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

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.

But iPerm you can bet min RM1, isn't it? Based on your post.

Cos the payout for starter and consolation is RM8 and RM3 for RM1 bet. It is supposed to be RM7.50 and RM2.50, if divided by 24.

Which means BJTOTO give RM0.50 more prize money, which means it is better value. Meaning RM8*24 = RM192 and not RM180.

Am I wrong, here? Please correct me on the iPerm min bet as I derived the info from your post.

I'm not saying will win. I'm saying if you're gonna buy, better to buy with iPerm24 due to slightly higher payouts. Meaning you get better value for money.

Like saying you want to buy cigarettes. 7- 11 sell RM15, kkmart sell RM14.50. Since you're going to smoke anyway, better smoke the cheaper cigarettes.

If still have to bet RM24, why the payout shows RM8 and RM3?

I'll analyze this weekend if I have time.

From gambler's perspective maybe not worth it. But mathematically speaking better value.

Yes I agree. If value is not a factor and I'm only going big or go bust, I'll definitely buy 1 number and bet my firstborn.

More like tens of million to one. Billion to one nobody will play because payouts will be very rare.

Of course. You can't have both ways. Lower probability, higher payouts, and vice versa.

We use expected return/value to make comparisons between probability and payouts to find what is the best value for money.

Like why some prefer to play slots while others play baccarat in casino.

Slots have lower probability but can one shot win big, whereas table games higher probability but hard to win big with small bet.

That's why number games appeal to the public more. The majority of people prefer to risk a small amount for the miniscule probability to win big.
However, in the end only the casino or house wins, due to the law of large numbers.

In short, more people prefer to have 1% chance to win RM100, than 50% chance to win RM2.

Double post

This post has been edited by kelvinlym: Apr 6 2017, 02:55 PM

Yes, simplicity is also a factor. Like why there are no craps tables in most casinos any more.

Games must balance simplicity, fun, reward and risk. It's an art by itself.

ALL lottery games are negative value. If positive then there will not be any of these games on offer. People will find out and exploit it.

Take blackjack for example, remember the MIT guys who counted cards. They were working with about 1 or 2% positive value. But they could identify when it's positive, so they bet big when value is positive.

In short, positive value games in lottery are non existent.

That's the reason I rarely play these kinda games. Only once in awhile like the Eurojackpot when the pot goes up to max and trickles down to the lower levels.

Purple Haze is my favorite.

Yeah, that's the problem with all games. In the end the house always wins.

Thanks for the feedback.

The expected return metric does not mean a better chance. It means that for every RM1 bet you make, you are expected to lose RM0.28, instead of the other systems where you are expected to lose more.

Also, your calculation is flawed because you are comparing a RM1 bet on 1 number 1234 with RM24 on iPerm.