teoria de jocs: joc cuatre torres

[01,01][02,01][03,01][04,01]
[01,02][02,02][03,02][04,02]
[01,03][02,03][03,03][04,03]
[01,04][02,04][03,04][04,04]


[02,02] = torre_{a}
[02,03] = torre_{a}


[03,02] = torre_{b}
[03,03] = torre_{b}


[01,04] = rey_{a} ( 1 paso )
[04,04] = rey_{b} ( 1 paso )


[01,01] = reina_{a} ( n pasos )
[04,01] = reina_{b} ( n pasos )


algoritme-dual en 3 moviments:
{
reina_{a}[01,01] ==> reina_{b}[04,01]
rey_{b}[04,04] ==> rey_{b}[03,04]
torre_{a}[02,03] ==> torre_{a}[02,04]
escak-mat_{b}
}
{
reina_{b}[04,01] ==> reina_{a}[01,01]
rey_{a}[01,04] ==> rey_{a}[02,04]
torre_{b}[03,03] ==> torre_{b}[03,04]
escak-mat_{a}
}


algoritme-dual en 5 moviments:
{
reina_{a}[01,01] ==> reina_{b}[04,01]
torre_{b}[03,02] ==> torre_{b}[04,02]
reina_{a}[04,01] ==> torre_{b}[04,02]
torre_{b}[03,03] ==> torre_{b}[04,03]
reina_{a}[04,02] ==> torre_{b}[04,03]
escak-mat_{b}
}
{
reina_{b}[04,01] ==> reina_{a}[01,01]
torre_{a}[02,02] ==> torre_{a}[01,02]
reina_{b}[01,01] ==> torre_{a}[01,02]
torre_{a}[02,03] ==> torre_{a}[01,03]
reina_{b}[01,02] ==> torre_{a}[01,03]
escak-mat_{a}
}


algoritme-dual en 8 moviments:
{
torre_{a}[02,02] ==> torre_{b}[03,02]
reina_{b}[04,01] ==> torre_{a}[03,02]
reina_{a}[01,01] ==> reina_{a}[04,01]
rey_{b}[04,04] ==> rey_{b}[03,04]
reina_{a}[04,01] ==> reina_{b}[03,02]
torre_{b}[03,03] ==> reina_{a}[03,02]
torre_{a}[02,03] ==> torre_{a}[02,01]
torre_{b}[03,02] ==> torre_{b}[01,02]
escak-mat_{a}
}
{
torre_{b}[03,02] ==> torre_{a}[02,02]
reina_{a}[01,01] ==> torre_{b}[02,02]
reina_{b}[04,01] ==> reina_{b}[01,01]
rey_{a}[01,04] ==> rey_{a}[02,04]
reina_{b}[01,01] ==> reina_{a}[02,02]
torre_{a}[02,03] ==> reina_{b}[02,02]
torre_{b}[03,03] ==> torre_{b}[03,01]
torre_{a}[02,02] ==> torre_{a}[04,02]
escak-mat_{b}
}