Category Archives: Programming

C# Reflexion & Attributes to C++

I develop a software for urban planing oriented ecology. Initially Polaris is a CAD software (similar to AutoCAD or MicroStation) with tools about geomatics engineering and earthwork engineering. So this software may be also used to compute the thermal performance of the building. My work concerns especially generic programming to improve software and a project of rainwater sanitation simulation with pollution aspect. In a word, Polaris use C# code, even through I consider myself as a C++ developer.

I think C# language proposes an interesting syntactic sugar around the code with Attributes. So, what is an attribute and how create this with C++.

C# Attribute

An attribute adds information to properties, methods or classes. These information can be used by the reflexion mechanism. The following example concerns an object with tree accessible properties and the aim is just to display the values with associated text.

class MyCounter
  [InformationAttribute("value of the counter")]
  public int Value {get; private set;}

  [InformationAttribute("minimal value of the counter")]
  public int Min {get; private set;}

  [InformationAttribute("maximal value of the counter")]
  public int Max {get; private set;}

  public void Incr()
    if(Value>Max) Max = value;

  public void Decr()
    if(Value<Min) Min = value;

  public MyCounter(int initialValue)
     Value = Min =Max = initialValue;
C# MyCounter

The code which displays the three values is:

public void Display(object obj)
  PropertyInfo[] props = obj.getType().GetProperties();
  foreach (PropertyInfo prop in props)
    object[] attrs = prop.GetCustomAttributes(true);
    foreach (object attr in attrs)
      InformationAttribute ia = attr as InformationAttribute;
      if (ia != null)
        string value = prop.GetValue(obj).ToString();
        string text = authAttr.Text;
        System.Console.WriteLine( text + ": " + value );
C# display method

An the output of the method (with a MyCounter) may be:

value of the counter: 20
minimal value of the counter: -5
maximal value of the counter: 23

The advantage of this code is to use the same method to display information of many different type. The description of the class is sufficient and the developer doesn't need to develop specific method for each object. An use of the reflexion mechanism may be to create graphical user interface: personally, I think forms design is a waste of time and I prefer work on computational mechanisms.

C++ version

When I have begun my project Imbricable, I have considered this way and I have copied an idea which I have found during my thesis in the Sofa-Framework. So, I have created tree classes which correspond to accessors, attribute and a container of accessors. The equivalent of the MyCounter class using a mechanism as the one developed in my project may be:

class MyCounter::BaseObject
    static Metadata meta_value;
    static Metadata meta_min;
    static Metadata meta_max;

    static Data<int> data_value;
    static Data<int> data_max;
    static Data<int> data_min;

     void incr();
     void decr();
C++ header of MyCounter class
#include "mycounter.h"

Metadata MyCounter::meta_value("value of the counter");
Metadata MyCounter::meta_min("minimal value of the counter");
Metadata MyCounter::meta_max("maximal value of the counter");

MyCounter::MyCounter(int intialValue), BaseObject(),
  data_value(new Data<int>(this, initialValue, &data_value) ),
  data_min(new Data<int>(this, initialValue, &data_min) )
  data_min(new Data<int>(this, initialValue, &data_max) )

  int value = data_value.get();

  int value = data_value.get();
C++ source of the MyCounter class

Metadata (attribute) are defined as static because this is the behavior of C# attributes and the attributes are not runtime modifiable. A no-static object should cause an avoidable memory consumption due to duplication of the text.

Data is a template/generic class which inherit from a undefined accessors class (BaseData).

And the equivalent of the display method:

void display(BaseObject obj)
  for(int i=0; i<obj.dataListSize(); i++)
    BaseData* data = obj.getData(i);
    Metadata* meta = data.metadata();
    std::cout << meta->text() << ": " << data->toString() << std::endl; 
C++ display method

So the mechanism requires the next classes to work:

class Metadata
  string _text;
  Metadata(string txt){_text = txt;}
  string text(){return _text;}
class BaseData
  Metadata *_metadata;
  BaseData(Metadata *meta){_metadata = meta;}
  Metadata * metadata{return _metadata;}
  virtual string toString()=0;

template<class C>
class Data:: public BaseData
   C _value;
   Data(BaseObject parent, C value, Metadata *meta):BaseData(meta){_value = value; parent.addToDataList(this)};
   C get(){return _value;}
   void set(C value){_value=value;}

Note: The method toString() should be override depending the used template (here Data<int>::toString() must describe the int/string conversion).


The C# syntactic sugar which concerns attribute is not difficult to recreate. Nevertheless, it is dependent of the reflexion and each properties may be registered to the object. In my project, I have added smart pointer (and the fact to share value), link to other object and attribute for methods. The main use of this mechanism concerns the user interface creation and the XML serialization.


The typeid function (C++) doesn't work


I'm modifying the structure of my project 'imbricable'. The aim is to distinct data and widget. In fact, Each class is composed of many properties. The object can be displayed on a user interface and properties may be changed. To do this, there is a class which is the support of each property. And the object which has a list with properties.

So when the graphical interface displays the content of the object, it goes through the list of properties and display them. To do this the class of property has a method named 'createWidget()' which returns a widget templated by type. For example: 'Data' return a 'TemplatedDataWidget'.

I have always thought it was a mistake, but I haven't smart solution because I have added two other properties mechanisms:
- LinkData: an interface to link an object to another.
- ProcessingData: an interface to define major methods. This one corresponds to a button in the graphical interface which start the method.

Using a templated widget have also a disadvantage: I need to overload methods of the 'TemplatedDataWidget' when I want use a new type, that means a labyrinthine system and a lot of copy-paste code with minor modifications.

These other properties types were overloaded the createWidget() method to create an other widget. The widgets of these types are similar independently than the type.

Initially, I have thought that using a factory hasn't a solution because I didn't know whether key I could have used. Indeed, the factory of the object uses strings as keys (understandable name), because the factory is used when users want to load from XML file or create manually objects but the factory of widgets should be just a GUI mechanism. GUI aspects are less important than register mechanism and using string means to define the name of type for each property. Second point, there is lot of templated Data, LinkData, ProcessingData.

Finally, I have found two choices: using dynamic_cast method to verify if the type corresponds or use std::type_info. And I have decided to use both of them:
- std::type_info in a map for specific properties: it can't be used for inheritance and compares two integers with 'hash_code()' method is faster in a map.
- dynamic_cast: it may concerns inheritance, so adding in the factory a widget for each type is unnecessary and it is possible to group similar cases. This second method to register needs to test each element of the factory.

So I have begun to modify the structure of my program. And when I have tried the new mechanism: this doesn't work. The object is found as BaseData (parent of Data, LinkData and ProcessingData) instead of the real object.


To understand the problem I have created a little project to test typeid() function.

class A
    std::string name;
    A() {name = typeid(*this).name();}

class B : public A
    B() : A() {}

int main(int argc, char *argv[])
    A a;
    B b;

    A* pa = &a;
    A* pb = &b;

    std::cout << typeid(A).name() << " " << typeid(B).name() << std::endl;
    std::cout << typeid(a).name() << " " << typeid(b).name() << std::endl;
    std::cout << typeid(*pa).name() << " " << typeid(*pb).name() << std::endl;
    std::cout << << " " << << std::endl;

    return 0;

This code return four lines, each one contains the type an object A and object B. Nevertheless, the third and fourth lines are not those expected.

1A 1B
1A 1B
1A 1A
1A 1A

The object pb is a pointer to A but it is set to a pointer to a B object. The expected result of typeid should be B instead of A.


If we can't use typeid in this case, we may think this function is useless: what is the interest of a method which use the current declared type instead of the real one?

In fact, this work only if  the parent class has polymorphic methods defined by 'virtual'.

class A
    std::string name;

    A(){name = typeid(*this).name();}

    virtual void dummy(){};
    //or virtual void dummy()=0;

It is no necessary to override the method in the class B. Now the result is correct.

1A 1B
1A 1B
1A 1B
1A 1A


This strange requirement isn't the problem of my project because the BaseData is already an abstract class. So what is the element I missing? just a problem of pointer: "PN10imbricable4core8BaseDataE". grrr

AI for Tic-Tac-Toe (Part 4)

Hello, this article is certainly the last about Tic-Tac-Toe and Artificial Intelligence. The first article (link) concerns the presentation of this little project and two bots using random behaviors: "Full Random" and "Partial Random". If there are two aligned cells, 'Partial Random' automatically places the third symbol to win. The second article (link) concerns two other bots: "The Trapper" and "The Brute". "The Trapper" places symbols to let two positions to win, So wherever the opponent plays, "The Trapper" wins. "The Brute" is an invincible bot, he knows each choice and its result, so he avoids bad ways. The third article (link) concerns the first learning bot and an interface for humans. The bot, named "The Bandit" defines choices depending of the probability to win or lose.

So, this article concerns a Neural Network bot. What is a Neural Network? I suggest you to see the skull of your favorite neighbor and you should discover an object composed with strange matter. In fact, this object is a brain and a brain is a Neural Network. The aim of mad scientists is to create robots which may replace humans: IBM has already simulated the brain of a monkey (results published during the International Conference for High Performance Computing, Networking, Storage and Analysis at Salt Lake City; SC12).

Neural Network is an complex subject and I have used this article to understand and implement the bot.

Neural Network

A Neural Network is composed of lot of Neurons and links between Neurons. A Neuron receives data from  Neurons and define a state (0 or 1) which will send to another Neurons.

A Neuron connected to others Neurons.
A Neuron connected to others Neurons.

The value of the state depends on the state of input neuron and a weight associated with each link. The computation is decomposed into two steps:  a weighted sum and a thresholding.

 sum = \sum_{i}^{\text{neurons_in}} weight_i \cdot input_i

 output = \begin{cases} 1, & \text{if } sum>\theta \\ 0, & \text{if } sum \le \theta \end{cases}

It's possible to use a activation function (for example: a sigmoid function) instead of the thresholding, but I prefer the second because the program is easier to  debug.

Simple example

I consider the Tic-Tac-Toe as a complex example. The simple examples described in this part will be a boolean function: XOR. The XOR have two inputs and one output and the behavior is defined in the next table.

 \begin{array}{c|c|c} \rm In 1 & \rm In 2 & \rm out \\ \hline 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{array}

In this example, I use five neurons, but the more complex choice, in neural network,  is the method to consider inputs and outputs. In the case of the boolean input I prefer using -1 and 1 instead of 0 and 1. In fact, if all of the inputs are set to 0, the computed sum of each neuron will be null for the first iteration. I think the system will converge speeder with this choice. For output, if the sum is positive, so the result is 1, else 0.

Example of neural network
Example of neural network. At Left, the inputs. At right the output. At the middle, the neurons.

So if the inputs are 1 and -1 (as the figure), the neurons calculate the weighted sum and result is compared with the threshold \theta = 0 (bias).

 \begin{matrix} (1 * 0.68) + (-1 * -0.21) = 0.89 &, \text{ as } & 0.89+\theta_1>0 & \text{ then } Out_1=1 \\ (1 * 0.57) + (-1 * 0.59) = -0.02 & , \text{ as } & -0.02+\theta_2 \le 0 & \text{ then } Out_2=0 \\ (1 * 0.82) + (-1 * -0.60) = 1.42 &, \text{ as } & 1.42+\theta_3>0 & \text{ then } Out_3=1 \\ (1 * -0.32) + (-1 * 0.53) = 0.85 &, \text{ as } & 0.85+\theta_4 \le 0 &\text{ then } Out_4=0 \end{matrix}

Next, the same mechanism is applied to the global output.

 (1*-0.44) + (0*0.10) + (1*-0.045) + (0*0.25) = -0.485

As the sum is negative, the brain believes that 1 \oplus 0 = 0. In fact, the result is wrong because the brain has never learnt the rules.

When a biological brain is punished, a chemical effect changes the weights of connections. With the numerical neural network, the learning system is a backward error propagation. Arbitrarily, we consider there are an error of -1 (the value needs to be negative; it is equal to the desired value minus current value).

Next, weights of connections are modified depending on the chosen error and the output value of the neuron. Rate is a constant parameter which reduces the effect of modification (here 0.05).

 weight {+}{=} (-1) * rate * output * error

Output may have two value 0 and 1, so, values are modified only if the state of the neuron is 1.

Backward error propagation in connections
Backward error propagation in connections

The next step is similar to the normal use of Neural Network: for each neuron, an error is computed as a weighted sum.

 sum_{\text{error}} = \sum_{i}^{\text{neurons_out}} error_i * weight_i

Next, the propagation depends of the value of the neuron:

 error_{\text{neuron}} = sum_{\text{error}} * output_{\text{neuron}}

Initially, the bias \theta, is set to 0. But, we need to modify it:

 \theta_{\text{neuron}} {+}{=} (-1) * rate * error_{\text{neuron}}

Finally, the error is sent to connections to modify their weight. The next figure shows the neural network after learning. The system had made mistake only nine times to converge to this solution.

Neural Network after learning phase
Neural Network after learning phase

8th competitor: 'The Brain'

The game Tic-Tac-Toe is a more complex case than the Xor function. So, a difficult will be the choice of inputs or outputs. The inputs corresponds at each cell of the game: If the cell is empty, then value is 0, if the symbol is a cross 1 and  if the symbol is a nought -1. The output corresponds at each cell too and the selected cell is the cell with the maximal value.

"The Brain" need to learn two things:

  • It must chose an empty cell.
  • It must avoid the opponent aligns 3 symbols

Now, we limit the learning to the first point, so the bot need to select an empty cell.

The first 1000 games, the bot made 4624 selection error. Finally, the system converges to 4614. The efficiency of the bot is low. The question "Why?" is complex to answer: maybe a problem with the number of neurons or their initialization, bad choice of parameters (rate/error) or output/input mechanism, bad programmer...

I have tested many solutions. For example, I have cheated and modified input value. With other parameters (-1 if empty cell and else 1), I have hoped to solve the problem of selection. Currently, I abandon this bot, because I have no idea to solve the problem.


The creation of this bot is a relative failure. In the article (link), the author tests the program with Tic-Tac-Toe and seem to have interesting results. But, the learning concerns particular cases set to the neural network and it doesn't learn by trial and error.

If we chose a constant error during the execution, values diverge and tend toward infinity. If we want to limit values, we need to use this formula:

 Error = Output-Desired

But we need to define a relative error to each cell. This means the learning needs to be assisted. I would like a bot which selects a cell, next, the program said that the bot has made a mistake. With assisted learning, the program informs to the bot where the bot can play (all positions). In fact, assisted learning works and the bot selects finally empty cells without error.

Nevertheless the  experiment of Neural Network doesn't provide the expected result: the bot isn't autonomous.

AI for Tic-Tac-Toe (Part 3)

The last time, I have added many chalengers to play to Tic-Tac-Toe (link). Theses bots are able to detect and create traps. The last bot use a tree of differents cases. So it knows the bad choices and avoid them. All of the presented chalengers are non intelligent bots. Before I descript Neural Network, there are a last-minute chalenger. Also, its the first intelligent bot because it can learn from its mistakes.

6th competitor: 'The Bandit'

The bandit is based on the Multi-armed bandit problem.

A bandit is a slot machine. The player inserts coins in a machine, push a button and if he is lucky, he can win lot of money. But when the player go to casino, he have the choice with many machines. What is the machine with the better probability to win?

The best way is the observation of the behavior of the machine and the attribution of a score at each machine. If the player wins with a machine, so the score will be increassed. If the player losses, the score will be decreassed. Before each game, the player chooses the bandit with the best score.

In the case of the Tic-Tac-Toe chalenger, 'The Bandit' doesn't know the criters to win. So it tests and learns. If the bandit losses, that means each choice of the game is bad and will be avoided. For each choice, 'The Brute' uses a tag to know the best path and 'The Bandit' prefers to attribute a score.

The algorithm of 'The Brute' is more complex than the algorithm of the 'The Bandit' because programmer need to define win conditions and found a stategy to provides these informations. 'The Bandit' needs only a tree of choices with score and selects the more valuable path.

The score of the choices is increased or decreased depending of the result of a game. There are différent stategy to determine the gain and the loss: is winning more important than lossing?

Battle #15: 'The Bandit' vs 'Full Random'

The next chart corresponds to the results of battles after the learning period. The X-Axis is the ratio between the value of gains and losses. At left of the chart, the bot receive no gain and only losses to modify the score. So the bot want avoid to lose and prefers a tie-end. At right of the chart, the bot receive only gains and the bot want win and reduces the tie cases.

Strangely, the 'Full Random' is the most dangerous opponent of the bandit and a 'fifty-fifty' strategy is sufficient again the others veterans. This is due to the randomize aspect of the opponent: if 'Full Random' have the posibility to win, it may choose an another cell and lets the victory to 'The Bandit'. Nevertheless if the bot learns with another opponent, it has less difficulty to fight 'Full Random'.

Battle #16: 'The Bandit' vs 'Full Random' (2nd round)

Here 'Partial Random' is the master of 'The Bandit'. It has teached basis of Tic-Tac-Toe. 'The Bandit' have no difficulty to learn and it losses less than 400 times again 'Partial Random'. The only problem of the learning concerns the case where there are no loss: If 'The Bandit' forget than it can loss, so it has more probability to lose.

Now, 'The Bandit' is more efficient again 'Full Random'. I have also tested others masters. 'The Trapper' isn't a good teacher, the results are similar than the battle #15. Maybe it is too specialized in traps cases. The teaching of 'The Brute' reaches the same level than those of the 'Partial Random'. I think the 'Bandit' just needs to learn the rules of the game.

Battle #17: 'The Bandit V2' vs 'Full Random' (3nd round)

I have designed a second version of 'The Bandit' because I have found many problems in the algorithm.

First, a fixed value (gains or losses) is added to the weight and this may become very high. So I have placed limits in the precedent version. I want to test another solution with weight incrementation which consists to use an variable gains/losses. So the new weights tend toward limits without crossing the limits. I think this modification have few impact but it allow to keep an order in the weight. In the case of a fixed gains/losses and the use of limits, two ways may have the same value but have drive to lose with different probability. So now, the gains/losses corresponds to a percentage between current weight and a limit.

Secondly, it is possible to modify the weight if the result is tie. But if the weight become negative du to ties, it may become lower than a lost match and the way may be modified and create an instability with the result. Now, the weight of tie way tend to 0 instead of the negative limit.

Thirdly, The learning is long and the game contains lot of similar cases with transformation (symmetry or rotation). Now, each time a weight is modified, the weight of similar gameboard is modified to improve learning speed. This choice is due to the next competitor which is very special: it is not possible to prepare battles with thousand of games.

This chart corresponds to the case with the variable gains/losses and the accelerated learning. The boot seems more stable and efficient. When gains are superior to losses, the learning needs more games before stabilization. In the other cases, the learning is fast.

7th competitor: ‘The Homo Sapiens’

I have just said than this competitor is particular: it is an biological computer with lots of sensors and actuator. So if I want use it to play Tic-Tac-Toe, We need to create an adapted interface. A possible interface may be pen and paper, but this is adapted to a match Homo Sapiens vs. Home Sapiens and we want to compare this competitor to other bots. So, the interface is composed of a keyboard, a mouse and a screen. The screen displays a 3x3 grid. Each cell of the grid may have three different contents: empty, 'X' or 'O'. The Homo Sapiens needs to use the mouse to select a cell.

Interface between Homo Sapiens and TicTacToe application.
Interface between Homo Sapiens and TicTacToe application.

The user needs to select two competitors (here "Homo Sapiens" and "Full Random") and to click on the button "play". Now, competitors are beginning the battle.

Example of battle
Example of match

The application and some bots have parameters. The user needs to click on the buttons with "cog-wheel" icon.

TicTacToe Interface with parameters widget
TicTacToe Interface with parameters widget

"The Homo Sapiens" allows to understand the behavior of "The Bandit": In fact, it always plays in the same way. So, it is very no fun to play again "The bandit". Even if "The Brute" cannot lose, its randomize behavior is more interesting.


"The Bandit" uses a learning approach to play in TicTacToe. Rules of the game are not defined to the bot and if rules changes, "The Bandit" may adapt its choices.

Historically, The Homo Sapiens is the first player which had played Tic-Tac-Toe. Nevertheless, it needs more time to select a cell and its behavior may be strange: it may solve complex cases and make stupid mistakes, chooses to lose or refuse to play. So, comparisons of efficiencies are difficult.

AI for Tic-Tac-Toe (Part 2)

The last time, I have talked about non-intelligent bot to play to Tic-Tac-Toe (link). The first bot is named 'Full Random' and chose a cell randomly. The second bot is named 'Partial Random', It work in the same way, except if there are two cells aligned with the same symbol. In this case, it fill the last cell to win or to avoid losing. Nevertheless, there are many possible traps.

The 'Partial Random' can align 3 cells and avoid that the opponent align cells (except the cases where there are traps)
The 'Partial Random' can align 3 cells and avoid that the opponent align cells (except the cases where there are traps)

3rd competitor: 'The Trapper'

Now, I present 'The Trapper'. It is an evolved version of 'Partial Random': it creates 'traps' if this is possible. It tests each move and selects one which allows to have two choices. If the opponent select one then the bot win with the second.

Create a trap
Create a trap

This competitor is not unbeatable. Many time it loses the initiative and the opponent can create traps.

Battle #5: 'The Trapper' vs 'Full Random'
Battle #6: 'Full Random' vs 'The Trapper'
Battle #7: 'The Trapper' vs 'Partial Random'
Battle #8: 'Partial Random' vs 'The Trapper'

4th competitor: 'Guided Trapper'

Last time, I have talked about a unbeatable bot. but I am maybe a liar. In fact, I haven't tested all combinations and I can't found my old code. So, I use my memory. I remember a tip: if the bot is the second player so its first move is to chose the central cell.

This choice allow to create a bot which prefers to tie than to lose.

Battle #9: 'Partial Random' vs 'The Guided Trapper (Version 1)'

You can compare battles #8 and #9. The difference concerns the position of the first move of 'The Guided Trapper'.

An weakness of previous bot is the losing of initiative: many times the bots have no choice, the first play to a position to avoid aligning, the second too and this fact create an trap. The previous bots, can’t predict a solution.

5th competitor: 'The Brute'

The next competitor, have tested all solutions by brute-force. So it knows the bad choices and avoid it.

Initially, it creates a tree with all possible solutions (255168 cases).

  • the first player can win in 131184 cases (51%).
  • the second player can win in 77904 cases (30%).
  • there are 46080 tie cases (19%).

The mechanism is simple: there are two tags for each choice: "lose" or "win".  If the current choice is winning, that means the previous player have selected a bad cell and the previous choice is tagged "lose". Now, if all future choices are losing then the current choice is winning.

If there are a winning case, that means the previous is bad. And if there are only losing cases, so the previous case is a winning choice.
If there are a winning case, that means the previous is bad. And if there are only losing cases, so the previous case is a winning choice.
Battle #10: 'The Brute' vs 'Full Random'
Battle #11: 'Full Random' vs 'The Brute'

This new bot can't lose. It's the best and displaying others battles seem useless.

Battle #12: 'The Brute' vs 'Partial Random'
Battle #13: 'The Brute' vs 'The Trapper'
Battle #14: 'The Brute' vs 'The Brute'


This second article shows three other competitors. One which is able to create primitive traps, the second which is guided in a particular case and the third which is unbeatable.

The Brute can be improved. Currently, it chooses a random cell among winning case and non losing case. The choices can be weighted to use weaknesses of the
opponent according to a method as the Multi-armed bandit

AI for Tic-Tac-Toe (Part 1)


Neural Network is a subject which interests me. Nevertheless, I was never idea about an application of the artificial intelligence. Recently, I remembered an old application I have created: a simple Tic-Tac-Toe. This game is easy, an "expert" can avoid traps and never lose. I have implemented a false intelligence in this game which was unbeatable. When you play, you have not thousand of combinations. First point, you can rotate the board and use symmetry to reduce the number of possible combinations. Second point, when the opponent have filled two cells in a line, you will fill the last one to avoid the opponent to win.

So, my question: is a neural network able to tend toward an unbeatable intelligence? Fortunately, a lot of people use Tic-Tac-Toe to explain Neural Network. I have found an interesting website (Neural network with learning by backward error propagation).

In the first step, I won't present Neural Network, but methods to create a bot to play to Tic-Tac-Toe. Even if I think this is an easy game, the aim is the understanding of the game. These bot could be used as reference to compare the performance of the Neural Network.

1st competitor: 'Full Random'

Before to talk about this AI, I present other competitors. The first of them is 'Full Random' and it plays randomly. If this player plays again itself the result is uncertain.

Battle #1: 'Full Random' vs 'Full Random'

The next chart shows the percentage of victories of this simple player. The first player has an important advantage.

2nd competitor: 'Partial Random'

The next competitor named 'Partial Random' use a random choice except if it can align three cells or if the opponent align two cells. This competitor is better than the first, but many traps exists.

The 'Partial Random' can align 3 cells and avoid that the opponent align cells (except the cases where there are traps)
The 'Partial Random' can align 3 cells and avoid that the opponent align cells (except the cases where there are traps)
Battle #2: 'Partial Random' vs 'Full Random'

This is the result if 'Partial Random' is the first to play.

Battle #3: 'Full Random' vs 'Partial Random'

This is the result if 'Partial Random' is the second player.

Battle #4: 'Partial Random' vs 'Partial Random'


This first article shows two competitors. One which play randomly and the second which prefers to align cells.

The battle #1 presents the real proportion of the different cases: 10% of Ties, 60% for 1st player and 30% for 2nd player.

The battle #4 shows the proportion of traps. So half of cases are traps: 30% for 1st player and 15% for second player.

Next time, I'll present you the third competitor. The unbeatable player.