Re: Mathematical Expectation?
There is a 15% chance that it will rain more than 1 inch, a 45% chance that it will rain but be less than an inch, and a 40% chance of no rain at all.
We make the following agreement, if it rains more than an inch you give me $3, if it doesn't rain at all I give you $2. if it rains but less than an inch we push.
Your expected value on this wager
(.15 * -3.0) + (.45 * 0.0) + (.40 * 2.0) = 0.35
You expect to make about 35 cents on this prop bet int he long run.
The formula is just the sum of (probability of event * result of event) over all possible events (the sum of the probabilities should equal 1.0).
Does this help at all??
Here's an actual poker example, let's say you hold
4 [img]/images/graemlins/diamond.gif[/img] 5 [img]/images/graemlins/diamond.gif[/img]
Board is
6 [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/heart.gif[/img] A [img]/images/graemlins/spade.gif[/img] J [img]/images/graemlins/club.gif[/img]
The pot has $200 and it's you and an opponent heads up, he bets $40 and then let's assume he's a drunk idiot flips over his pocket aces and is like "beat this you loser".
We now have all the information we need to make a proper EV decision.
We have 4 cards that will make us a straight and a winning hand over his three aces. Every other card we lose. THe odds of us catching one of our 4 cards is roughly 8% (we'll say 8.0 even to keep the math pretty).
Thus we examine our EV of calling or folding
EV of folding = 0
EV of calling = (.08 * 240) + (.92 * -40) = -17.60
(I'm not factoring in river action for simplicity).
It's clear we should fold, we simply do not have hte right odds to call the bet. You can see how this EV calculation cahnges if we had moer outs (say we had an open ended straight flush draw) or if the pot was much bigger (say $1000 with still $40 to call).
The problem with poker ist hat it's imcomplete information so your math is guess work, and you haver very odd scenarios.
For example calling may have -EV and raising has even worse -EV, but you think your opponent is weak and may fold to a raise, thus you have to try to figure out hte % chance he will fold to a raise and factor that into your raising EV calculation.
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