Calculate Arbitrage/Scalp bet with different spreads?

[DeucesUp]

[ QUOTE ]
This is the line I am having trouble with:
<< (T –L) / L (T+2) + 1 = percentage won.

In his example (T-L) would not equal 1.55

[/ QUOTE ]

You're right 1.55 is a typo:

(T –L) / L (T+2) + 1 = percentage won

(1.55-1.45) / 1.45(1.55 + 2) + 1
=
(.1) / 1.45(1.55 + 2) + 1
=
(.1) / 1.45(3.55) + 1
=
(.1) / 5.15 + 1
=
(.1) / 6.15
=
0.0162
=
1.6%


If you've balanced the amount bet such that you win the same amount no matter who wins by using (T + 1) /( L + 1) x L then you can use a simplier equation of:

%won = (amount won) / (amount wagered)

Amount won is 1.55 - 1.51 = 0.04 (this is amount won if the +155 team wins, but will be the same if the -145 team wins except for rounding error: (1.51/1.45)-1=0.04.

Amount wagered is 1.51 + 1 = 2.51

%won = (1.55 - 1.51) / (1.51 + 1)
=
0.04 / 2.51
=
1.6%


Note however that these are not these are not optimal bet sizes for this scalp. I'll let you see if you can figure out why. Here's a hint: The above gives you the highest guaranteed profit, but not the highest expected profit. You want to maximize expected profit.