14 Secrets to Win Singapore 4D Revealed!

Secret #1
Probability of any direct 4D combination is 23 / 10, 000 or 1 / 434

Secret #2
The actual median for 4D is 288 draws, or 2 years. You will have a 50%
strike rate when you buy 4D direct numbers within the last 2 years.

Secret #3
ABCD number make up of 24 different permutations. As such, the
median is 288/24 = 12 draws (1 month).

Secret #4
AABC number make up of 12 different permutations. As such, the
median is 288/12 = 24 draws (2 months).

Secret #5
AABC may have twice the payout of ABCD numbers, but ABCD have a
higher frequency of striking.

Secret #6
4D may be random but there is always a pattern and trend behind it at a
particular stage in time. In other words, it follows some loose
mathematical law.

Secret #7
Each person learning curve, risk appetite and perception is different.
You will have to find your own comfort zone in putting $$$ down on a
number.

Secret #8
Be happy. Be positive in your outlook and thinking. Avoid anything
negative at all. Negative words, actions and even thinking will strongly
affect your chance of striking 4D. If that happens, any super duper
system isn‟t going to work.

Secret #9
A negative attitude and thinking will only breeds more its same kind (as
in positive attitude and thinking too). It is a vicious cycle that isn‟t going
to do no one any good at all. Don‟t get caught in it. When you are
unhappy, angry, worried or even sick, don‟t gamble.

Secret #10
We need patience and perseverance when the going is not that
smooth, the financial ability to weather through the inevitable bad-luck
stretch occasionally before we can see hits happening.

Secret #11
Law of probability dictates that selecting numbers from a higher
frequency is better than those in the lower percentile.

Secret #12
A win is a win. Whether it is a big win or small win, it is important to
keep the winning streak alive. Maintain the flow and it will be a matter of
time when the Big Win comes.

Secret #13
In any game of chances, there will be periods of „dry spells‟. It is that
unavoidable cycle that every 4d punter loath. The only thing you can do
is to scale down your bet during this period of time. There is nothing
you can do about it; got to bite the bullet when it comes.

Secret #14
Have certain guidelines in place for your 4d investment strategy. Scale
down your bet when the going is tough but when the hits start coming
back, then it is business as usual.

What are the odds of winning Toto?

4D-stats-768x402

TOTO Odds

Recall (from the Combinations section) that the number of ways in which r objects can be selected from a set of n objects, where repetition is not allowed, is given by:

Crn=n!r!(n−r)!\displaystyle{{C}_{{r}}^{{n}}}=\frac{{{n}!}}{{{r}!{\left({n}-{r}\right)}!}}Crn=r!(nr)!n!

We can write (and type) the left hand side more conveniently as C(n,r).

Now let’s look at the probabilities for each prize.

Group 1 (Choose all 6)

The odds of winning the top Group 1 prize are 1\displaystyle{1}1 in C(49,6). That is:

1C(49,6)=113,983,816\displaystyle\frac{1}{{{C}{\left({49},{6}\right)}}}=\frac{1}{{{13},{983},{816}}}C(49,6)1=13,983,8161

=7.15×10−8\displaystyle={7.15}\times{10}^{ -{{8}}}=7.15×10−8

That is, there are 13,983,816\displaystyle{13},{983},{816}13,983,816 ways of choosing 6 numbers from 49 numbers but there is only one correct combination.

So there is 1 chance in 13,983,816 of getting the Group 1 prize.

This means we have to buy almost 14 million tickets (at a cost of $14 million) before we can confidently say we will probably win the top prize…

Group 2 (5 + additional)

Odds:

C(6,5)×C(43,1)C(49,6)×143\displaystyle\frac{{{C}{\left({6},{5}\right)}\times{C}{\left({43},{1}\right)}}}{{{C}{\left({49},{6}\right)}}}\times\frac{1}{{43}}C(49,6)C(6,5)×C(43,1)×431

=25813,983,816×143\displaystyle=\frac{258}{{{13},{983},{816}}}\times\frac{1}{{43}}=13,983,816258×431

=12,330,636\displaystyle=\frac{1}{{{2},{330},{636}}}=2,330,6361

=4.29×10−7\displaystyle={4.29}\times{10}^{ -{{7}}}=4.29×10−7

Explanation: We chose 5 of the 6 winning numbers [C(6,5)], and chose the correct “additional” number from the 43\displaystyle{43}43 remaining numbers that did not win anything [C(43,1)].

There is 1\displaystyle{1}1 chance in 43\displaystyle{43}43 that we chose the additional number, so multiply by 143\displaystyle\frac{1}{{43}}431.

So there is 1 chance in 2,330,636 of getting the Group 2 prize.

Group 3 (5 correct)

Odds:

C(6,5)×C(43,1)C(49,6)×4243\displaystyle\frac{{{C}{\left({6},{5}\right)}\times{C}{\left({43},{1}\right)}}}{{{C}{\left({49},{6}\right)}}}\times\frac{42}{{43}}C(49,6)C(6,5)×C(43,1)×4342

=25813,983,816×4243\displaystyle=\frac{258}{{{13},{983},{816}}}\times\frac{42}{{43}}=13,983,816258×4342

=155,491.3\displaystyle=\frac{1}{{{55},{491.3}}}=55,491.31

=1.80×10−5\displaystyle={1.80}\times{10}^{ -{{5}}}=1.80×10−5

We chose 5 of the 6 winning numbers and chose 1\displaystyle{1}1 number from the 43\displaystyle{43}43 remaining numbers that did not win. In the Group 3 prize, we cannot include the “additional” number, so we need to multiply by the probability of the remaining 43\displaystyle{43}43 numbers not containing the additional number, which is 1−143=4243\displaystyle{1}-\frac{1}{{43}}=\frac{42}{{43}}1431=4342.

So there is 1 chance in 55,491 of getting the Group 3 prize.

Group 4 (4 + additional)

Odds:

C(6,4)×C(43,2)C(49,6)×243\displaystyle\frac{{{C}{\left({6},{4}\right)}\times{C}{\left({43},{2}\right)}}}{{{C}{\left({49},{6}\right)}}}\times\frac{2}{{43}}C(49,6)C(6,4)×C(43,2)×432

=13,54513,983,816×243\displaystyle=\frac{{{13},{545}}}{{{13},{983},{816}}}\times\frac{2}{{43}}=13,983,81613,545×432

=122,196.53\displaystyle=\frac{1}{{{22},{196.53}}}=22,196.531

=4.505×10−5\displaystyle={4.505}\times{10}^{ -{{5}}}=4.505×10−5

We chose 4 of the 6 winning numbers [C(6,4)], and chose 2\displaystyle{2}2 numbers from the 43\displaystyle{43}43 remaining numbers that did not win anything [C(43,2)]. But we chose 6 numbers originally, so there are 2\displaystyle{2}2 chances in 43\displaystyle{43}43 that we chose the additional number, so multiply by 243\displaystyle\frac{2}{{43}}432.

So there is 1 chance in 22,197 of getting the Group 4 prize.

Group 5 (4 correct)

Odds:

C(6,4)×C(43,2)C(49,6)×4143\displaystyle\frac{{{C}{\left({6},{4}\right)}\times{C}{\left({43},{2}\right)}}}{{{C}{\left({49},{6}\right)}}}\times\frac{41}{{43}}C(49,6)C(6,4)×C(43,2)×4341

=13,54513,983,816×4143\displaystyle=\frac{{{13},{545}}}{{{13},{983},{816}}}\times\frac{41}{{43}}=13,983,81613,545×4341

=11082.7577\displaystyle=\frac{1}{{1082.7577}}=1082.75771

=9.236×10−4\displaystyle={9.236}\times{10}^{ -{{4}}}=9.236×10−4

We chose 4\displaystyle{4}4 of the 6\displaystyle{6}6 winning numbers and chose 2\displaystyle{2}2 numbers from the 43\displaystyle{43}43 remaining numbers that did not win. Once again, we need to consider the probability of the additional number not being one of our 2\displaystyle{2}2 remaining (non-winning) numbers. This probability is 1−243=4143\displaystyle{1}-\frac{2}{{43}}=\frac{41}{{43}}1432=4341. So we multiply by 4143\displaystyle\frac{41}{{43}}4341.

So there is 1 chance in 1,083 of getting the Group 5 prize.

Group 6 (3 + additional)

Odds:

C(6,3)×C(43,3)C(49,6)×343\displaystyle\frac{{{C}{\left({6},{3}\right)}\times{C}{\left({43},{3}\right)}}}{{{C}{\left({49},{6}\right)}}}\times\frac{3}{{43}}C(49,6)C(6,3)×C(43,3)×433

=246,82013,983,816×343\displaystyle=\frac{{{246},{820}}}{{{13},{983},{816}}}\times\frac{3}{{43}}=13,983,816246,820×433

=1812.068\displaystyle=\frac{1}{{812.068}}=812.0681

=1.23142×10−3\displaystyle={1.23142}\times{10}^{ -{{3}}}=1.23142×10−3

We chose 3\displaystyle{3}3 of the 6\displaystyle{6}6 winning numbers [C(6,3)], and choose 3\displaystyle{3}3 numbers from the 43\displaystyle{43}43 remaining numbers that did not win anything [C(43,3)]. But we chose 6\displaystyle{6}6 numbers originally so there are 3\displaystyle{3}3 chances in 43\displaystyle{43}43 that we chose the additional number, so multiply by 343\displaystyle\frac{3}{{43}}433.

So there is 1 chance in 812 of getting the Group 6 prize.

Group 7 (3 correct)

Odds:

C(6,3)×C(43,3)C(49,6)×4043\displaystyle\frac{{{C}{\left({6},{3}\right)}\times{C}{\left({43},{3}\right)}}}{{{C}{\left({49},{6}\right)}}}\times\frac{40}{{43}}C(49,6)C(6,3)×C(43,3)×4340

=246,82013,983,816×4043\displaystyle=\frac{{{246},{820}}}{{{13},{983},{816}}}\times\frac{40}{{43}}=13,983,816246,820×4340

=160.905\displaystyle=\frac{1}{{60.905}}=60.9051

=1.642×10−2\displaystyle={1.642}\times{10}^{ -{{2}}}=1.642×10−2

We chose 3\displaystyle{3}3 of the 6\displaystyle{6}6 winning numbers and chose 3\displaystyle{3}3 numbers from the 43\displaystyle{43}43 remaining numbers that did not win. Again, we need to consider the probability of the additional number not being one of our 3\displaystyle{3}3 remaining (non-winning) numbers. This probability is 1−343=4043\displaystyle{1}-\frac{3}{{43}}=\frac{40}{{43}}1433=4340. So we multiply by 4043\displaystyle\frac{40}{{43}}4340.

So there is 1 chance in 61 of getting the Group 7 prize.

System Entries

In most Lotto and Toto games, you can buy a “System”. Your chances of winning increase, but of course, you pay more as well. For example:

System 7 means you choose 7 numbers (instead of the usual 6). This gives you 7 times the chance of winning (so it costs 7 times as much), since it is equivalent to buying 7 different 6-number games, or C(7,6). Say you chose 1, 3, 5, 7, 9, 11, 13 as your 7 numbers. You have the following 7 ways of winning if the 6 winning numbers happened to be:

1 3 5 7 9 11
3 5 7 9 11 13
1 5 7 9 11 13
1 3 7 9 11 13
1 3 5 9 11 13
1 3 5 7 11 13
1 3 5 7 9 13

System 8 means you choose 8 numbers and it gives you the equivalent of 28 ordinary bet combinations, so costs 28 times as much, or C(8,6)\displaystyle{C}{\left({8},{6}\right)}C(8,6).

Similarly, System 9 gives you C(9,6)=84\displaystyle{C}{\left({9},{6}\right)}={84}C(9,6)=84 ordinary bet combinations, System 10 gives C(10,6)=210\displaystyle{C}{\left({10},{6}\right)}={210}C(10,6)=210 ordinary combinations, System 11 gives C(11,6)=462\displaystyle{C}{\left({11},{6}\right)}={462}C(11,6)=462 combinations and System 12 (the maximum in the Singapore game) gives C(12,6)=924\displaystyle{C}{\left({12},{6}\right)}={924}C(12,6)=924 combinations.

The probability of winning with a System 12 is 924\displaystyle{924}924 times the probability of winning when you buy 1 game, that is:

92413,983,816\displaystyle\frac{924}{{{13},{983},{816}}}13,983,816924 or 1\displaystyle{1}1 in 15,134\displaystyle{15},{134}15,134.

In the Singapore game of TOTO, 6 numbers plus one “additional” number are drawn at random from the numbers 1 to 49. In the Ordinary game, players spend $1 and they choose 6 numbers in the hope of becoming instant millionaires.

A prize pool is established at 54% of sales for a draw. Typically, $2.8 million dollars is “invested” in each game – and games are offered twice per week. This is quite a lot for a country of 5.5 million people…

Plenty of other countries have similar Toto games, usually called Lotto. The more numbers in a game, the worse your chances become.

Summary of the Prizes (Singapore Toto)

Grp

Prize Amount

Winning Numbers Matched

1

38% of prize pool (min $1 M)

6 numbers

2

8% of prize pool

5 numbers + additional number

3

5.5% of prize pool

5 numbers

4

3% of prize pool

4 numbers + additional number

5

$50 per winning combination

4 numbers

6

$25 per winning combination

3 numbers + additional number

7

$10 per winning combination

3 numbers

According to statistics, this is the probability of winning 4D

Are you into buying 4D? If you have been an ardent fan of this relatively harmless form of gambling, I’m sure you must have thought about the odds of winning the first price many times haven’t you?

Well then, let me let you in on some statistics of winning something from Singapore Pools each time you put your money on 4 random numbers.

The statistics I’m about to broadcast may come as a shock to some of you, others maybe not so much. You see, I’ve asked those who purchase 4D around me before if they knew what they were getting themselves into monetary wise and they almost always replied, “Well, it’s all for that glimmer of hope to change our lives once and for all.”

It’s not a bad thing, really. I mean, we all resort to something in a bid to change our lives right? Putting a small amount of money in a gamble for larger winnings is just what they do. But the chances of even winning that consolation or starter prize though is just too low for me to ever consider joining in “just for the fun of it”.

Okay, here goes. According to Singapore Pools, the odds of winning any prize is 1 in 435. Not too bad right? Keep in mind this is for “any prize” and, I’m sure, not the prize you are looking to win. Following this, it is a 1 in 1,000 chance of winning a consolation prize or a starter prize.

Now comes the best part and possibly the part everyone is waiting for. The top 3 prizes. If you want to get anywhere near winning one of these, this is the kind of odds you are up against.

For all 3 top positions, you have a 1 in 10,000 chance of winning. Seriously, what are the odds of winning? Well, that’s “hope” for you right there.

To many people, this is just another pastime for them to wither some of their time away and give them something to look forward to. For others, it is a chance for them to hopefully change their lives around.

If you are still very sure that one fine day, you will emerge victorious, then please be my guest and continue doing what you need to do.

There is no right or wrong when activities are practiced in manageable doses. I’m hoping these statistics will have made some of you think twice the next time you are at a 4D booth and marking out those ‘winning numbers’ on that rectangular sheet of paper.

It can be a shot at winning some money but it should never be done to the extent of wrecking your life altogether.