1. Find Solution of game theory problem using oddment method

Player A\Player B	B1	B2	B3
A1	7	1	7
A2	9	-1	1
A3	5	7	6

Solution:
1. Saddle point testing
Players

			Player `B`
			`B_1`	`B_2`	`B_3`
Player `A`	`A_1`		7	1	7
	`A_2`		9	-1	1
	`A_3`		5	7	6

We apply the maximin (minimax) principle to analyze the game.

			Player `B`
			`B_1`	`B_2`	`B_3`		Row Minimum
Player `A`	`A_1`		7	1	7		`1`
	`A_2`		9	-1	1		`-1`
	`A_3`		[5]	(7)	6		`[5]`
	Column Maximum		`9`	`(7)`	`7`

Select minimum from the maximum of columns
Column MiniMax = (7)

Select maximum from the minimum of rows
Row MaxiMin = [5]

Here, Column MiniMax `!=` Row MaxiMin

`:.` This game has no saddle point.

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2. Dominance rule to reduce the size of the payoff matrix
Using dominance property

			Player `B`
			`B_1`	`B_2`	`B_3`
Player `A`	`A_1`		7	1	7
	`A_2`		9	-1	1
	`A_3`		5	7	6

Also, no course of action dominates the other

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Reduced matrix is

			Player `B`
			`B_1`	`B_2`	`B_3`
Player `A`	`A_1`		7	1	7
	`A_2`		9	-1	1
	`A_3`		5	7	6

Find column difference `C_1-C_2`, `C_2-C_3` and row difference `R_1-R_2`, `R_2-R_3`

			Player `B`
			`B_1`	`B_2`	`B_3`		`C_1-C_2`	`C_2-C_3`
Player `A`	`A_1`		7	1	7		6	-6
	`A_2`		9	-1	1		10	-2
	`A_3`		5	7	6		-2	1
	`R_1-R_2`		`-2`	`2`	`6`
	`R_2-R_3`		`4`	`-8`	`-5`

Find oddments of individual strategies using determinants
Oddment for `A_1` = det `|[10,-2],[-2,1]|=|10-4|=6`

Oddment for `A_2` = det `|[6,-6],[-2,1]|=|6-12|=6`

Oddment for `A_3` = det `|[6,-6],[10,-2]|=|(-12)-(-60)|=48`

Oddment for `B_1` = det `|[2,-8],[6,-5]|=|(-10)-(-48)|=38`

Oddment for `B_2` = det `|[-2,4],[6,-5]|=|10-24|=14`

Oddment for `B_3` = det `|[-2,4],[2,-8]|=|16-8|=8`

So Oddment matrix is

			Player `B`
			`B_1`	`B_2`	`B_3`		Oddments
Player `A`	`A_1`		7	1	7		6
	`A_2`		9	-1	1		6
	`A_3`		5	7	6		48
	Oddments		`38`	`14`	`8`

Sum of A Oddment `=6+6+48=60`

Sum of B Oddment `=38+14+8=60`

Here these sums are equal

Find probabilities of individual strategies
`P(A_1)=6/60=1/10`

`P(A_2)=6/60=1/10`

`P(A_3)=48/60=4/5`

`P(B_1)=38/60=19/30`

`P(B_2)=14/60=7/30`

`P(B_3)=8/60=2/15`

Value of game `V=(7*6+9*6+5*48)/60`

`=336/60`

`=28/5`

Optimal strategy for `A=(1/10,1/10,4/5)`

Optimal strategy for `B=(19/30,7/30,2/15)`