based on a text by John Loewenthal, creater of Borel, the bridge hand generator and simulation tool for DOS.
In this context a simulation is a set of bridge hands that has been generetad to simulate a real or a constructed situation at the table.
Suppose that the bidding goes 1NT - 3NT and that you have tho choose a lead from either Queen or Jack to four of a major suit. You elect to lead from your Queen and this results in an overtrick, while a lead from the Jack would have killed the contract. Your experience tells you that this was just unlucky. Is this true or should you lead from the Jack the next time?
Now is the time to try a simulation. Enter your hand and ask Bridge D/A to generate some deals that fit the given occasion, the 1NT - 3NT bidding. Then you go through the deals and if either major suit lead is better in a significant number of cases, you have an answer. If not, may be the winning decision is just a random one.
You will always find, though, that even if all the generated deals fit the occasion, not two of them are alike. Sometimes the responders got a balanced hand with 12 hcp and sometimes AQ10xxx of clubs without anything on the side. The different types occur according to normal probabilities, which means that if the lead from Queen to four is best a significant number of times, you may well assume that your choice is the correct one if the hands vary according to probabilites. Good bridge is based on such grounds.
Your bridge judgement is the result of your utilized experiences. But bridge is a much too unpredictable game for you to prove more than a few theories. A good player does what his experience has taught him works. The problem is that life is too short for us to aquire enough experience of all types of situations. You wont even experience many quite normal situations, like the one above, more than a few times in your bridge life, and you will very seldom find them in the litterature.
Simulations can give you practical experience from hundreds of deals at the same time, which will help you to develop your bridge judgement. By going through all the steps of a careful simulation, you may get more experience than those who has to wait for the situation to occur at the table.
A keyword here is utilized experience. Its not enough just to examine the result of a simulation if you want to develop your bridge, since the specific cases you have produced hardly ever will occur again. You have to apply the result of your simulation on other, similar situations. To be able to do this, you must find out why a simulation gives a specific result.
Suppose that a lead from Jack to four proves to be the winner(!) in the lead problem after 1NT - 3NT above. (It produces at least one trick more than other leads, and happens to give you a better chance to beat the contract.) Why?
Suppose that a careful study of the results show that none of the leads are very rewarding (as attacking leads), but that the lead from the Queen more often cost a trick when partner is weak in the suit. Therefore the lead from the Jack is the better passive lead. The conclusion is that the stronger partner is, the better the lead from the Queen will work. May be this will be confirmed by a second simulation, where you limit the responder to less than opening strength. So, may be your learned wisdom is correct after all: a passive lead is best if you dont have a good attacking alternative and the defence has limited assets. The simulation confirms this and show furthermore that if responder is an unpassed hand, your partner more likely has a weak hand.
A simulation is done in three steps:
Step (1) and (2) means a lot of work. Is it worth the trouble? This depends on how keen you are to learn to play winning bridge. Step (3) sounds tough, but will be much simpler the less alternatives you work on.
Bridge D/A offers a graphical interface, which will simplify the input of parameters for the simulation i.e. the description of the closed hands. The difficulty is to decide the parameters.
When Bridge D/A has produced the deals, you have to analyze them. This will normally be even harder than to define the parameters. The process involves lots of speculations and uncertainty, but the better bridge player you are the easier this part will be. This also means that the more simulations you make, the better bridge player you will be, and the easier the simulations will become. Anyway, the Bridge D/A has done its work and cant help you anymore.
You must examine every deal and decide:
Suppose that you in our lead problem examines the effect of leading the Jack. On one specific deal the dummy appears with KQ98 and declarer holds Ace and one. Since he doesn't see all the cards he cant imagine that you have led the Jack from Jack to four, so sooner or later he may well take the finesse to your partners ten. If this gives you more tricks than you otherwise would, you should register a plus for the Jack opposed to a small one in the same suit!
One way to evaluate many deals is to use Simu-points: Use a scale from 0 to 10. Give one alternative, for example a low one from the Queen, 5 points on every deal regardless of how it works. Then you give the Jack suit lead more than 5 points if it works better than the Queen suit lead, less if it is less successful and 5 points if it gives the same result. You estimates the points on the probability for the lead to be a winner or loser, taking into account the difficulties in doing such analysis. If, for example, the lead from the Queen gives declarer eleven easy tricks after having driven out your Ace of diamonds, while a lead from the Jack would have given the defence five tricks (or may be three in a pair s contest), you give the successful lead 10 points opposed to 5 for leading from the Queen. If declarer has a guess for eleven tricks after the lead from the Jack, you give it 7 or 8 points.
This methods works for multiple alternatives as well. You may give the lead from the Queen 5 points and then another for the Queen, a small from the Jack, the Jack itself etc. After having analyzed all your deals, you add up your Simu-points for each alternative and calculate the result from these figures.
If the situation you analyzes primarily is a psychological one (like judging what an opponents would bid with spedific hands in competition), may be you should consult som who can help you. Let them analyze the deals independently before you set the Simu-points. If you instead does this by yourself, you must be aware of the risk that you may try to support one of your own pet theories, or chose what you wuld have done at the table. I you try hard to show that you are wrong though, youll probably find the standard choice.
How do you calculate the reliability of the simulation results?
Suppose that you generate 100 deals for our lead problem, and find that the lead frrom the Jack is a winner by 540 to 460. How confident can you be that the lead in question really is the better one? Is the result just a random coincidence?
There is a statistical test, called Chi-square which tells you the probability for a certain Simu-point over a certain number of deals if the alternatives are equal. If the Chi-square test shows just 5% probability for two equal alternatives to give a specific result, you may draw the conclusion that the two alternatives are not equal.
Even if the Chi-square test isnt the most advanced mathematical exercise that mankind know of, it still involves some heavy mathematical stuff, and furthermore you must have access to a set of tables to be able to make a final estimation of the result.
If you just consider two alternative bridge actions (like a small from the Jack or a small from the Queen against three notrumps), here is a neat simplification:
If you consider more than two alternatives, this simplified method will not work, so you have to go through a complete Chi-square test.
The purpose of the simulation is to prove either that one alternative is significantly superior to the other, or that the alternatives are rather equal.
For a typical simulation with two alternative actions you should start with about 20 deals, say three pages in the Bridge D/A. If one of the alternatives departs from average on more deals than the square root of the total number of deals, you simulate as many deals again and calculate on the total number. If the result still isnt significant, you run another simulation and if you after about 60 deals still doesnt have a significant difference, you may conclude that there is none.
When you analyze the results you shoud note why an alternative works on one deal an why it doesnt on another. I you cant understand why a simulation gives a certain result, you have not learned anything useful.
When you think that you understand why the outcome is one or another, you should verify your theory with one more simulation. But this time you should change the parameters a little so that the result should be different if your theory is correct. If the new result doesnt depart form the old one in the way you thought it would, your theory isnt correct.
In the lead problem the lead from the Jack for example shows to be the best. When you examine why, the more passive lead (the one from the Jack) seems to be better the weaker your partner is. And when your partner is stronger the lead from the Queen (the more attacking) seems to work better.
You can and should confirm this theory with a second simulation, where the responder is limited, for example as a passed hand. If the Jack suit lead still is significantly better, your theory about the reason is wrong! (Maybe the body makes the lead better, or maybe your partners strength isnt a key factor, or maybe something in your minors is critical.) The fact is that if you cant vary the simulation to get an expected improvement for the Queen suit lead, you must conclude that a lead from Jack to four is generally better than from Queen to four, which really isnt a revolutionary discovery!
Another test could be to simulate the lead from the same hand after 1NT - 4NT. If your theory about your partners strength is correct, the Jack suit lead should win with a greater margin than against three notrumps.
When you have found a theory that works, you have improved your bridge judgement and will in the future make the correct decisions at the table in situations that you just studied.