Margin of 4-D

The margin for a bet on an event is

1-(bet odds)/(occurrence odds)

which will lie in the interval [0,1]; it is typically expressed as a percentage. This percentage shows that if you bet a large number of times, u can expect to be losing that percentage of the cumulative wager.

I shall now try to find a rough estimation for the margin for 4-D for a 1-dollar big bet. This is certainly flawed, since the winning numbers can be repeated.

let's calculate a weighted average of the bet odds. If i'm not wrong, the odds for the prizes are as follows for a 1-big bet:

consolation - 60,
starter - 250,
3rd - 500,
2nd - 1000,
1st - 2000

Therefore the weighted average for the betting odds will be:
{[(60+250) x 10 + 500 + 1000 + 2000] / 23} = 6600/23

Obviously, the occurence odds will be 10000/23.

Margin = 1 - (6600/23)/(10000/23) = 1 - 0.660 = 0.340 = 34.0%

You can conclude that you lose about 34.0% of the total wager you ever betted. Imagine the amount of money the bookmakers are earning...