You often hear complaints about the ‘game’ being rigged against regular people, but if you had a chance to play a game with the odds in your favour, would you fair any better? One investment firm’s experiment suggests the answer is no.
The Experiment
Participants were given a (digital) coin to flip and $25 to bet on the outcome. A normal coin toss is known to have 50/50 odds to come up either heads or tails. The experiment’s twist was that the coin used had a 60% chance of coming up heads and only a 40% chance of tails.
Flippers could make any sized bet, down to a minimum of a penny, and had thirty minutes to make as many bets as they could until they stopped, ran out of time or went broke. A correct guess doubled their bet, while an incorrect guess would forfeit it. They were told that there was an undisclosed maximum amount they could each win, and whatever amount they had remaining at the end of the thirty minutes would be given to them in real cash!
The people selected for the experiment were mostly college students in economics and finance, or young professionals in the finance sector itself.
How well did they do?
Before I tell you, perhaps you’d like to play the coin flip game yourself? The investment fund makes the same offer in their paper detailing the experiment. How you fair can teach you a lot about yourself, as we’ll get into shortly.
You can play the game here (with a reduced time limit of 10 minutes):
https://elmwealth.com/coin-flip/
Alright, back to the results.
The participants didn’t do all that great, which shocked the researchers. Only one-fifth of them reached the max payout of $250. A third of all subjects either went broke or left with less money than they started with! Keep in mind that this sample size is skewed towards individuals who should have a good grasp of concepts like probability, statistics and risk-reward ratios in investing and gambling.
Why did they do so bad? It can boil down to three main reasons:
1. Not Managing Risk Properly
Nearly a third of the subjects bet it all on one coin flip. Ugh.
Having a 60/40 edge doesn’t mean you can’t lose a bet. The first priority should be to get on the right side of it. Picking heads every time guarantees your win rate over time to be 60%. This means you will win more bets than you lose, but you will lose, sometimes multiple times in a row.
What is the chance you’ll lose your first flip? 40%
What is the chance you’ll lose two flips in a row? 40% x 40% = 16%
Given this, if you bet half of your $25 on bet one, and the other half on bet two, you have a 1 in 6 chance of going bust!
That seems a bit risky to me, when in the right hands this game could become a money-printing machine.
Accounting for five losses in a row, the odds of going broke with $5 bets go down to 1% or 1 in 100.
That seems like a better risk management plan to me. We still don’t know if this is the best strategy, but we’re getting there.
Many of the edges we get in life are small ones. These can compound into major advantages over time, but we need to account for the risk of being ruined before we can get there.
2. Using Faulty Reasoning
Surprisingly to the researchers, half of the subjects bet on tails at least 5 times during the course of their games. A lot of these instances came after the coin landed on heads a bunch of times. Many thought the coin was ‘due’ to land on tails.
What they failed to understand is that each coin flip is an independent event. Past results do not have any bearing on future results. Each coin flip has a 60% bias towards heads. Pick heads!
Another trap people can fall into is the idea of having a ‘hot hand’ at making the correct guess. Needless to say, the result of the coin toss is not influenced by you having guessed the previous results correctly. Many participants fell into having an illusion of control over the results of a random event.
3. Failing to Find the Best Strategy
I think we’ve established how not to go bust, and that we should pick heads each time. Now, how much should you bet to maximize our upside?
Perhaps a group of pro gamblers would’ve been better suited to beat this game than students of finance. The researchers posit they’d have a better chance of being familiar with the Kelly Criterion. In a game where you have the edge, this formula delivers an optimal betting strategy to grow your funds. It balances the risk of ruin with the quickest path to victory. Being quick is relevant when only having a 30-minute time limit.
The Kelly Criterion: Bet Size = 2*p-1, where p is the probability of winning.
In our game, this would work out to 2*0.6–1 = 0.2.
We should bet 20% of our starting capital, which is $5.
It doesn’t end here. The formula is dynamic based on our pool of capital.
If we lose the first bet, we should lower our next to 20.) If we win, we should up our bet to 30.)
This way, we are consistently betting 20% of our capital, and we can scale up or scale down our absolute bet amount based on our running success rate in the game.
How would an unworldly losing streak look like with this system? It would take 29 successive losses until you could no longer bet the minimum of $0.01!
How about with a winning streak? How many turns would it take to get to max winnings? The answer is 14:
What Can We Learn?
The investment firm highlights the potential correlation between excelling at this game, and making sound decisions in investing. It should be noted that the participants selected for this experiment probably knew more about investing than the average person, yet many of their understandings of risk and probability seemed lacking.
In the course of investing, day trading, or any other risky, complex undertaking, many more variables come into play than the odds of a coin flip. Rather than picking ‘heads’ or ‘tails’, determining if you correctly picked ‘buy’ or ‘sell’ is not as clear cut in the post-mortem.
However, if you fundamentally cannot come to terms with the optimal strategy in a simplified situation like this, should you be confident in your next Robinhood investing scheme?
Perhaps.
Or maybe just flip a coin on it instead.
Here’s a link to the study: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2856963