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Game Theory and The Battle of Sinhgad

Game theory and battle of Singhad

In March of 1670, in the middle of one night, Tanaji Malusare attacked Singhad on Shivaji’s orders. He , his brother Suryaji and his maternal uncle Shelar mama, and the soldiers climbed the cliffs to enter the fort and caught the fort army by surprise. In the battle that ensued, Tanaji was killed. The soldiers started running back to the ropes they used to climb. At this time, Shelar mama ordered to cut the ropes, cutting the only retreat option of soldiers. Soldiers turned back and Maratha army won the fort.

All kids in Maharashtra read this story in history books. The story is discussed more for heroics and pride then for the excellency in military tactics and leadership.

Today Let’s do a little analysis of this battle using basics of game theory.

Explaining basics of game theory is outside the scope of this post. For those of you who do not know what is game theory, please google search game theory or visit Wikipedia article on game theory. Go ahead and read it. Trust me, game theory is fun mathematics.

In short, this relatively new branch of mathematics explores the way individuals or group of individuals evaluate their choices, prioritize and make decisions. No matter the difference in our personalities, it is surprising to find that when faced with a problem and multiple choices, almost all of us resort to some common strategies.

Let’s talk about Sinhgad battle as a game. On battlefield, there is actually a slight conflict in the objective of individual soldier and the army he/she is in. For the viewpoint of individual soldier, his/her own contribution is very insignificant. If others run away, individual cannot make any difference. But if the individual runs away, the others can still win. So seemingly there is no problem if an indivudual runs away.

But if he/she loses life, then the loss to the individual is huge. Thus the risk in running away is less than the risk in fighting. So the default choice of individual soldier is to run away.

If every individual thinks like this, that is the end of the army.

Enter a leader in the picture, Tanaji in this case. Leader will oversee the army, will enforce discipline and will punish if somebody runs away. So this fear of enforcer added to the motivation of winning the battle stops the soldier from running away. So as long as there is enforcer, there is this added risk to running away. So total risk of running away now becomes more than risk of fighting. Thus soldiers fight.

When Tanaji fell, for an individual soldier, the risk of fighting suddenly became more than risk of running away. Thus most of the soldiers started running away.

Now Shelarmama comes in picture. At this point, he had several choices. He could have continued doing he was doing, fighting and hoping soldiers could come back and follow his example. Or he could have stopped fighting and started trying to stop the soldiers who were running away.

Shelarmama did not do any of the above. He did exactly what an excellent military commander would have done in this case. He went and cut off the ropes to retreat.

Now no need of talking. The only two choices faced by soldiers were to jump off the cliff and die or to turn and fight back. The risk of running away suddenly increased to infinity, while the risk of fighting the battle remained the same. So soldiers turned back and fought.

Purely from humanitarian viewpoint, the decision made by Shelarmama is actually against humanity. Because he increased average risk to human life. However as a army commander, at that time and place, this was very right thing to do.

The chart below shows the risks in fighting and risk in running away for individual soldier at different states. When Tanaji was dead, three hypothetical choices Shelarmama are analyzed. It is clear that the choice Shelarmama made is the best choice for winning the battle.

Choice Tables:

case 1:- Tanaji Alive

Soldier’s Choice Risk
Fight Medium
Run High

Most rational choice for a soldier: Fight

Case 2:- Tanaji Dead

Shelarmama choice 1: Leave fight and try to convince soldiers

Soldier’s Choice Risk
Fight High
Run Low

Most rational choice for a soldier: Run

Shelarmama choice 2: Focus on fighting and hope soldiers follow the lead

Soldier’s Choice Risk
Fight High
Run None

Most rational choice for a soldier: Run

Shelarmama choice 3: Leave fight and try to threaten soldiers with punishment

Soldier’s Choice Risk
Fight High
Run High

Most rational choice for a soldier: Uncertain

Shelarmame choice 4: Cut off the ropes

Soldier’s Choice Risk
Fight High
Run Extreme

Most rational choice for a soldier: Fight


There is no question about dedication and bravery of Tanaji. However the award for excellent military tactics goes to Shelarmama. This shows why bravery is not the most important quality of a commander. General MacArthur said once “The excellent military leader has two things. Clear sight of objectives and clear understanding of his forces. Bravery is what results after that.”

The similar technique was used by General Montgomery in WW-II when fighting against German General Romel in Africa. The day Montgomery arrived to take charge, he burned all the bridges and trenches built for retreat. The same technique was used by Alexander the great in his battle against Porus. Alexander made his forces cross the river to attack Porus army. Thus, their back pressed to river, Alexandar’s forces knew that retreat was not an option.

This technique almost always has an adverse secondary effect on the opponent army. When they see that their attackers reduced to a desperate state, they expect fierce fight. So their morale goes down.

Sadly after 100 years, Maratha army lacked any Shelarmama on the battleground of Panipat. When Vishwasrao fell, Maratha army dissolved, leaving giant wound on Marathas that would take decades to heal.

May it be battleground, or may it be personal life. One thing is clear. History cannot be made unless the ropes to retreat are cut off.


25 Responses

  1. Excellent article.With the help of story the article is able to generate enough interest in Game Theory

  2. This really an excellent post. This is entirely an different analysis of the war of Sinhagad that we have never studied in history books of Maratha History. From this post we can conclude if there was any one like the vision of shelarma than Malharrao Holkar maratha history and in turn indian history would have been diffrent.

  3. A very good post. Very thought provoking and instructive – not just for a battlefield but for all walks of life. There is just one slight correction – the ropes were cut not by Shelarmama but by Suryaji, the brother of Tanaji.

  4. great analysis
    this blog helps in blossoming and keeping alive the wisdom of great maratha warrior Shivaji
    jai bhavani
    jai shivaji

  5. very good article, pl help me with more infromation on tanaji.

  6. This is a very good article you also request send about sant TUKARAM AND MANY MORE THAT LIKE

  7. Excellent article. Would be wonderful to analyze other tactical battlefiled scenario, especially Afzal Khan slaying.

  8. Thanks Mahesh,

    It would be interesting to analyze Afzal Khan slaying. May be sometime soon.


  9. interesting 🙂

  10. Wow..nice analysis indeed.. and yes, why don’t you perform a similar analysis on the Afzal Khan incident too……I guess guerilla warfare is an excellent homeground for the application of game theory.would be an interesting idea to study some other instances of small armies winning against their larger in in number adversaries!

  11. […] maratha, mathematics, military, panipat, peshwa, politics, shivaji, sinhgad Tags: shivaji In one of my previous post, I have done analysis of the Battle of Sinhgad using game theory. Several readers mentioned they […]

  12. […] them from repeated attacks by Muslim rulers. More on Shivaji’s valor and prowess here and here. Growing up in Bombay(that is how it is for me!) as a kid, I’ve heard numerous stories of how […]

  13. The diagram explains the logic of games theory very effectively. It is a refreshingly new perspective to the Sinhgarh battle-legends apart.
    Jaymala Diddee

  14. This this was great stuff 🙂
    I wonder why isn’t this approach taken in our education system to make history and maths more interesting!?
    Btw, how much time did you spent analysing and preparing for this post?
    Do keep it up!

  15. Very nice post. Application of game theory to an historical event is quite an interesting stuff. Enjoyed reading it.

  16. Here’s the flaw or a loophole in your argument:

    I too have been hearing these stories for ages! And have always tried to run these stories in my mind to check how the hell could things have worked.

    Flaw no 1: Military commanders, except in an exceptionally motivated small force [usually a Task Force/SWAT kind of unit], need to increase the risk for running away more than that of fighting. Here’s your flaw – this risk cannot be imposed by staying at the front of the group. Military leaders are always at the back of the group. So that they can impose that threat.

    Now we’ve all heard about how Tanaji was the first to climb up using his ghorpad. Maybe he reached first up on the fort. But that doesn’t mean the fighting started when he touched his feet up there. The group usually regroups before acting where the leader is always put in a position of safety higher than that of foot soldiers.

    And to take a fort you need what maybe 100/200/300 mawlas [soldiers]? Motivating this high number can be done only when you are at the back of the group. History books indicate that this number was 402, of which 342 made it to the top because 60 died while climbing up the rope and the rope gave away.

    Flaw no 2: Assumption – Shelar mama cut the ropes because the troops would not run away. There is a good chance that if Tanaji was at the rear of the bunch, HE was the one who ORDERED the ropes to be cut so that the troops wouldn’t run away. Maybe he was not at the back end of those 340 odd soldiers, but he could have planted Shelar mama to do that work.

    My point of argument is cutting ropes [de-risking death via fighting] can be a Standard Operating Procedure. It sometimes is a well thought of move. It can be an SOP in cases like: 1) the battle is too critical and it has to be won; 2) the leadership thinks the battle can be won and the troops don’t and as much a big-gun Tanaji can be, troops will run away once they are not sure of winning.

    So my point of debate is that we in your post might be giving credit to Shelar mama against a good chance that it was Tanaji’s move – not ruling out that he might have discussed about it with Shivaji!

    Flaw no 3: Death of Tanaji – If Tanaji was at the back of the group, how did he die? Here’s my explanation. The no of Maratha casualties reported in this battle is very low – the no is at around 50 out of the 342 who made it up to the top. This means something.

    There is a good chance that the situation that we apply to the leader dying and the troops running away might be more true in case of Mughals rather than the Marathas.

    The number of Mughal troops that night on the fort is pegged anywhere between 1500 to 1800. I remember my aaji telling me that “baara shey” [1200] Mughal troops ran away from Sinhagad – which was considered as point of shame with the Maratha troops that time.

    The point is, Tanaji’s action plan would have been to have Udhaybhan dead as quickly as possible. Good chance that this work would have gone to a small unit which is fast moving and sharp in attacking, getting the job done and getting out. Now there are two reasons why Tanaji would have mostly been a part of this group. First, though weaker than the second, good chance that this task force would not know how Udhaybhan looked like, rather few knew how he looked like. This seems like a trivial point but I have noticed Purandare write this couple of times in his book on Shivaji [not with reference to Sinhagad, but generally about problems in assasination of an enemy]. Tanaji could be a few who would have known, though am not claiming it that he did.

    Second point, and much more related, is, to claim that “Udhaybhban has fallen and we the Marathas have won” – the deciding claim, Tanaji HAS to be around. I guess hence two warriors, Tanaji and Udhaybhan who were military leaders and were supposed to at the back of their respective groups landed up fighting each other.

    Flaw no 4: Distance between the fight of Tanaji and the ropes. Story goes that Tanaji lost his shield and then he defended with a cloth tied to his arm but got cut by Udhaybhan’s sword and finally died; but Shelar mama pounced back on Udhaybhan and killed him.

    Natural military leadership – The forces always know who’s the next in command. So if something happens to Tanaji, even if he fell while climbing the ropes and did not at all make it to the top, there would have been not only a back-up who would take over, but good chance he too had a back up. The more you are at military odds in terms of lesser strength of soldiers on your side, the more is the chance that you will have backup leaders taking over.

    So if Shelar mama killed Udhaybhan, the troops would rally behind him if he is the next in line. Hence no need to cut the ropes – hence even more a reason that the ropes were cut initially by Shelar mama on command of Tanaji.

  17. Hi,

    A nice post.Yes we can make all of our life with a Game theory model.The problem is that we cannot predict anything with Game theory.Zero sum game can be said only after the game is over.John Nash himself haven’t predicted of a Noble prize for him with Game theory (A Beautiful Mind).Can anyone say the Saddle point in the above post.If it is known to the opponent he might have won.that’s the Game.THE LIFE.

    Keep posting such articles

  18. Good analysis! I’m working on project about Shivaji & maratha warriors can you help me out in analysing more events in Shivaji and others, like Escape from agra, his approach towards building a team at younger age say 14-17 yrs etc. This game theory really make things easy to understand. Keep up the good work. You can contact me on shivrajpa@rediffmail.com.

  19. Really very nice article with a excellent analysis and also links to the game theory. however I would like to mention one more great military strategist word of wisdom which predates all mentioned generals and strategist here.

    Master Sun (or Sun Tzu/Sun Wu) wrote in his famous The Art of War, “put your soldiers on death ground and there is nothing that they can’t achieve!”. This is exactly what was done by Shelarmama and also by many other generals in history e.g. when Eisenhower planned invasion of Normandy, he made sure that there is no possibility of retreat for soldiers from beaches in north western France and we all know result, even though Germans were well prepared, allied forces pushed their defenses and in couple of month were in Paris !

  20. Amazing article.

  21. ‘History cannot be made until ropes to retreat are cut off’

    What an awesome quote. Absolutely fantastic article.

  22. Excellent Article!! Hats Off!! to you..
    History cannot be made until ropes to retreat are cut off’

    GOLDEN quote. Absolutely fantastic article! you need to write more about our Maharashtra history!

  23. Interesting article. it makes person interested to know about Game theory. However, it is not based on the facts how the battles are fought. When soldier is on battle field and motivated and indoctrinated enough, running away is not really an option. Only in surgical strikes it is kept as an option with retreat / escape plans are well thought of and routes covered. In commando operations, it is expendable force operation, where soldiers know that they either succeed and return with medals or rapped in flag. They are trained that way. Sinhgad battle is more of a expendable.force. Hence cutting off return track is a part of strategy. Also psychology of soldiers is not necessarily amenable to Risk Vs safety payoffs like game theory. Otherwise do you think pilots will go deep in enemy territory and strike or Bajiprabhu Deshpande would have fought till death or freedom fighters like Madanlal Dhingra shot British officer is theater or few misguided youth from safety of their home will go to Iraq to join terrorists when death is certain? Some are motivated for good cause others are brain washed for bad cause. However, those who are not motivated enough, run away when faced threat, then weaker elements start chain reaction.
    Nevertheless, interesting argument.
    I know both Game theory as a faculty and author of OR book and soldier with 25 years experience with post graduate in Military strategy.

    Group Captain D. P. Apte (Retd)

  24. Very well written article, and applicable till this date, when Modiji demonetizes the currency notes in India.

  25. hi kedar siddhesh here..i am a writer and actor by proffession,.would like to get in touch with you regarding the article you have posted above on game theory, shelar mama, tanaji malusare battle of sinhgad…need to talk with you in person, this is my email id pls leave a mail along with your contact number i will get in touch with you..siddheshelar@gmail.com

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