A 3 x 3 tic tac toe(ttt) is often 1 of the games we played when we are young. This is a simple game where we must try to occupy 3 straight boxes before our opponent does. if u sit down for just a few minutes and think about this game, u will find that there are only a couple of "death traps" for a basic 3 x 3 ttt. to save u the trouble, u can just read this blog entry.
typically for all ttt, the 100% sure win move is to form 2, or rarely more than 2, (n-1) intercepting lines (n is equal to the number of boxes on 1 of the side of the board) and the death trap is completed when u place the seed on the intercepting box of the 2 lines. the finishing moves of ttt are T-formation, distorted V-formation, X-formation, +-formation, L-formation, t-formation and distort X-formation(the last 2 are only for n greater than 3). other than that, u would win because ur opponent made a fatal mistake. if u dun understand abt wat do i mean, u can refer to this picture.
the 1st set is a T-formation and the 2nd set is a distorted V-formation.
L-, T- and distorted V-formation
X- and +-formation
t- and distorted X-formation(only for n greater than 3)
the following information is mainly only for a 3 x 3 ttt, maybe i will work on advance ttt later (eg n x n, 3D ttt). 3D ttt is fun, i made a 3D 5 x 5 ttt toy when i was in poly but it was too bulky and not very convenient to bring around. hee...currently, i'm designing a collapsible 3D ttt toy with the help of a fren who owns a workshop of his own.
the opening step of 3 x 3 ttt is very important because this is the point where death traps can be set. So if u r making the 1st step, make sure u set the death trap for ur opponent or beware of the death traps set by ur opponent. by observing a 3 x 3 ttt carefully, there are only 3 different steps to make; the centre box(1), the side boxes(4) and the corner boxes(4).
1) if u mark the corner box (higher recommended!!!), u have set a 75%(6/8) death trap for ur opponent and the finishing move is either a distorted V-formation or a X-formation. by doing so, u will limit ur opponent to 5 possible moves but 3 of 5 are death traps.
- as long as ur opponent did not mark the centre box, ur chances of winning is very high. even if he marks the centre box, then i would recommend u to mark the corner box at the other end, praying that u can still form a L-formation.
-the last possible move will be s/he marking the only corner box, that is on the other end with respect to ur box. u must mark the centre box to set a 66.6%(4/6) death trap, other moves will likely result in a draw game. Again, u will be limiting ur opponent to 3 possible moves; the side box beside his/her corner box(2 in total), the side box away from his/her corner box(2 in total) and the corner box(2 in total). if s/he picks the corner box, dat's it. this is be a draw game. if the corner box is taken, use either a T-formation or distorted V-formation to win this game.
- if the side box nearest to ur corner box is marked by ur opponent(there are 2 of them), u can either use a T-formation or X-formation move. to use the T-formation, u will have to mark centre box and s/he will try to block u. next, mark the intercepting box and u will win. for X-formation, mark the corner box that is beside the other unmarked side box next to ur corner box and ur opponent will guai guai take the other side box in between ur 2 corner boxes. then, u will mark the centre box to form a X-formation death trap.
- if ur opponent marks the corner box that is nearer to urs (there are 2 of them also), u can only need to use the L-formation to win. ur next move must be the corner box nearest to ur opponents box, then s/he will mark the centre box to block u. next, u will mark the last corner box to block him/her and also, complete ur L-formation.
- if ur opponent marks the side box further away from ur corner box (also 2 of them available), there will can only use the X-formation move to win this round. u need to mark the corner box furthest away from ur opponents box, then s/he will automatically mark the side box to block u. ur next move will be completing ur X-formation, by marking the centre box.
2) if u mark the centre box, u have set a 50%(4/8) death trap to ur opponent and ur killing move will be a T-formation. by marking the centre box, u limit ur oppenent to 2 poosible moves; either the side or corner box.
- if s/he marks the side box, it's time for a smile to appear on ur face, because s/he has fallen into ur death trap. Next, plant ur circle at either 1 of the corner box beside ur opponent's box and s/he will try to block u by marking the corner box. lastly, it's time to mark the intercepting box to form a T-formation killing move.
- if s/he marks the corner box, s/he will be out of ur trap and this game will very likely to be a draw or u can still try a T-formation move.
3) if u mark the side box, haha...u have form no 0% deathtrap and the probability of draw is very high. however, if ur opponent is careless, u will still for a +-formation or T-formation killing move.
Lastly, if u see someone is able to counter all the death traps after a few games. Then very likely that person is an expert in ttt or read this blog entry b4...haha...
Patterns of ttt.
i have sort out the possible starting moves for a couple of 2D ttt and found a standard pattern.
n = possible starting moves
1 & 2 = 1
3 & 4 = 3
5 & 6 = 6
7 & 8 = 10
9 & 10 = 15
u can see that the number of possible starting move is always 1+2+3+4+5+6+7+........+n. haha...i'm lazy to sort out the formula, maybe u can help me...haha...or i will put it up in advance ttt entry...meanwhile, just wait hor...
+ BL updated @ 3:19 AM
