The Framework for Making Bets

“Alec, can we hop on a quick call? I have a private placement that I believe is worth your time.”

John detailed the specifics of the investment, a gold-focused exploration in a region of Canada, known for finding gold with a great team. The geologists have studied the area and believe the targets are worth drilling, he says.

The most important thing I’ve learned about making bets with incomplete information is knowing which questions to ask. This allows me to gather the missing information I need to calculate the expectation of the bet in question.

I’m very well versed in calculating the expected value (EV) of a bet in a hand of poker because I’ve mastered the odds. But my ability to deduce what my opponents are holding doesn’t help me evaluate the efficacy of finding gold under the earth’s surface.

But I do know what information I need, and therefore, what questions to ask.

So, I asked him, “What are the odds that we find gold?”

“About 1 in 100.”

“And what happens to the price of the stock if we find gold?”

“It depends on the size of the rock and content of the gold.”

“Go on.”

“Most rocks pull out one gram of gold per ton. That means they have to move one ton of useless rock to find one gram of gold, which is why the price of gold is so high. Some rocks have much as 10 grams. This is called the grade of gold. There’s known to be historically high-grade gold here.”

“So, on average, it’s fair to say that if they find a rock, the grade of gold will be twice as high – 2 grams per ton – meaning the mine will be worth twice as much as a normal one, and, all things being equal, this will reflect in the stock price?”

“That’s correct for the grams per ton, but in this market, investor sentiment is high, and if they find anything, the price can go up multiples.”

“Five times?”

“More like ten. And keep in mind, the story isn’t dead if they drill a duster in the first round. We can still cash out at a small loss, maybe 20%.”

I thanked him for his time, hung up the call, and quickly ran the numbers.

Recall this simple formula for making bets:

Expected Value = (Amount Won * Probability of Winning) – (Amount Lost * Probability of Losing)

Assuming we make a $1,000 investment, plugging in the numbers, we get the following:

EV = Probability of Finding Gold x (10x of $1,000 investment) – Probability of Not Finding Gold x (20% of $1,000).

If you run those numbers, you’ll get an expectation of -$98 or a loss of roughly 10%. Not very good odds.

A few things worth noting: I don’t mean to sound like I think I’m smarter than John. I’m not. If he called me for a trade, it’s because the bet seems profitable. It’s possible I got some of the odds wrong. That said, the outcome is rather irrelevant; it’s the methodology used to arrive at the conclusion that matters.

Second, I trivialized some of the dialogue for illustration purposes. Of course, when it comes to investing, there are unknown variables which are difficult to quantify.

How can we be certain the price will 10x upon finding gold? What if it goes up 5x or 20x?
How do you attribute a definitive probability to the size of the rock?

The list goes on. What’s important is to understand that any guess is better than none. Over time, as your expertise increases in a given field, you’ll be able to better attribute accurate values to your inputs, resulting in more precise EV calculations.

You can apply this simple framework to any bet you’re debating. I hope it helps you make better decisions both on and off the felt.

Alec

P.S. If you want to learn how I make bets in poker, see this post.