Negative expected value in gambling ·
Further reading — Module 04
Compound Interest in Reverse
Most people understand what happens when a small positive return is repeated over time. At first, the difference barely seems worth noticing. Given enough repetition, it becomes difficult to ignore.
Gambling has its own version of that principle.
When the expected value is negative, repetition works in the other direction.
01 — The familiar idea
Small percentages become powerful through repetition
Compound interest is powerful because a relatively small percentage can produce a much larger effect when it is applied repeatedly over time.
The individual percentage may not look dramatic.
It is the repetition that changes the scale.
That same idea provides a useful way to think about negative expected value — but with an important difference.
02 — Turn the sign around
What happens when the advantage is negative?
Imagine a gambling proposition with an expected loss of 5%.
That does not mean every £100 wagered will produce a £5 loss. Individual results can move sharply in either direction.
It means the mathematical expectation is a £5 loss for every £100 wagered.
As the amount wagered increases, so does the expected loss.
The same 5% negative expected value applied to increasing amounts wagered.
This is not compound interest in the literal sense. The stake does not have to grow, and previous losses do not have to be reinvested.
What grows is the exposure to the same mathematical disadvantage.
03 — The number that matters
Turnover, not the next bet
A player might sit down with £100 and choose to bet in £10 stakes.
Ten £10 bets would be £100 of turnover — but that does not necessarily mean the £100 has gone.
Some bets will win. Some will lose. Money returned from winning bets can be wagered again.
So the same £100 bankroll can generate considerably more than £100 of total wagering.
A £10 stake placed 100 times creates £1,000 of turnover, even though the player may never have had £1,000 in front of them.
At a 5% negative expected value, £1,000 of turnover represents an expected loss of £50.
The bankroll did not need to be £1,000.
The turnover did.
The view from behind the tables
From behind the tables, we watched players arrive with a few hundred pounds and gamble for hours, staying beyond dinner times and bedtimes, cycling money they had won back across the tables again and again.
For some, the hard stop came only when there was nothing left to bet.
The player watched the balance.
The house watched the turnover.
Final thought
Think back to your last night in a casino. How much did you really gamble?
How much money did you actually expose to that negative expected value?
Was it the money you started with?
Or the total amount you wagered as money was won, returned and wagered again?
What was the expected value on everything you turned over?
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