Comparing values

I have some monetary values that, lets say, represent the bets placed on a
game.

Suppose x is the bet placed to win and X is the payoff won for that bet.

Now I want to compare two possible bets x and y and figure out which one is
the best.

Now one could say that the best bet is simply the one with the highest
expectation but it would seem that if the variablity of that bet is large it
might not be a good bet(for pratical reasons).

I was thinking about forming the ratio X/x and comparing that with Y/y and
in essense it would allow me to get the most bank for my buck. The problem
is that even though it would reveal how to get the most money with the
smallest bet, it might be a good idea to try to maximimze the payoff too.

i.e., I could place a bet of $2 and get 10 or $6 and get $25. Even though
10/2 > 25/6, the difference is not so much that one wouldn't want to go
ahead and place $6 to get the $25. Technically one might not think this
could occur since you could place 3 seperate bets of $2 each and get $30.
This is not the point since I'm dealing with a much more complex problem but
this example highlights the issue.

I suppose in reality it stems from the fact of one wanting to try to
maximimize there rate of gain. It might be theoretically better to bet $2
each time to maximize the payoff but in reality there are time constraints
and limited number of games and such.... Just like if you could find a sure
fire way to have your expectation > 0 but its so small as to be impractical.


So, while I want to minimize the bet I want to maximize the payoff(which in
effect will increase the avg rate of gain).

The problem then is that these are two conflicting ideas and I can't see how
to handle it. There seems to be some concept I'm missing or something I
need to include so that I can do this. (i.e., I need to quantify what it
means to have a "practical" bet.).

Anyone have any ideas about this sorta stuff?

Thanks,
Jon


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