[knsmith85]

[ QUOTE ]
That was always my contetnion, but now I have a name for it, The utility function, I like it. I play every now and then, just for S&G's (S**ts and Giggles), but the Reward for winning far far far out weighs the $5 I spend a week on it.

ANd since the odds for the MM jackpot are 135,145,920, and taxes take out 48%, then the jackpot would have to be higher than $200,015,961.60 to make this +EV. And it has hit that high on occasion.

[/ QUOTE ]

I think this is actually pretty easy to represent in an equation.

Without the Utility Function (U), the EV equation is:

EV = -x + J*(x/p)

Where p = probability, J = jackpot value, and x = bet amount. If we take x to be 1, when the Jackpot exceeds the reciprical of the probability, you have a +EV. Since this doesn't really happen (because of multiple winning and more notably taxes), you always have a -EV.

However, things change when we consider U. Say your net income is $36.5k per year, or $100 per day (we'll say there are no taxes whatsoever on typical income). Of that $100/day, a loss of 1% of it is what we'll say the cutoff is for significance. So we have part of the utility function... that which we take from our willingness to lose a small amount of money.

Now, we need the part of U that comes from the enormous signifiance in winning a certain amount. For this exercise, we'll call that amount $1 million dollars.

So U is applicable when x <= $1.

So we can call U = J/1000000 as long as x <= $1.

Simply adding this to our original EV equation, we get:

EV = -x + J(x/p) + U, or EV = -x + J(x/p) + J/1000000

This value now becomes positive when J and p are in a certain ratio.

I think I probability messed this up somewhere, so if someone could please correct me, I'd appreciate it.

Thanks,
Kyle