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Dicing with death

The most popular game in Pension City UK – the gambling capital of the world – is very straightforward. In its simp lest form, it involves rolling a single die until you get a one, when the game stops. For each throw, you rec eive £163;1,000. So, if you get a one on the fourth throw, you get back £163;4,000.

The companies in Pension City employ mathematical exp erts to calculate the stakes for such games. These exp erts have calculated that the average amount paid out to gamblers is £163;6,000, so the stake is set at that level plus a bit more for costs and profits (which we will ignore from now on).

Of course, not all the gamblers in Pension City get £163;6,000. One in six gets only £163;1,000 and most people are out by the fourth throw. However, about one in eight at least double their money. Those lucky enough to stay in the game for a long time benefit from the losses of those who go out early.

The real-life equivalent of this game is the level single-life annuity. The principle is the same – those who live for a long time benefit from the misfortune of those who die soon after retirement.

There are many variants of the basic game. One guarantees you a minimum number of throws even if you get a one early on while another inv ol ves throwing two dice until you have thrown a one on both. Of course, the stakes are higher for these games than for the basic one.

Under another variant of the game, the payment inc reases with each throw. For your stake of £163;6,000, you receive £163;500 for your first throw. However, this increa ses by £163;100 for each throw, so you get £163;600 for the second, £163;700 for the third and so on. Those who are out early rec eive much less than under the basic game but those who are lucky get a lot more.

About one in 40 will get back over five times their stake. The break-even point compared with level payments comes at the 11th throw, which is long after most people are out of the game.

The real-life equivalent is the escalating annuity. Again, the dynamics are similar. You must exceed your life exp ec tancy to be better off with an escalating annuity than with a level one. But for those who live to 100, it is spectacularly better value (see Table One below).

A fairly recent development in Pension City is a game where payments are not fixed in advance. Instead, you throw two dice. As before, as soon as you throw a one with the first die, you are out. The other die decides how much you get for each throw.

For a £163;6,000 stake, you start with a nominal payment of £163;700 for the first throw. The payment for subsequent throws may increase or dec rease dep ending on the number thrown with the second die. If the number is a three, the payment is unchanged. However, if you throw four, five or six, it inc reases by £163;100, £163;200 or £163;300 respectively. But if you throw a two or a one, it decreases by £163;100 or £163;200 respectively.

So, if you throw a five the first time and a two the second time, your payments would be £163;900 and £163;800 respectively. Chance does not just determine how long you stay in the game but also how much you get for each throw.

This time, the real-life equ iva lent is an investment-linked annuity, either with-profits or unit-linked. This offers pros pects of increasing payments if returns are good but with the risk that payments could fall in bad times.

The latest game in Pension City has been devised in res ponse to punters who were unhappy at losing so much if the first die went against them. They argued that they should be able to draw payments from their stake at each throw, with the subsequent amount increasing or decreasing with the value on the second die. When the first die came up one, they should get back the rem ainder of their stake rather than the pension company keeping it.

The authorities were slig htly uneasy about this new game but deci ded to allow it as long as it was chan ged to the more conventional game after the third throw.

The first group of punters received a nasty shock when they conver ted to the traditional game. It so happe ned that the second die came up three each time, so it had neither increased nor decreased their pots. Having paid their £163;6,000 stakes, they withdrew £163;1,000 on each throw, exactly what they would have got in the original game. They therefore expected to receive £163;1,000 a throw in the future.

However, the companies pointed out that only £163;3,000 was left for each punter after the withdrawals, so they only offered £163;500 a throw after the game reverted to the basic version. The punters had not ris ked the heavy losses of those who went out of the game early and that was reflected in their future payments.

This new game is equivalent to income drawdown and the unwelcome shock for the punter is mortality drag. If you die during drawdown, your fund is not lost as it is available to your dependants as cash or an annuity. But the other side of the coin is that, if you survive, you do not benefit from the cross-subsidy from those who have died. So, you need an extra return on your money(see Table Two below).

Which option is best for an individual from a mortality viewpoint depends heavily on their individual circumstan ces, including their health and whether they have dependants. But, whatever option is chosen, the risk must be clea rly explained.

They may not get good value if they buy an annuity and die quickly. On the other hand, they could end up with a lower ultimate pension if they defer annuity purchase.

While a level annuity may give the highest starting inc ome, an escalating annuity may be better value in the long run because it gives some protection against inflation.

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