Given all the hoohah about gambling, casinos and counseling on compulsive gambling – I believe nothing beats the power of pure demonstration of payoffs from the games using Mathematics. I hate gambling, not only because it is a vice but also how it epitomizes people’s ignorance of the workings of probability and chance. Perhaps I should have a little lesson teaching people how to calculate their payoffs from their bets. I’ll just use 4-D as an example. Betting on ‘Big’ will yield the possible prizes: 1st – 2000, 2nd – 1000, 3rd – 490, Starter – 250 & Consolation – 60. Betting on ‘Small’ yields 1st – 3000, 2nd – 2000 & 3rd – 800. Note that the numbers are the rewards on a dollar stake, which means winning consolation would yield 60 times your capital (stake), when betting ‘Big’.

So in effect, betting ‘Big’ on a single number would yield payoffs calculated as follows:
Payoff: Reward – Cost (stake)

Payoff from 1 dollar bet on ‘Big’: 0.0001 X (2000 + 1000 + 490) + 0.001 X (250 + 60) – 1 = -0.341

Note that the net payoffs of lottery is almost always negative (unless the lottery organization is a sucker) and for a dollar bet, the net loss in this case is about 34 cents. This means long term betting of $10 on the same number for ‘Big’ would produce expected loss of $3.41 and so on.

How about betting ‘Small’? The payoffs are worse (a greater loss):

Payoff from 1 dollar bet on ‘Small’: 0.0001 X (3000 + 2000 + 800) – 1 = -0.42

Needless to say, this mathematics should be simple enough for grown-up gamblers to understand. They are basically feeding the lottery staff with their compulsion and I guess this doesn’t really differ much from contributing to corrupted charity organizations. So what sets [lottery] gamblers apart from fools? I guess nothing much.


  1. this is purely probability. which means it will only approach your calculations when the sample size increase(you bet a lot of times.) So, who knows if you are lucky and manage to win with just a small size? Then wouldn’t the payoff be worthwhile?

  2. In fact, the sample size is assumed to be infinite in all probability calculations; but that’s not to say that we should ignore the results of such calculations grounded on mathematical reality. To say ‘what if you are lucky’ is to be ignorant of probability – you probably know there’s a chance you get strike by lightning in the open even if there’s no rain, no matter how slim it is, so going by your theory of ‘what if’, isn’t the best bet to stay in shelters all your life?

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