# Winning the game

Ostensibly, this article is about investing for retirement. “Winning the game” essentially means that you have saved enough to fund a decent retirement. Without going into details (what means “decent retirement” and “enough”), I will discuss a gambling analogy. Why the house wins, and the difference between expectation value of the game and the probability of winning the game. Once the reader understands those differences then I shall show how it applies to retirement funding.

## Expectation value

Statistically, the expectation value of a random event is the sum of the product of the payouts (Pi) times the probability of that payout (pi), summed over all possibilities, i. For simplicity’s sake here, I will limit the games to win/lose so the expectation value collapses to the probability of winning times the payout – no sum needed.

As an example, consider a roulette wheel: one that is fair; contains 50 consecutive numbers, (no 0 or 00); pays 48 to 1 on the number that hits; and the player always forfeits the bet. Players may only bet on numerical outcomes – no red/black, odd/even or any group bets. This game has a slightly lower house advantage as compared to Vegas style roulette (4% v 5.3%). Since this paper is about investing, not gambling, I have changed the game a bit just to make the math simpler – it does not affect the overall result.

Clearly, at this wheel, a gambler makes a \$1 bet on a number and has a 2% chance of winning. The expectation value of winning is \$0.96 (0.02*\$48). Of course we have to subtract the cost of betting – and that is \$1 as the gambler always forfeits the bet. The net result is the house wins \$0.04 for every dollar bet.

In Summary, the gambler expects to lose 4% of his bet each and every time he spins the wheel. I shall rely on this example throughout this analysis.

## Probability of winning.

Given the preceding, one wonders (not inappropriately) why anyone gambles. Well, besides the camaraderie and free drinks, there is excitement. Obviously if the house just took all the bets and returned 96 cents to each of the gamblers, no one would ever win, there would be no excitement, and Las Vegas would still be a small train/truck stop in the desert.

However, consider a game where 50 gamblers show up to the roulette wheel, and each bets a dollar on a different number. The wheel spins and the result is straightforward – the house wins \$50 from the 50 initial bets (remember all bets are forfeit), and pays \$48 to the one winning gambler. The house advantage is 4% (\$2 win of the \$50 bets). Of the original 50 gamblers, one of them is a winner. Probability of being a winner is 2%.

Now, let’s spin the wheel again. Each gambler bets the same number; another 50 bucks is bet, and another gambler wins (there is a 4% chance that the same gambler wins again – but let’s ignore that). The net result after 2 spins is the house is up \$4; two gamblers are up \$46 (they have bet 2\$ and won \$48); and each of the remaining 48 gamblers is down \$2.

If luck should continue in this way (a new number comes up each spin), Then after 30 spins, the net result is

1. There are 30 winners at the table. Each has won one spin for \$48, and lost a dollar on each of the 30 spins. Net result 30 gamblers have won 18\$ each.
2. The House has won. It wins \$2 on each hand and is therefore winning \$60.
3. There are 20 losers at the table. They have bet a total of 30\$ each and none has won.

Here is where things are interesting. Over half the gamblers think they are winners (why not, they are). And yet the house is winning.

Is this a likely outcome? No, we have ignored the possibility of the same player winning twice. But, This is the basic idea behind designing a table game. Make sure that the house has an advantage and ensure that there are plenty of winners around the table.

### Can you win at gambling?

Clearly, given this roulette game, the house will win. That is a result of the expectation value. But, with plenty of players as I set them up, there is also a guarantee that there will be at least one and likely many winners after 30 spins. That is despite the negative expectation there is still a significant probability to win.

And therein lies the difference between the expectation value of the game and the probability of winning the game.

But, if you want to win – you must walk away.

When I stated that the winners must walk away, I don’t mean leave and come back later with a different stake, I mean leave and never return.

My mother (among many others) sincerely believed (bless her heart as she passed away a few years back) that taking her winnings home today and returning tomorrow helps her to win. It doesn’t. If your expectation value is negative, there is no way to win if you continue to gamble. The house keeps taking money out of the game, so if you keep playing sooner or later all of the money ends up with the house. The only way to win is to be among the early winners (that is, be lucky) – and leave.

Please note that early winners are not likely to become losers because lady luck “remembers” or is fickle. These people are likely to be losers in the future because everyone at the table is likely to be a loser if they play long enough.

### What has this to do with retirement investing

Well, first off let’s note that generally speaking the market is not a zero sum game. Two investors (gamblers) can each invest 100 dollars and while the markets rise 10%, one can walk off with \$108 and the other with \$112 (neglecting the brokerage fees). As you can see there is a clear “winner” and “loser” – but even the loser comes out ahead.

Many people have written that timing the markets is not possible – it is almost certainly not advisable for the average investor. That being said and assumed true for this analysis, it does not mean that there are not winners and losers.

Yes, if everyone invests the same amount in the same things at the same time sure everyone will walk away with the same earnings. But that is not the case – whether someone has tried to time the markets, or just times their vacations differently. Different careers, different start dates, marriage, home buying, job changes etc. all effect the timing and size of investments. Not everyone will get the same outcome over the same time range and not all investors are invested over similar time frames.

Since the outcomes, on average should turn out to be very similar over time, and there is variability to the outcomes, there are certain to be winners and losers.

I was very lucky to begin my career in 1985. I had very little in the markets on Black Friday in October 1987. From 1987 through 1999 I invested significant amounts into both personal savings and retirement savings. As the markets boomed from the Black Friday crash through the end of the century (the Dow jumping nearly a factor of five) my savings showed significant gains.

Whether I did better or worse than the average investor of that time frame is irrelevant – that time frame was a winner compared to most (all?) time frames. The end result is that I had more savings after a 14-year career than many would have after a 30-year career. I sure felt like I played and won.

### Winning the Game

What is an investor (gambler) to do if he wants to be a winner – walk away. And stay away.

Equity markets are much like casinos. As pointed out above, they are not necessarily zero sum games – in fact everyone can lose or win. But, much like the gambler, if you want to win – you have to be prepared to walk away.

Sure, you can get started in the markets, happen to be lucky by starting investing just as the markets decide it is time to grow rapidly (1987-1999). But if you had hung on in 2000 you would have seen much of your winnings evaporate – and probably would have been worse off by the spring of 2009.

In fact, according to an SP500 return calculator (https://dqydj.com/sp-500-return-calculator/) your return (including reinvested dividend) for investing from March 2000 through March 2009 would have been negative 5.3%. Continuing to hold through on through March 2019 would have resulted in a gain of “only” 5.6% per annum. In January of 1990 thirty year treasuries could be purchased that were guaranteed to yield around 6.5%.

If you got out in 2000 (as I did), is that market timing? Not really. If you walk away and don’t come back, all you have done is won. There was no “timing” to enter the markets – it was just luck. Exiting the markets required no knowledge of the future markets direction, no belief in the markets “reverting to the mean”, just an analysis that I had indeed won.

The only “risk” I took by exiting the markets with a lifetimes worth of gains (after a 14 year career) is the fear of missing out (FOMO) had the markets continued to climb.

Today offers another opportunity for the markets to produce winners. From October 1987 to January 2000 the markets generally had a five-fold gain. A similar trend started in February 2009 with the markets starting near 7000 and sitting around 25000 today – a 3.5 fold increase. If you had begun your career in 2008, you would have lost a large fraction of your initial – but very small savings. From 2009 onwards you would have experienced serious outsized gains.

It is very likely that a person that began putting 10-15% (say 10k) of his yearly earning into retirement savings might have a quarter million dollars in the market today. For a young person (probably circa 40) to have that level of savings is definitely a win.

The average 401(k) balance for 60-69 year-olds (as of the beginning of 2019) is 180K. The median is only 63K – and this lucky individual has amassed 250K by age 40. Yes, he has saved (whereas most of his colleagues have not) but he has benefited from luck by entering the markets at the right time – a time that he didn’t chose but rather was thrust upon him.

If during that time frame you had saved “enough” then maybe it is time to claim a win. Take your money and depart the markets for lesser but more secure pastures. Even if that 250K or so is insufficient lifetime savings, the investor should consider “locking in” the gains, getting into some seriously more secure savings vehicles.

## What to do with the winnings

Well, if you walk away, you must do something with your winnings. These are several opportunities that can essentially guarantee an outcome – without the risk of losing (or winning): Annuities, Bonds, CDs, or savings accounts.

Equity markets are not the only game in town. Bond markets can now, have in the past, and probably will in the future, offer reasonable returns

Bond markets (CDs, savings accounts etc.) come with their own set of risks (creating winners and losers) but the earnings and the variations are smaller. Sticking with insured or government bonds essentially guarantees your earnings without risking losing (or winning). They won’t beat the markets on average but they are unlikely to lose money. Further, if you invest in TIPS you are not even likely to lose money to inflation.

Again, as with the equity markets you might feel like you lost when the markets move higher (FOMO) but remember – you won that game. If you feel like you won (like I did) bond markets may possibly the best game in town.

Current long term interest rates are around 3%. If the young man (that started his career in 2008) takes his 250K and invests in 3% return bonds and continues to save 10 – 15% of his earnings he could have more than half a million dollars retirement account in 15 years (at age 55). That is certainly likely to be on the high side of retirement balances when he retires.

Even if he saves no more outside of the 250K – by age 65 he will have nearly a half million saved.

That’s a win – with essentially no risk of losing.