Tag: opponent

Archery tournament design

Over the last couple of days, I switched on the TV in order to “jinx” two of India’s more promising archers in their respective games at the Olympics. On Monday evening, I switched on the TV to see R Banerjee (forget his first name) lose a close game in the round of 32. Yesterday, I watched Tarundeep Rai shoot well but still get well beaten by an absolutely in-form guy named Kim (from Korea, where else?). As I watched these matches, I was thinking about the nature of competition in archery.

Archery is a fundamentally single-player event. You are competing against yourself, and how well you do is not supposed to be affected by how well someone else does. There is no direct opponent you are playing against who tries to prevent you from scoring. In some ways, you can consider it to be similar to running. The only element of competition is the pressure that is exerted upon you be opponents competing simultaneously. In this context, it is indeed surprising that the archery event has been designed as a one-on-one knockout, like you would expect for a direct-opposition sport like tennis.

An event directly comparable to archery in terms of fundamentals is shooting – there again, there is no impact of one player on another’s performance but for the pressure exerted by means of simultaneous competition. Shooting, however, goes the “races” (running/swimming) way by means of having heats where only one’s absolute performance matters in terms of score matters (there is no limit on the number of the number of finalists from one heat; the best 8 or 10 participants across heats make it).

Then why is it that archery, which is fundamentally similar to these sports in terms of fundamental concepts, relies on head-to-head competition, and that too with no repechage? Yesterday, I watched Tarundeep Rai come up against an absolutely inspired Kim – Kim was in such imperious form that irrespective of how well Rai would have done he wouldn’t have qualified. Rai didn’t play badly, “against” any other opponent or on another day, he would have definitely done better. In a “direct combat” sport (such as tennis), one can point to the luck of the draw and similar matters. But in a distinctly non-combative sport such as archery why should artificial tournament standards be designed and that extra bit of luck be introduced?

I hope the archery administrators realize the stupidity of the curent format and move to one that is similar to what we see in shooting today.

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.

Chowka Baarah

Yesterday after a gap of about fifteen years, I played chowka-baarah. For starters, the name intrigues me. It translates into four-twelve (I suppose), but that doesn’t make sense. Essentially, there are two primary variations of this game depending upon the size of the grid used (5 by 5 or 7 by 7), and these two numbers are “big numbers” in different systems. In the 5×5 version, the “big scores” are 4 and 8, while in the “7×7” system, it’s 6 and 12.

A certain variety of seashells (called kavaDe in Kannada) are used as dice, four of them in the 5×5 version and 6 in the larger version. The “score” of the dice is determined by the number of kavaDes falling “face up”, and if all fall face down, the score is twice the number of dice. So if you have 4 shells and all fall face down, you get 8 points. I haven’t done much research on this but I do think the probability of a die falling “face up” is much more than the probability of it falling “face down”. I don’t know the exact probability.

The game itself is like Ludo; your pawns going round and round in circles and inward in order to reach the centre of the square when it “queens”. The first player to queen all their pawns wins. There are concepts such as doubling pawns (they act as a pair hten, move in pairs only on even throws of the die, etc.), cutting (if your pawn reaches a square where an opponent’s pawn is, the opponent’s pawn “goes home”, etc. Simple game, and widely played in a lot of “traditional households”.

Considering that I had stopped playing this game when I was still quite small, i had never realized the strategies involved in playing the game. Back then I’d just generally move whatever pawn i fancied nad somehow my grandparents would move in a way in order to simply enable me to win. It was only yesterday that I realized that the game is not as simple as I thought, and that strategy dominates luck when determining how you do.

It’s not like bridge, where card distributions are exchanged across pairs in order to take the luck out of the game. Nevertheless, I realize that the number of “turns” in the game is large enough for the probabilities in the seashells to balance out across players. Rather, the decision that you need to make at each turn regarding which pawn to move is so important that the importance of this drawfs the number you threw! Again you will need to keep into account stuff like the distribution of your next throw, your opponent’s next throw and so on.

I think I have a thing for games with randomness built into them rahter than those that are completely a function of the players’ moves (like chess). I think this is because even with the same set of players, games with randomness built in lead to a larger variety of positions which makes the game more exciting.

Coming back to Chowka Baarah, the other thing I was thinking of last night was if sunk cost fallacy applied in this, when I was trying to decide betwen a reasonably advanced pawn and a backward pawn to decide as to which one to save. Finally I decided that apart from the loss in terms of the pawn being sent home, other things that I had to take into consideration when I moved was about which pawn capture would be more valuable for the opponent, probabilities of differnet pawns getting captured, potential danger to other pawns, etc.

It’s a fun game, one of the most fun “traditional” games. Maybe one of the most “strategic” traditional games. Miss playing it for the last fifteen years or so.