Tuesday, April 30, 2013

Getting a Handle on the Cost of Cars

I’ve seen the cost of cars broken down to the cost per kilometer of driving, and I’ve seen it broken down to cost per year. However, neither approach seems to measure costs in the way I want. So, I set out to figure out how to model the cost of my car. I want a better idea of what it costs to have a car and how much it costs to drive it.

I began by recording all my car costs in the following categories:

– Purchase price
– Fuel
– Maintenance and repairs
– Licensing
– Insurance

I recorded the month of each cost so that I could use historical Consumer Price Index figures to adjust for inflation. For example, to adjust a cost of $100 in January 2010 when the CPI was 115.1 to March of this year (CPI 122.9), calculate

($100/115.1)*122.9 = $106.78.

Then I added up the adjusted costs in each category to get the totals in today’s dollars. The big question is what to do with this data at this point. One possibility is to work out the cost per kilometer. But this seems misleading because it overstates the marginal cost of each new km driven. Working out the cost per year is also misleading because the cost per year depends on how much you drive.

Fixed and Variable Costs

I decided to try to break the costs into fixed and variable costs. I think of the fixed costs as the cost of having a car available. Even if I never drive it, having a car costs money. Then the variable costs are proportional to the number of km driven.

The question now is how to divide up the 5 categories of costs into fixed and variable costs. The initial purchase price is partly fixed and partly variable because the more you drive a car the sooner you have to buy a new one. A guess is that a car rarely driven would last about twice as long as a car driven as far as I drive in a year. So, I split the initial purchase price 50/50 between fixed and variable.

Fuel is 100% variable, and maintenance and repairs are mostly variable, say 80%. Licensing is 100% fixed. Insurance is mostly fixed, but costs do rise the more you drive. I treated insurance as 70% fixed.

Next I divided up the 5 categories of costs into fixed and variable costs based on these percentages. I then took the fixed costs and divided them by the number of years I’ve owned my car (13). One exception is that I divided 50% of the initial purchase price by 17 as a (possibly optimistic) guess of the number of years I would have it in total.

I divided the variable costs by the number of km I’ve driven (317,739). One exception is that I divided 50% of the initial purchase price by a (possibly optimistic) guess of the total number of km I’d drive the car (400,000).

Total costs

(See here for the car cost spreadsheet I used.)

The final costs for my car are

Fixed: $4550 per year, plus
Variable: 34 cents per km.

The way I interpret these results are that just having this car available to me costs $4550 per year, and actually driving it costs me another 34 cents per km.

How to use this information

The $4550 per year seems quite high. I guess owning a luxury car with 300 horsepower costs money. I’ll probably make a different choice when this car finally grinds to a halt.

Even the 34 cents per km is expensive when you think about it. I’ve played ball at a diamond 20 km away from my home for many years. The round trip has cost me $13.60 per game. Before I went through this exercise, this was an invisible cost. If the parking lot at the ball diamond had instituted a $2 charge, I would have complained bitterly, not realizing that I was already paying $13.60 per game.

Flying or driving to a vacation in Florida is a different decision when I think about the 34 cents per km. The return trip to Florida is about 4500 km, or $1530. So much for driving to save the flight costs for my wife and I of about $500 each.

Armed with this new information about the cost of my car will make me think differently about the cost of trips. Paying $200 for a train ticket for a 1000 km trip seems expensive until I realize that the cost to drive is $340. I’m very likely to choose my next car to have lower life-cycle costs.

Monday, April 29, 2013

When Should You Start Collecting CPP?

The standard age to start collecting CPP benefits is 65, but you may get a reduced pension as early as age 60, or get a larger pension by starting as late as age 70. A factor affecting the decision of when to start collecting CPP that I hadn’t considered before is the penalty that comes with years when you make no CPP contributions.

Most descriptions of how to calculate your CPP benefits are too hand-wavy to be useful. However, Doug Runchey wrote a great post at the Retire Happy Blog on how to calculate your CPP retirement pension. I used this post to work out my own projected CPP benefits.

I worked out 3 scenarios: collecting at age 60, 65, and 70. When you take your CPP before age 65, your benefits are reduced, and if you postpose benefits until after age 65, your benefits increase. We’re working through a transition period right now, but by 2016 and beyond, the reduction before age 65 is 0.6% per month and the increase after age 65 is 0.7% per month.

This means that if payments start at age 60, the payment amount is reduced 36%, and if they start at age 70, they are increased 42%. It’s important to understand that any reduction or increase is permanent. If you take early CPP at age 60, you won’t get back to normal payments at age 65; the 36% reduction applies for the rest of your life.

In each of my scenarios, I assumed that I wouldn’t be working past age 60. The only variable was the start date of collecting CPP. This means that the longer I delay collecting CPP, the more years I will have without making any CPP contributions. Unfortunately, this reduces CPP benefits more and more the longer I delay CPP benefits.

A very simple analysis of CPP payments takes the 36% penalty for starting at 60 and the 42% bonus for starting at age 70 and declares the benefits at ages 60, 65, and 70 to be in the ratio 64:100:142. However, when I did the full calculations for my situation, which included the penalty for years without contributing, the ratio was 72:100:129.

Based on just these factors, I should take CPP at age 60 if I don’t expect to make it to age 78, should take CPP at 65 if I expect to live to between 78 and 88, and should wait until age 70 if I expect to live past 88. However, another important factor in the timing of starting CPP benefits is the return I expect to make on my savings.

If I expect to make a positive real return on my savings, then the age cut-off ages of 78 and 88 rise. The bottom line for me is that unless the CPP rules change or my working plans change, I’m likely to start collecting CPP benefits at age 60. Each person’s situation is different, though. Your mileage may vary.

Friday, April 26, 2013

Short Takes: ETF Tracking Errors, Cheap Business Banking, and more

Here are my posts for this week:

Making the Most of the Principal Residence Exemption

The Canadian Guide to Will and Estate Planning

People Respond to Incentives

The Hidden Cost of Active Investing

Here are my short takes and some weekend reading.

Canadian Couch Potato explains the different reasons why an ETF might fail to exactly track its index.

Canadian Capitalist looks at some cheap options for business banking.

The Blunt Bean Counter says that delays in sending out tax slips has compressed the time he has to work on tax returns. He vows to make changes for next year to reduce his stress level.

Preet Banerjee interviews Kyle Prevost, co-author of More Money For Beer and Textbooks, in his latest podcast.

Million Dollar Journey says it’s abnormal for the stock market to produce close-to-average returns.

Big Cajun Man says that if you keep important financial information on your computer, you need to do backups.

Thursday, April 25, 2013

The Hidden Cost of Active Investing

Few investors understand the long-term drag on returns that comes with active investing. Even if you guess right your share of the time, the higher volatility that comes from a more concentrated portfolio costs you money. I did a small experiment to illustrate this effect.

Jim started 20 years ago with $20,000 that he planned to invest in only Microsoft and AT&T. He gave $10,000 to one money manager with instructions to always keep the money split evenly between the two stocks.

Jim split the other $10,000 between two money managers, Alice and Betty, and instructed them to decide each day whether Microsoft or AT&T would perform better. Alice and Betty always invested all the money they controlled in one stock or the other. By coincidence, Alice and Betty disagreed every day about which stock would perform better. Each money manager alternated days between being right and wrong.

Based on this setup, the actively-managed money was invested “correctly” exactly half the time and every day one of the pots was invested correctly and the other incorrectly. You might think that the actively-managed money would end up at exactly the same portfolio value after 20 years as the even-split money management.

However, this isn’t the case. The actively-managed money grew from $10,000 to $90,042. But the even-split money grew from $10,000 to $117,918. This shows that the active money managers had to be right more than half the time just to break even. The return boost that comes from diversification is a kind of free lunch for passive investors.

Wednesday, April 24, 2013

People Respond to Incentives

My family frequently blows through the limit our internet provider places on the number of gigabytes (GB) per month we get without extra fees. Frequent pleas from me had little effect. Warnings from our internet provider when we reached 75% and 100% of our allotment for the month were ignored. Then I came up with an economic solution.

Each computer in my house has a desktop network meter that measures internet usage for the month. Each member of my family gets an equal share of the “free” GB each month. Then any overage fees are shared by all of us in proportion to the amount we exceeded our shares.

Here’s an example. Suppose a family of 3 has a limit of 75 GB per month (25 GB each) and one month they use 5 GB, 35 GB, and 55 GB. The overuse is then 0, 10 GB, and 30 GB, respectively. If the overuse fee is $40, then the second person pays $10, and the third $30.

Making my family actually hand over cash seems to have made quite a difference. I no longer harp about internet usage, and we haven’t had any overuse fees since I put this plan in place. We’ve used small economic incentives to improve harmony.

Tuesday, April 23, 2013

The Canadian Guide to Will and Estate Planning

Douglas Gray and John Budd have published the third edition of their book The Canadian Guide to Will and Estate Planning. They do a good job of explaining in simple language the bewildering array of ways to protect your estate from taxes when you die.

The range of topics covered includes building your estate, wills, trusts, probate, taxes, U.S. taxes, cottages, family businesses, charity, insurance, advisors, retirement care, and funerals. It’s almost enough to make me renounce all my worldly possessions – almost.

I won’t try to summarize this book and further – even at 400 pages, most topics are covered quickly. The main value of this book to me was to become aware of possible estate planning strategies. Actually acting on this information likely requires further investigation or professional help.

For the rest of this review, I’ll point out some parts of the book I found interesting, surprising, or I disagreed with.

CDIC Coverage

“You are protected up to a maximum of $100,000 for each separate deposit.” This may be technically true if you define “separate deposit” correctly, but this definition will not line up with what most people understand the words to mean. Similar deposits get lumped together. It’s best to read the details at the CDIC web site.

Financial Advice

“Unless you consider yourself an expert in the markets, and in forecasting the economy and interest rates, you should have a professional manage your investment portfolio.” Unfortunately, the professionals can’t do any of these things either. The real game is to invest in a way that allows for the possibility of a wide range of outcomes.

Disinheriting Family

Apparently it is quite difficult to disinherit a child or spouse. If you feel strongly about doing this, you’d better get some good advice, because the authors explain that various laws give spouses and children rights that can supersede your wishes.

Wills and Marriage

“A will is automatically revoked by law if the testator enters into a legal marriage after the will has been made.” There are some exceptions to this, but in general you need to look at your will whenever you get married.

Caution on Trusts

“Trusts are complex, and costly to set and maintain year-to-year.” Trusts can save on taxes and solve certain problems, but they are generally only worthwhile for large sums of money.

Final Income Tax Returns

The executor must file a final tax return for the deceased and must file another tax return for the estate to cover the time after death.

RRSP Tax Surprise

If you leave your RRSP to one child and the balance of your estate to another, the entire RRSP will go to the first child, and the balance of the estate will pay the income taxes on the RRSP withdrawal. This can skew the size of each share in a way you didn’t expect.

Electing Out of the Spousal Rollover

Ordinarily, you can leave property to a spouse without triggering capital gains taxes, and the spouse simply takes the property at your adjusted cost base. However, if you have a large capital loss from previous years, you may wish to elect out of the rollover to use up the capital loss and save the living spouse future capital gains taxes.

Principal Residence Exemption

See my previous post for a discussion of reducing taxes by taking advantage of the flexible principal residence designation.

Insurance Agents

“One might think that insurance agents’ ... recommendations on the need for, and the volume of, life insurance that is required in a situation are ‘product and sales driven’” to create commissions. “In the writers’ experience, this is not the case.” I’m sure there are many honest insurance agents, but fewer than half of the ones I’ve dealt with had integrity.

Executor Duties

The authors provide a comprehensive list of executor duties in the appendices. This list is long and may make me a little less likely to agree to be executor for too many more family members. On the other hand, maybe it gets easier after you’ve been through it a couple of times.

Life Insurance

According to a chart in the appendices, to have $5000 available to spend each month, you would need investible assets of $2.2 million and require life insurance to close the gap between your current assets and $2.2 million.

Conclusion

Overall, I found this to be a useful book that manages to take dry subjects that are often described with impenetrable jargon and makes them comprehensible.

Monday, April 22, 2013

Making the Most of the Principal Residence Exemption

Canadians don’t have to pay capital gains taxes on their principal residences. However, the definition of “principal residence” is quite flexible making it possible for families who own a second property, such as a cottage, to save substantial amounts on their taxes.

Douglas Gray and John Budd, in their book The Canadian Guide to Will and Estate Planning, explain that your principal residence isn’t necessarily your “main place of residence.” If you own a vacation property, “as long as you, your spouse or at least one of your children occupy the vacation property for some period or periods of time during the year, that is enough to bring you within the principal residence definition.”

“The fact that you show your home address on your income tax return does not mean that you are designating your house as your principal residence.” Further, “it is not generally necessary for you to decide which property is to be designated as the principal residence for capital gains tax purposes until the year that either property is sold or disposed of.”

Calculating your taxes owing on a property sale begins in the usual way by taking the proceeds of disposition and subtracting your adjusted cost base to get the capital gains amount. Then you get to reduce this capital gains amount by the “exemption fraction,” which is based on the number of years it was your principal residence. The exemption fraction is

1 + number of years after 1971 the property is designated as your principal residence

divided by

number of years after 1971 you owned the property.

Partial years count as full years in this fraction. The purpose of the “1+” in the numerator is presumably to deal with the fact that a family with just one property may move in the middle of the year, but only be allowed to designate one of their homes as their principal residence for that year.

An Example

Sue and Bob bought their home in 1994 and a cottage in 2004. They sold both in 2013 for a $200,000 gain on the house and a $150,000 gain on the cottage. They owned the house for 20 years and the cottage for 10 years.

If they designate the house as their principal residence for the entire 20 years, they will have to pay capital gains taxes on the cottage gain of $150,000. But, look at what happens if they designate the cottage as their principal residence for 9 years and the house for 11 years:

Cottage exemption fraction = (1 + 9)/10 = 100%.

House exemption fraction = (1 + 11)/20 = 60%.

Now the cottage gain is entirely tax-free and they only have to pay capital gains taxes on 40% of the $200,000 house gain, or $80,000. This is a reduction in capital gains of $70,000 compared to declaring the house as their principal residence for the entire 20 years. Assuming Sue and Bob pay 23% capital gains taxes, they save $16,100.

For families with vacation properties, it definitely pays to understand these rules when it comes time to sell homes and cottages.

I am not a tax expert. I relied on the information in Gray and Budd’s book to construct this example. Seek professional tax advice, particularly when dealing with large sums of money.

Friday, April 19, 2013

Short Takes: Mutual Fund Fees, Getting Out of Debt, and more

It was a short week for me because I was off playing some golf in Florida. My only post for this week was

Leasing a Car is not Like Renting It

Here are my short takes and some weekend reading.

There is a serious problem with Canada’s mutual fund industry. In a letter to the Canadian Securities Administrators (CSA), Steadyhand Investment Funds clearly explains this problem and how to fix it. My favourite part of the letter is a quote from a mutual fund investor who clearly does not understand how advisors get paid: “Our financial advisor is such a nice man. Every year he takes us out for a wonderful dinner. I wish we could pay him [in] some way.”

Mr. Money Mustache shows a young couple how to change their finances to climb out of debt and prepare for a family.

Canadian Capitalist and Canadian Couch Potato review iShares’ latest currency-unhedged ETFs.

The Blunt Bean Counter discusses some tricky tax situations related to travel expenses for rental properties, declining a tax-free rollover to a spouse, and pooling charitable donations between spouses.

My Own Advisor has a sensible reaction to stock tips in an investment newsletter he read.

Preet Banerjee offers some options for cutting down on bank fees.

Big Cajun Man discusses his experiences with boomerang children.

Million Dollar Journey explains that an increase in your property’s assessed valued doesn’t translate directly into an increase in your property taxes.

Monday, April 15, 2013

Leasing a Car Is Not Like Renting It

A colleague of mine has seen me throwing away a lot of paper over the past couple of years, and I explained that I’m trying to live a life with fewer things. The way I see it, my possessions tend to own me rather than the other way around. This colleague recently told me that I inspired him to do the same thing, and he began by leasing instead of buying his most recent car. He sees leasing as like renting instead of owning.

The social thing to do in this situation would be to say something like “that’s great – enjoy your new car.” But, I’m no good at saying things I don’t believe. I had to tell him that I didn’t agree that leasing a car is like renting it. For one thing you often end up paying for about half of the car. Further, the details of lease contracts push much of the risk back onto the consumer.

This colleague really hasn’t significantly reduced his exposure to the risks of owning a car. Further, because lease contracts are complex, few people understand them enough to figure out if they’re getting a good deal or not. If you believe that car dealerships don’t take advantage of this asymmetry of understanding, I’ve got a nice bridge I’d like to sell you.

The main thing that consumers see is that lease payments tend to be lower than car loan payments. However, at the end of the lease, the consumer has no equity and may be on the hook for extra charges depending on the car’s mileage and other factors.

So, leasing a car is not really like renting. Most people would be better off to save up for a car and buy what they can with their savings, even if it means buying a very modest used car.

Friday, April 12, 2013

Short Takes: Cartoonist’s Financial Advice, Clamp-Down on Advantaged ETFs, and more

Scott Adams of Dilbert fame has some very funny takes on active money managers and investing like Warren Buffett.

Canadian Capitalist explains how the latest federal budget clamps down on ETFs that use fancy derivative arrangements to turn income into capital gains.

Larry Swedroe reports that the 2012 study comparing actively-managed mutual fund returns to benchmark indexes shows that active managers lost again last year.

Canadian Couch Potato explains why you should avoid automatic dividend reinvestment in taxable accounts.

Mr. Money Mustache has some sensible thoughts on living a life without line-ups.

The Blunt Bean Counter explains “how financial institutions misreport or don't adjust their realized capital gain/loss reports for the adjusted cost base reduction on flow-through shares.”

Big Cajun Man explains the generous matching of contributions to a Registered Disability Savings Plan (RDSP).

My Own Advisor has a sensible set of 2013 financial goals and is on track so far this year.

Wednesday, April 10, 2013

Fraser Institute Studies Public and Private Sector Wages

The Fraser Institute recently released a study indicating that public sector workers enjoy 12% higher wages than private sector employees after controlling for a number of factors including age, education, tenure type of job, and location. Unfortunately, this 12% figure understates the real gap.

Because the study’s authors could not get sufficient data to measure non-wage benefits, such as pensions, insurance, and vacation, they couldn’t properly compare total compensation between the public and private sectors. The 12% figure would certainly rise if we had this data.

There is another important factor as well: competence. “In 2011, 0.6 per cent of government employees lost their jobs—less than one sixth the job-loss rate in the private sector (3.8 per cent).” In the private sector, it is weaker workers who tend to lose their jobs. Even when the official reason for job loss is the elimination of a position, the truth is that companies do their best to eliminate poor performers. The government does a poor job of getting rid of people who can’t or won’t work.

To be clear, I’m not saying that all government workers are weak. In any large population you get a lot of variance. But because too many poor performers get to keep their government jobs, the average competence gets dragged down compared to the private sector. The result is that some government workers could not get and keep a similar private sector job. On average, these people would have to find lower-paying work if they had to move to the private sector.

If we had a way to measure this competence effect, public sector wages would start to look even better. So, the Fraser Institute’s figure of a 12% wage gap significantly understates the real gap if we factor in non-wage compensation and competence.

Tuesday, April 9, 2013

RBC Outsourcing of Temporary Foreign Workers

The Royal Bank of Canada (RBC) is indirectly replacing 45 Canadian workers with foreign workers through contracting firm iGate. This move has sparked outrage for good reason. This isn’t a case of sending work overseas; these foreign workers are coming to Canada to displace Canadian workers.

This is all being done under the temporary foreign worker program which allows RBC “to hire foreign workers on a temporary basis to fill those jobs, but only if a Canadian isn’t available to do the work.” However, these IT-related jobs in question at RBC are not high-skill jobs. There are plenty of Canadians who can do this work.

The real issue is money. RBC could easily get a flood of Canadian IT employees if they bumped up the hourly wage they pay. Any apparent shortage comes from trying to pay below the market-based wage.

It makes sense to allow companies to bring in foreign workers for jobs requiring rare skills, but that is far from the case here. The fact that RBC is actually replacing existing workers makes the financial motive even more transparent.

Widespread objection to RBC’s move isn’t just a knee-jerk reaction from organized labour. I’m rarely accused of being left-leaning. I believe in free markets when there are enough players for genuine competition. However, this move by RBC to cut costs is bad for Canada.

Monday, April 8, 2013

Looking for Signs in Stocks and Real Estate

They say that stocks are poised to crash just after everyone is unanimous about the wisdom of getting into stocks, and that they’re set to rise just after everyone is sure stocks are dead. Presumably, it works the same for real estate. I heard something recently that sounds like either a good sign for stocks or a bad sign for real estate in Canada.

I hosted a get together where a friend who is a real estate agent told us about one of his clients. This client is frustrated with years of poor results from stock mutual funds and plans to pull all his money out and try to generate better returns buying real estate and collecting rent.

This sort of thinking is great for real estate agents, but I’m doubtful it will work out very well for this investor. I know people who are well-suited to be landlords, but most of us are not. This story feels like either a great sign for stocks now that the last person is getting out, or more likely a terrible sign for real estate in Canada now that the last holdout is jumping in.

Just to be clear, I have no confidence at all in my ability to read such signs. I have no intention of changing my investing strategy to use this information in any way. But, it sure feels like a sign that stocks will outperform real estate in Canada over the medium term.

Friday, April 5, 2013

Short Takes: Cyprus Cash Grab, Helping Lottery Winners, and more

My posts for this week were

Dice Gambling System
Trying to Beat a Casino

Here are my short takes and some weekend reading.

Canadian Capitalist says there is little reason to fear a reduction in insurance on bank deposits in Canada.

Potato has a take on what you can or can’t do to avoid a Cyprus-like seizure of your assets by a cash-strapped government. In nations with their own currency, there is a much easier way to take purchasing power away from the masses: just print more money to pay debts. The resulting inflation is the silent killer of wealth.

My Own Advisor thinks the Ontario Lottery and Gaming (OLG) Corporation should help lottery winners get good advice on making their money last. I can’t imagine OLG giving this more than a passing thought unless they think such a program would somehow help drive more lottery sales.

Big Cajun Man says that while money may not buy happiness, debt often brings unhappiness.

Retire Happy Blog has some suggestions for beginning do-it-yourself investors.

The Blunt Bean Counter is descending into another busy tax season but chose to share a few different ideas about taxes and other things before he gets swamped.

Million Dollar Journey did a net worth update as an April Fools’ post, but I couldn’t find the joke.

Tuesday, April 2, 2013

Trying to Beat a Casino

Yesterday’s post was an April Fools' joke. However, the simulation results for the casino dice game of craps were real. As commenter Patrick figured out, the catch was that the strategy called for betting negative amounts.

The “system” starts out with $100 bets and goes up by a dollar after a win and down by a dollar after a loss. However, we will lose slightly more often than win. So, the bet amount will keep going down until it hits zero and then become negative.

Of course, casinos won’t allow gamblers to bet negative amounts. This is effectively like reversing the role between casino and gambler. It’s no wonder that a gambler who uses the system starts out losing while the bets are positive and ends up winning after the bets become negative. The only way I know to beat a casino at craps is to get them to gamble at your craps table.

This kind of hidden problem with experiments and simulations doesn’t just appear in cooked-up April Fools' jokes. A study by Schleef and Eisinger on asset allocation schemes concluded that investors should increase their stock allocations over time. However, this conclusion was just an artifact of a problem with how their simulations sampled historical returns. Poorly constructed studies can produce all kinds of crazy results.

Monday, April 1, 2013

Dice Gambling System

We all know that Las Vegas was built with gamblers’ losses. The casinos love gamblers who think they have foolproof systems. So, when I was introduced to a new system for playing the dice game craps, I first ignored it. Then after hearing more, I decided to simulate it to prove that it is worthless. The amazing thing is that I didn’t get the results I expected.

The system involves only playing the simple pass-line in craps; it ignores all the other more complicated bets. It’s well known that the odds of winning this bet are 244 out of 495. So, out of 495 plays you expect to lose 7 more times than you win. On each bet, you either double your wager or lose it. So, after 495 plays, you expect to be down by 7 times your bet size.

I wrote a little simulator for craps and tested it first on a simple case. Start with $10,000 and wager $100 at a time and see what happens after many bets. The expected result is to lose all your money, eventually. With a bankroll of 100 times the bet size, the expected number of bets before losing all the money is

100 x 495 / 7 = 7071.

I ran a million trials on my simulator. In every single one of them all the money was lost eventually. The average number of bets before the money ran out was 7066, which lines up nicely with the expected answer above. There was some variation, though. The shortest trial was 344 bets, and the longest 110,188 bets.

So far, everything was going according to theory.

The System

Then I tried simulating the new craps system to prove it doesn’t work. The system involves starting at $100 bets and adjusting the next bet size based on the previous result. When you win, you bet a dollar more the next time. When you lose, you bet a dollar less the next time. Another rule is that you never put more than 1% of the bankroll at risk each bet (rounded down to the nearest dollar).

The result I expected was that the betting would stop when the bankroll hit $99 and the next bet size became $0 because of the 1% limit rule. However, that’s not what happened.

On the first simulation, after 100,000 bets, the bankroll grew to $510,610! This was totally unexpected. How could the bankroll grow so much? I decided to run 10,000 simulations of each of 4 cases: 1000 bets, 10,000 bets, 100,000 bets, and one million bets. Here are the results:

1000 bets: $8715
10,000 bets: $6580
100,000 bets: $598,949
1,000,000 bets: $85,587,100!

The system starts out losing money, but then gradually begins winning and produces explosive growth. It takes a while, but this system would eventually break a casino.

As many have guessed already, this post is an April Fools joke.  However, the simulation results are real.  See tomorrow's post for an explanation.