtra. They, however, chose to bat on and block the game, and both teams finally ended up with zero points. It maybe because they also see Saurashtra as a competitor for “relegation”, but I thought this was irrational. Why would they deny themselves one point – if only to deny Saurashtra three points? It’s all puzzling.

Going forward, though, I hope the Ranji Trophy rules are changed to make each game a zero sum game (literally). Or else they could adopt the soccer scoring of 3 points for a win and 1 for a draw (something I’ve long advocated), first innings lead be damned!

Charades of obscurity

Having “played” dumb-charades (DC for short) competitively at a school and college level, I don’t particularly enjoy playing it casually. I’m prone to getting annoyed when people around me (either on a picnic, or a party) exclaim with great enthusiasm that we should play DC. Till recently I used to think it was like chess – where my enthusiasm for the game has been killed purely because I played it competitively, but now I realize there are more reasons.

The challenge with “competitive” DC is that it is a timed game. You are judged based on how fast you can act out a certain name/place/animal/thing/. Because of this the clues need not be too hard, and there is a fair degree of challenge in acting out even simple things. Apart from this, the clues are set by a neutral third party which means they can all be trusted to be of approximately similar standard, so there is some sort of a level playing field there. Then, you have teams that have practiced well together, and have clues for all the trivial stuff, and you have a game!

With casual DC, there are several problems. Firstly, the games are not timed. Secondly, the teams haven’t practiced together at all, so it takes ages to communicate even straightforward stuff (which is why the games aren’t timed). And then the clues are usually given to you by your competitor. And for some reason, casual DC always has to be movies. No books, no places, no animals, no personalities, nothing.

The f act that the games are not timed, combined with the fact that the clues are given by the competitor, means that the game usually gets into a downward spiral of obscurity. You don’t want your competitor to guess the movie easily, so you give a vague movie. And they reply with something vaguer. And so forth, until teams have to check IMDB to find out if the movies actually exist. By which time all the enthusiasm for the game is lost.

On a recent trip (with colleagues, as part of our CSR initiative. more on that in another post) we played casual DC, and after some 10 clues it had gotten so obscure that nothing was guessable. I’d lost interest when someone suggested we do Kannada movies! Now, that’s something few people would’ve played – DC with Kannada movies as clues, because of which we could give clues while not keeping them too obscure (but it was hard. I completely bulbed trying to act out “Kalasipalya”).

Still, my hatred for casual DC remains, and I try as much as possible to not play it. Maybe next time I’ll impose conditions (like timing, choice of subjects, etc.), and refuse to play if they want to do English movies with infinite time.

Relationships and the Iterated Prisoner’s Dilemma

It was around this time last year that something snapped, and things have never been the same again. Until then, whenever she threw some tantrums, or we had some fight, I’d always give her the benefit of doubt, and unconditionally apologise, and make an effort to bring the relationship back on track. But since then, I don’t feel the same kind of sympathy for her. I don’t feel “paapa” for her like I used to , and have questioned myself several times as to why I even aoplogise, and not expect her to do that.

The optimal strategy for Iterated Prisoner’s Dilemma has been shown to be a strategy called “Tit for tat”. To explain the problem, you play a series of games against an “opponent”, and in each iteration, each of you choose to either “cooperate” or “defect”. For each combination of choices, there is a certain payoff. The payoff looks similar to this, though the exact numbers might be different. In this table, the first value refers to the first player’s payoff and the second represents the second player’s.

Player 1/ Player 2	Co-operate	Defect
Co-operate	1 / 1	2 / 0
Defect	0 / 2	0.5/ 0.5

So you play this game several times, and your earnings are totalled. There was a tournament for computer programs playing this game sometime in the 1960s, where the winner was “tit for tat”. According to this strategy, you start by co-operating in the first iteration, and in every successive iteration you copy what your opponent did in the previous iteration. Notice that if both players choose this strategy, both will co-operate in perpetuity, and have identical payoffs.

Relationships can be modelled as an iterated prisoner’s dilemma. You can either choose to be nice to your partner (co-operate) for which you get a steady return, or you can choose to be nasty (defect), in which case you get a superior payoff if your partner continues to be nice. If both of you are nasty simultaneously both of you end up getting inferior payoffs (as shown by the Defect-Defect box in the above matrix).

Early on in the relationship, I was very keen to make things work and did my best to prevent it from falling into any abyss. I played the “Gandhi strategy”, where irrespective of her play, I simply co-operated. The idea there was that whenever she defected, she would feel sympathy for my co-operative position and switch back to co-operate.

So something snapped sometime around this time last year, which led me to change my strategy. I wasn’t going to be Gandhi anymore. I wasn’t going to unconditionally defect, either. I switched to playing tit-for-tat. You can see from the above table that when both players are playing tit-for-tat, you can get into a long (and extremely suboptimal) sequence of defect-defects. And that is what happened to us. We started getting into long sequences of suboptimality, when we would fight way more than what is required to sustain a relationship. Thankfully it never got so bad as to ruin the relationship.

Periodically, both of us would try to break the rut, and try to give the relationship a stimulus. We would play the co-operate card, and given both of us were playing tit-for-tat we’d be back to normal (Co-operate – Co-operate). Soon we learnt that long defect-defect sequences are bad for both of us, so we would quickly break the strategy and co-operate and get things back on track. We weren’t playing pure tit-for-tat any more. There was a small randomness in our behaviour when we’d suddenly go crazy and defect. In the course of the year, we got formally engaged, and then we got married, and we’ve continued to play this randomized tit-for-tat strategy. And the payoffs have been a roller coaster.

Today I lost it. She randomly pulled out the defect card twice in the course of the day, and that made me go mad. While in earlier circumstances I’d wait a few iterations before I started to defect myself, something snapped today. I pulled out the defect card too. Maybe for the first time ever, I hung up on her. Do I regret it? Perhaps I do. I don’t want to get into a prolonged defect-defect sequence now.

And I hope one of us manages to give the relationship enough of a stimulus in the coming days to put us on a sustained co-operate co-operate path.

IPL Fixing

If Chennai beat Punjab today, then both RCB and DC will go through to the semis. Right now all three teams (Punjab, Bangalore, Hyd) are on 14 points and Punjab has a significantly lower NRR than the other two. So irrespective of who wins tomorrow’s game, it is likely that both are going to go through.

If Punjab lose tonight, then Kumble and Gilly can sit down and “cut the IPL melon” and decide among themselves who wants to face Chennai and who wants to face Delhi. And fix tomorrow’s match accordingly. As long as either RCB wins or if DC doesn’t win by a big margin, both go through. Splendid stuff.

Which is why, in football, in all leagues all last round games are played simultaneously. This happened after in the 1982 world cup, Germany and Austria figured out that as long as Germany would win 1-0, both would go through to the quarters ahead of Algeria. So Germany scored quickly, and then both they and Austria just passed the ball around for the rest of the game and chucked out Austria Algeria.

however, the iPL is more about money and about TRPs than about real competition so we are unlikely to see the last four games being played simultaneously.

Update

Ok so through some expert analysis I’ve come to the following conclusion after yesterday’s games.

1. Deccan Chargers are through irrespective of today’s result

2. Royal Challengers Bangalore can also be through even if they lose. All they need to make sure is that if Deccan bats first, then the margin of victory is not more than 75 runs. If Bangalore bats first, they need to make sure that Deccan takes at least 10 overs to reach the target.

Note that these numbers are approximate and will vary with the exact score that is made. But these two numbers can be taken as a ballpark.

Bottomline is that unless RCB mess up royally, Punjab are on their way home.