Expectancy formula

Coin Toss 1/1 @ 50%


Six Sided Dice 5/1 @ 16.7%


Had an issue with my RAND() formula
Used If Rand() > P(Win) then $Gain else $Loss
But it's actually If Rand() < P(Win) then $Gain else $Loss

 

Rand()


Rand()+Rand()


Rand()+Rand()+Rand()


But our luck to either win or lose a bet doesn't follow a normal distribution.
If we flip a dice we have 1/6 chance to win vs 5/6 to lose.
There is no shape across the probabilities.
it's 1/N which is Rand()

 

Found a 5th formula: it gives the expected average win $ amount (which can also be negative, meaning loss):
5) Expectancy = AvgWinAmt * pWin + AvgLossAmt * (1.0 - pWin)

I'm still not sure which of the formulas is the correct one.
I would need more input & opinions, and more time myself to study/research/test to convince myself...

 

That’s the one.
95% will tell you they use this one.
The remaining 5% are either freaks or idiots.

 

@Sekiyo, do you know the PnL diagram ("curve") of options constructs, like that of a Collar construct (ie. LongStock + ShortCall + LongPut)? --> Here's a visual example, and below is the screenshot of it.

For example a Collar with these parameters :
LongStock: Spot=100
ShortCall: DTE=180, Strike=120, IV=50, Premium=7.3237
LongPut: DTE=180, Strike=85, IV=50, Premium=6.7301

Can you, or anybody else, compute the Expectancy for such a bullish Collar construct?

I'm currently working on this very, nasty, problem...

 

Maybe you should create another thread in options.

Never really tackled the problem.

 

ATTN: BugFix / Clarification:
here AvgLossAmt has to be entered as a negative number!

 

In reality it's a number that changes with each trade.
Not sure of the value of such a number.
For any given time period take your account balance and subtract it from your starting balance and divide by the number of trades you made. (assuming you didn't add capital)
If you go on tilt your next trade, the expectancy can change drastically

 

@deaddog, I need it in a different context, or for a different purpose, as written in above postings since the beginning, ie. as a better or advanced "reward/risk" ratio...
Of course it indeed changes with each trade as it's about the trade itself, not really about the account...

 

In betting you have
1) the implied odds
2) the true odds

1. Implied odds is based on Reward to Risk,
The market is more or less efficient,
Therefore
0.5R trade is 2/3% and E(x) is 0
1.0R trade is 1/2% and E(x) is 0
2.0R trade is 1/3% and E(x) is 0

You can calculate P(Win) as
Risk / (Risk + Reward)

Because Probabilities and Payouts are interlinked
Again … Most of the time the market is efficient

2. True odds is based on your own model.
Markets are not always 100% efficient,
The risk / reward isn’t always fair

Maybe you know the coin is loaded,
Market is paying 1R implying 50% win
But you know the coin has P(Head) ~60%

You can have an edge which is
P(Win)x(Reward/Risk)-P(Loss)
Your edge is 0.6x1-0.4 or .2

You’re going to earn 1/5 of your bet in average.

But @deaddog is down to earth.
It’s tough to apply this, rigorously to the market.

Because the parameters aren’t static.
But the implied odds should be a good estimation.

If you risk 10 to get 5
Assume P(win) to be 2/3 and E(x) = 0

Unless you have good prior probabilies (Advantage) to update the implied ones in a bayesian way. The odds should be fair.

We ain’t smarter than the market.
But … Sometimes … The market is irrational.