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The Formula Every Trader Should Know

This formula proves if the lottery is better than your strategy

Author

Matthew Enubuje
March 26, 2024

Have you heard of Expected Value (EV)?

It's a formula used in finance, statistics, and game theory to detect and evaluate the expected outcome or value of a probabilistic event or decision-making scenario.

A simplified version of the formula:

EV = (percentage of winning x winning value) + (percentage of losing x losing value)

A positive EV indicates long-term profitability.
A negative EV indicates losing over the long run.

Have I bored you yet?

Well, you’ll have a rude awakening once I show you that EV proves that playing the lottery is statistically better than some high win-rate trading strategies.

How the hell is this possible?

Don’t get me wrong, playing the lottery isn’t profitable at all.

But let me break it down by comparing playing the UK lotto and using a 90% win-rate Forex strategy.

Breakdown of The UK Lotto:

The most recent UK lotto has a £2 million jackpot. You have to get 6 numbers correct out of 59 given numbers. That’s a 1 out of 45,057,4741 chance of winning the £2 million (0.00000715112% of winning).

Let’s calculate the UK Lotto’s EV:

  • EV = (0.00000002216 × £2,000,000) + (0.99999997784 × -£2)

  • EV = £0.0444232 + -£2

  • EV = -£1.96

Breakdown of The High-Win Rate Trading Strategy:

A 90% win-rate Forex strategy where you get many small wins but risk 50% of your balance when you lose. With a £1,000 balance, you’ll win £50 9/10 times and lose $500 1/10 times.

Let’s calculate the High-Win Rate Strategy’s EV:

  • EV = (0.9 × £50) + (0.1 × -£500)

  • EV = £45 + -£50

  • EV = -£5

By opting for the 90% win-rate strategy instead of the lottery, you would subject yourself to approximately a 155.10% increase in the expected loss rate over the long term.

EV comparison of the UK Lotto and a 90% win-rate strategy.

What’s The Takeaway From This?

Definitely not to play the lottery. It would be profitable if the expected value is positive – a £10 million jackpot and a price of £1 to play would make it.

However…It would still statistically take 45,057,474 tries to win.

It’s not worth it!

The Takeaway: Make sure your trading strategies have a positive EV.

Do the EV formula on your trading strategies and continuously adjust them until their EVs are positive.

I can’t remember the last time I heard a trading influencer mention important formulas like Expected Value. Do you? Probably not.

That’s why we use this publication as an opportunity to bring forth unpopular aspects of trading that can change the way you trade.

See you soon!