This is a post to discuss the mathematics behind Sports Toto 4D as well as other 4D games and lotteries. The honourable advocado has a post at https://forum.lowyat.net/topic/4231708 which explained in detail the games provided by Sports Toto with the rules and payouts.

This post is to shed light on the odds, risks and strategy of these games, for better understanding to punters.

I will try to explain the mathematics, hopefully in simple English. I'm by no means a mathematician, so if my mathematics are wrong, please point it out. Constructive criticism will be accepted, useless comments ignored.

First things first.

1. It is assumed that the numbers being picked are random and not pseudo random.
2. I do not condone nor condemn gambling. This is purely from a mathematics perspective and to give punters a well-informed decision to improve their strategy and money management.

I'll start with the normal 4D games.

1. Rules and payout/prizes please refer to https://forum.lowyat.net/topic/4231708

2. There are 10000 possible combinations, therefore the odds to hit straight up is 1 in 10000 or 0.0001 or 0.01%. But there are numerous prize levels and payouts based on the prizes, therefore it's not 0.01% to win something (with these odds, no one would be playing).

3. Let's go with the calculation. We normalise the bets to RM1, which is the smallest denominator we can play (and for easier calculation).

4. We look at expected return for each RM1 bet, then when we compare what we expect to get, we'll know which strategy to go for (or rather which strategy has more value.



5. If you buy the BIG bet, your odds to win something, anything is 0.23% (cell E8). But because there are varying prizes, your expected return is -RM0.36. In layman terms, every time you bet RM1, you expect to lose RM0.36 to TOTO. This is also the profit that TOTO makes per bet (before expenses, taxes etc).

6. For SMALL bet, the odds are smaller to win something, which is 0.03%, and expected return is about the same -RM0.35

7. For better value for money, the SMALL bet is the choice, but you will see less chances to win something, but when you win, you win more. The RM0.01 difference is for TOTO to offset the higher cost of more people claiming prizes for the BIG bet.

Calculation (Google Sheets)

Next we move on the iPerm bets, where things get much more interesting.



1. The expected value is -RM0.28 for the BIG bet. Why the big discrepancy? This is because of the Starter and Consolation payouts. TOTO does not want to bother with cent payouts, therefore they pay RM8 and RM3 for those prizes instead of RM7.50 and RM2.50, which is RM180/24 and RM60/24 respectively.

2. For SMALL bets, there are no differences.

Strategy: Buy iPerm 24 BIG bet to maximise your value. You will see later that other iPerm bets will not match the iPerm 24 BIG bet.

Here are the rest of the iPerm bets.

iPerm 12



iPerm 6



iPerm 4



TLDR: Buy iPerm 24 BIG.

I'll analyse the Jackpot games when I have time.

This post has been edited by kelvinlym: Apr 6 2017, 01:47 PM

Don't bluff la

They deducted 80RM from prize 200RM

40% tu

I like where this is going. Parking dulu.

Just tell what number will win.

odds are 1 thing
you will never kena 1 is another thing because everything is arranged

This Saturday apa number for 1st Prize?

all betting is losing $$$ , don't bet

As long don't buy is 0% chance to win

Huat ah

actually dont need to calculate expected return, just calculate total payout then can know buying small is better value in long term. many layman doesn't understand what is expected value.

and i am sure the toto number generator is completely random, not pseudo random, if pseudo random then people will make money out of it already.

Go buy gaming company shares better than betting.

just tell me which no to win.. tldr

Parking

How abt Da Ma CAI?

Yeah, but iPerm 24 BIG has the best value. Small does not differ much from BIG bets.

I agree with the random generator comment. But some people still try to look for patterns and some swear by it.

There is so such as thing as true random. If you can figure out how the the number generator generate numbers, you too can be rich.

Gambler fallacy at work.

*puts tissue paper on table*

But, Daddi no Kasi. How?

Great discovery...

So Iperm 24 BIG is basically just invest RM24 for any number kah?