Apologies in advance for a long post. Because most people probably won't bother reading it, I'll say up front: don't invest €100 or €1,000 in Prize Bonds and expect to win anything. You almost certainly won't.
I said elsewhere on this thread that if you don't understand the odds, Prize Bonds are not for you. Understanding probabilities does not seem to come easy to many people. There is also the fact -- well documented by psychologists in many studies -- that we tend to be over-optimistic about the risks we take.
Let's look at some of the objections. Dublin had a 95% of beating Donegal in the football. If you'd bet on them you would have lost your shirt. Actually, the
best odds offered by Paddy Power were about 91% ( = 10 to 1 on). The total odds given for the three possible outcomes also sums to 109%, so if the odds offered reflect the actual amounts of money laid (which they will -- it's a bookie!), Paddy Power have a 9% margin no matter which way the cookie crumbles.
Prize Bonds differ from this in two crucial ways. First, the margin is in the punter's favour. The Prize Bond company pays out more than it takes in, since a percentage is paid out in prizes and the bonds themselves are always redeemable. Of course, there are the important matters of inflation and the opportunity cost versus other investments, but the point remains -- you can't "lose your shirt".
The second, and perhaps more important point (and certainly the least understood) is that, unlike Dublin vs. Donegal, you are not betting on a single event. Bear with me, and consider the following. Suppose you had €100k to invest and you knew you could get 2.5% return on deposit. Someone comes to you and says: "Instead of putting the money on deposit, lend me your money for a year. At the end of the year I'll give you your money back. We'll also flip a coin. If you win the toss, I'll give you a €5k bonus, otherwise you just get your €100k back and no bonus". Well, it's easy to see that this is the same as taking the €2.5k you would have earned on deposit, and betting it on the flip of a coin to either double it or lose it. Would you bet €2.5k on a coin toss? Probably not.
Now let's change the scenario. Instead of one coin toss at the end of the year, we'll have a hundred coin tosses and divide the €5k bonus across them. For every one you win, you get a bonus of €50. You get nothing for each toss you lose. You can still win a maximum of €5k. Are you gambling away your €2.5k on a coin toss now? Not at all. Clearly things are different. The most likely outcome is that you will win 50 coin tosses and get a €2.5k bonus, the same as your deposit rate.
Now, here's the bit that's really hard to understand. Even though winning 50 out of 100 coin tosses is
the most likely outcome, it is still
a very unlikely outcome. The odds are only 8%, or less than one in twelve. But here's the thing: you also have a slightly lower but still nearly 8% chance of winning 49 tosses, or 51 tosses. The total chances of getting between 49 and 51 wins adds up to nearly 25%, or one in four. This give you a decent chance of getting only slightly worse, or slightly better than your 2.5% return. But of course, the same applies to 48 wins or 47 wins or 52 or 53. With a hundred tosses there is a great chance you'll get
near the average return (higher or lower) even though the chances are quite low that you'll get
exactly the average return.
What if, instead of 100 tosses, there were only 10, or 5, or 2? Well then the odds get "lumpier". We know that for a single coin toss you are basically gambling on an evens chance. Heads you get €5k, tails you get nothing. For two coin tosses worth €2.5k each, you have one chance in four of winning nothing, one in four of winning €5k, and two in four of winning €2.5k (on either the first toss or the second toss). With more and more tosses, and dividing the prizes up evenly across the tosses, the odds of an "average" return get better and better. You become less and less likely to get no return at all, or the maximum possible return.
So, to understand Prize Bonds, you have to understand that the amount you invest determines the "number of tosses". On one Prize Bond or 100,000 Prize Bonds, you will get the same percentage return in the long run -- but it might take thousands of years with the single Prize Bond. You are much more likely to get an average return with the higher number of Prize Bonds.
So with all that said, let's go back to the specific objections raised:
The likely returns on prize bonds are dependent on the amount invested.
That can't be right, the probability of winning is the same no matter what amount is invested.
Yes, you are right, the
percentage return will be the same in the long run no matter how much is invested. But to get that percentage return in a timeframe of one year, or any other specific timeframe, the odds of achieving it with a low investment are negligible. You'll get your money back some day, but humans have a limited investment time horizon by definition. The "odds" I am talking about are not the betting odds, which are the same for everyone as you say, but
the odds of getting the average return in a given timeframe. That's a completely different thing -- the "likely returns" versus the returns that are guaranteed as long as you have an infinite amount of time to wait.
This is why the Casinos win and the Punters lose.
Casinos win because, like Paddy Power, they have a margin on the odds. For example, they pay out evens on red/black at roulette but the actual odds
aren't evens because of the green zeros. They understand that although they could lose -- every now and again someone beats the house over a single evening -- in the long run, over literally millions or billions of games, they cannot lose. They will get their guaranteed percentage. The same is true of Prize Bonds. In this case the margin is in your favour. Over billions of draws, you will get your guaranteed percentage. However, if you have one Prize Bond it will take hundreds of years for it to be entered in billions of draws. If you have €100k in bonds, you get entered in 16,000 times more draws than a single bond. This does not change your average percentage return, but it dramatically changes how long it takes to achieve it.
95% != 100%......Dublin had a 95% chance of beating Donegal today.....
Yes, but even with the odds heavily in your favour there was still an appreciable chance that you would lose everything. You cannot lose everything on Prize Bonds. Not only that, but when I say there is a 95% chance that you will beat the deposit rate if you put €100k into Prize Bonds, I don't even mean there is a 5% chance that you will get zero return. In fact, your chances of getting at least half the net instant access deposit rate are 99.99%. There is a negligible 0.01% chance of you getting less than half. Don't forget the upside odds too. As well as a 95% chance that you will get at least the instant access rate, there is a 5% chance that you will get double that. And there is a nearly 50% chance that you will get one and a half times the instant access rate.
I had a large four figure sum in Prize Bonds for several years and never won a cent. I'm pretty sure the 95%+ you mention is inaccurate.
This is a total misunderstanding (albeit a completely common one). The numbers I quoted are for €100k invested. How many people noticed I was talking specifically about €100k and
only that amount in the previous paragraph? I reckon no matter how many times I say it, nearly everyone looks at that and, like you, thinks "wow, he's saying I have a 95% of getting a better return from Prize Bonds than on deposit". They leave out the €100k which is completely crucial to the calculation. Your odds for a "large four figure sum", lets say €5k, are completely different. You have a nearly one in three chance of getting
nothing at all in a given year. (Incidentally, the comparison to the demand deposit rate is different too, because you can get a better rate on €5k than €100k -- the banks limit the amount on which they pay better rates).
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The calculations for working out your likely returns for any given investment in Prize Bonds are complicated. (I'll happily show the maths here if anyone is interested. I also have a spreadsheet, but you'll need Excel 2010 or later with macros enabled -- I use macros for Stirling's approximation for large factorials. You'll also need at least a decent grasp of arithmetic to understand what the spreadsheet is telling you, even if you don't care about the underlying maths). Unfortunately you can't just do the calculation once and extrapolate from one amount, say €100k, to another, say €5k. You can't just divide by 20 -- it's a different calculation in each case. There are some graphs for different amounts earlier in the thread.
Disclaimer: I haven't invested in Prize Bonds myself, but only because of extenuating circumstances. I'd happily invest a large 6-figure sum, and may well yet do it. I definitely wouldn't do it with a 4-figure sum, or most 5-figure sums, for the reasons outlined above. Hence the warning in the very first paragraph. But for my large 6-figure sum I'd happily bet anyone here that I will do as well or better than the demand deposit rate after tax. The odds are better than twenty to one in my favour.