50/50 Betting Math

I understand that if you bet $1 1000 times, you will end up with $0 profit, with 500 losses and 500 wins.

Can someone explain to me what happens when you throw in the variance of bet sizes?

For example... 219 of the bets are $1, 486 are $3, and 295 are $5.

Assuming 50/50 odds

 

I'm not a gambler a friend of mine is confident that sizing makes a difference.

I told him the three bet sizes would just average out is this correct?

 

Yes

 

Your equation is autistic so you obviously didn't pay attention lol

 

Would ten bets of different value at a 50/50 win rate still put you even?

 

Gonna have to call in the big guns on this one @Sythe

 

Because you didn't factor in that you'll win half of them as well.

But let's move on from the first example and focus on ten bets of different value.

 

Variance is still higher on bigger bets, meaning with bigger bets your actual value will differ more from the expected value than on a smaller bet

Your bet size is the expected value of the bet if it's 50/50 odds - so different bet sizes don't matter for the EV but it does for the variance

 

Yeah I figured it would average in the first example that's what I told him.

But how do you calculate the variance in ten or one hundred different sized bets? That's a better way to put this I guess. @Searchy

 

You're not guaranteed to end up with +/-0, it's just the statistic probability. The more bets you make the closer you get to evening out. i.e. if you made a billion $1 bets you would likely be pretty close to 50%.

In your scenario you bet $3152 and wind up with a similar amount of money due to the 50% odds

 

Variance is the average of the squared differences from the mean.

 

So that number will be + or - on the end result or of each event?

 

Thank you @Sythe

 

Still zero EV gained and in an infinite number of events you'll have the same amount of money as when you started

Bet size does not matter, although I'll add that larger stakes is more likely to deplete your bankroll faster than if you stayed at 1$ over and over but yeah

 

Sythe provides shelter for the wrong type of autism, unfortunately. You're expecting to find your rain man amongst a flock of window lickers.

 

No