# Chances

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.