Gaming theory applied to UL illustrations yield surprising results…

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I adapted mathematical gaming theory to the illustration of Universal Life. But I was not content to limit myself to theory. Using that theory I built a slot machine to demonstrate the application of this theory. Will you take the insurance gamble at

It is interesting to note that if an advisor wants to sell a complex investment such as options, he must pass a rigorous exam to show he has the necessary knowledge to do so. In the insurance industry, an agent can sell one of the most sophisticated financial product ever invented called Universal Life without having to demonstrate that he has a basic understanding of grade 12 math. Do you see something wrong with that?” Richard Proteau

Investing in the market is a gamble! You can either win or lose.

When you buy an insurance product such as Universal Life as an investment you are taking quite a gamble. In fact, we could view the illustration used to sale this product as the “BET” that the consumer is making when buying this product.

Skilled gamblers understand the odds and potential to win or lose associated with their gamble. Sadly the same cannot be said of most consumers. When we apply gaming theory to the purchase of a Universal Life, it reveals some very interesting results.

If you gamble, whether it is in a game of chance or buying an investment, you should know how much money you can lose or win in theory. This predicted future gain or loss is called expectation or the expected value (EV). It is the sum of the probability of each possible outcome of the gamble multiplied by its payoff value. The EV is therefore the average amount one can expect to win for each bet if the same bets are repeated many times.

Let’s look at this by using the simplest gamble which is the tossing coin. Let’s assume the bet is you win $1 if the toss is heads and you lose $1 if the toss is tails. The expected value is

(.5 * 1) + (.5 * -1) = 0 which means that this is a fair game and if the coin is tossed a large number of times you should neither have lost or won any money.

Now let’s assume the bet is changed to winning $1 if heads is tossed but you lose $2 if tails is tossed. The expected value is (.5 * 1) + (.5 * -2) = -.5. So now you are expected to lose 50 cents or 50% of your bets. So if you were doing this bet 100,000 times, your expected loss is $50,000.

The expected value of the bet is not to your advantage, because the bet is low, you could still decide to take the gamble. However if the bet was $100,000, it would be an entirely different matter.

Let’s apply the concept of Expected value to a Universal Life illustration. Let’s assume the illustration is done at 6% and I assume the probability to make 6% to be 70%. The expected value of this Universal Life illustration would be:

(.7 * 6) + (.3 * -6) = +2.4%

Any gambler would see this as a very good gamble. But something is missing. The MER is missing from this equation like it is missing from the illustration. Let’s assume the MER of the Universal Life is 4%. Therefore to meet the 6% illustration rate you must make 10%. This changes your probability. There is no way that the probability of making 10% is 60%. It must be changed to 40%. The new expected value is

(.4 * (10 – 4)) + (.6 (-(10 – 4)) = – 1.2. Suddenly the expected value goes from positive (a good bet) to negative (a bad bet).

Our equation is still wrong since it does not account for the opportunity cost associated with investing into a Universal Life. If you had not invested in the Universal Life you would have used another investment. Let’s assume it is a mutual fund with a MER of 2%. Accounting for the difference in MER, the expected value is now:

. (.4 * (10 – 4)) + (.6 (-(10 – 4 + 2)) = -2.4. So now the illustration, as a bet has gone from being a bad bet to being a VERY bad bet. No gambler would make such a bet.


Using the power of technology, I have built a slot machine to demonstrate this. In all aspects of social and economic activities we are moving toward technological singularities that will forever change the future. So far the financial industry has been sheltered from such changes. It is our goal to use this technological singularity to give back to consumers control and ownership over their financial affairs. CoStacks is our main project towards this objective. We believe that if such a project is successful, it will forever change the financial industry. In 2017 we will be starting our crowdfunding campaign and first initiative towards the completion of this project. CoStacks will do to financial planning what WordPress did to blogs…


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