Identify, Exploit, Subordinate, Elevate, Repeat
Monthly Allocation for 19 October 2020 as follows , with a $170.32 investment amount
| Counter | Quantity | Price | Investment Amount |
| OCBC Bank (O39) | 19 | $8.780 | $166.82 |
| Total | $166.82 |
Average Price of existing Portfolio counters
| Counter | Total Shares | Avg Price |
| OCBC Bank (O39) | 479 | $10.1666 |
| SIA (C6L) | 645 | $8.6553 |
Following up my thoughts in my previous article on TOTO: Winning over the long run — Go BIG or Go HOME, I was pretty interested to zoom into a particular bet type for the lottery as it seemed to present a better chance (or probability) of winning at a lower cost.
Singapore Pools launched iTOTO on 17 Nov 2015. iTOTO is akin to a lite-version of System 12. While 12 numbers are picked from between 1 — 49 for both, the key differences between the 2 bet types are:
| Bet type | Number of Ordinary entries | Cost |
| System 12 | 924 | $924 |
| iTOTO | 924 | $33 |
Probability of winning a prize for both System 12 and iTOTO
Being essentially the same type of bet (save the cost and prize won) as 12 numbers are chosen, System 12 and iTOTO both mathematically share the same probability of hitting a prize in the respective Prize Groups.
One thing that got me thinking: IF they are basically the same “bet type”, wouldn’t it make sense to skip Ordinary to System 11 bets (even System 12 in this case) and go long-term on iTOTO bets? The risks seemed substantially smaller and winnings proportionate to your risks taken. I somehow feel that there must be more than meets the eye — Singapore Pools had no reason to be creating a “better bet type” advantageous to betters.
Bringing back the current bet prize table for the different prize groups:
The way prize amounts are calculated for iTOTO ticket holder for each Prize Group is slightly advantageous when compared to a System 12 ticket.
| The prize amount for each winning iTOTO unit is the prize amount of the winning Quick Pick System 12 Entry divided by 28. The prize amount will be rounded up to the nearest 10 cents. |
Is the above text obvious enough? Let’s examine further for 2 Prize Groups. First up, for Group 7 Prize Group winner:
| System 12 ticket | iTOTO ticket (1 unit) |
| Claims $10 x 84 shares = $840 | |
| $10 / 28 = $0.357 = $0.40 (rounded up) Claims $0.40 x 84 shares = $33.60 |
Another example, for Group 6 Prize Group winner:
| System 12 ticket | iTOTO ticket (1 unit) |
| Claims ($10 x 56 shares) + ($25 x 28 shares) = $1,260 | |
| $10 / 28 = $0.357 = $0.40 (rounded up) $25 / 28 = $0.893 = $0.90 (rounded up) Claims ($0.40 x 56 shares) + ($0.90 x 28 shares) = $47.60 |
One unique point to note for 3 matched numbers: You are still in the red (-$84) for a System 12 bet, but stay ahead (+$0.60) with an iTOTO bet.
I have mapped out the rest of the other Prize Group potential winnings using 14 Sep 2020 draw as a reference, if you were holding on to 1 unit of iTOTO ticket versus System 12 ticket. To summarise:
| Winning numbers | TOTO (System 12) | iTOTO (1 share) | iTOTO (28 shares) |
| 6+1add | $2,424,533.00 | $86,605.80 | $2,424,962.40 |
| 6 | $1,107,119.00 | $39,560.30 | $1,107,688.40 |
| 5+1add | $249,018.00 | $8,905.50 | $249,354.00 |
| 5 | $21,294.00 | $777.00 | $21,756.00 |
| 4+1add | $7,462.00 | $273.70 | $7,663.60 |
| 4 | $3,640.00 | $140.00 | $3,920.00 |
| 3+1add | $1,260.00 | $47.60 | $1,332.80 |
| 3 | $840.00 | $33.60 | $940.80 |
One might ask, why not buy 28 units of iTOTO instead of System 12? For one, it is near impossible to know which batch of iTOTO you are buying into (e.g. 15th unit out of 28 units). There is a high possibility of buying across iTOTO combinations, whether in a scenario with many people buying in at the same time or few buying in at all.
TOTO prize amounts, at least for the top tier Prize Groups 1 — 4, varies as a percentage of the prize pool. Betters are happier when more people buy TOTO. The higher the sales revenue, the higher the potential prize amount for that draw. Betters are even happier when no one (including themselves when it happens) wins the top Prize Groups. This leads to prize money cascading to the next prize group or snowballing to the next draw.
TOTO however is also a shared-winnings game. The more winners there, the more the pie has to be cut within each Prize Group to be shared equally.
| Prize group | Numbers matched | Prize amount |
| 1 | 6 nums | 38% of prize pool (Minimum Guaranteed of $1,000,000) |
| 2 | 5 nums + 1 add | 8% of prize pool |
| 3 | 5 nums | 5.5% of prize pool |
| 4 | 4 nums + 1 add | 3% of prize pool |
| Total | 54.5% of prize pool |
We look at the recent largest TOTO draw for this year, the TOTO $12 Million Hong Bao Draw.
TOTO $12 Million Hong Bao Draw 2020 had 20 Group 2 winners (and more actually)
Even though the Group 1 Prize was a jackpot amount of $12 million, Group 2 as compared to regular draws, was so much smaller by each winning share. This is evident of more winners, small pie. In fact out of these 20, 4 are iTOTO group bet tickets. This means that each iTOTO group winning share is further divided into 28 units — each unit ticket holder stand to win about $3630 from the Prize Group 2 category. This has not included winnings from the other lower Prize Groups.
When 1 iTOTO combination wins, you potentially have to share the pie with 27 other unit holders (and more). With affordability, it means more iTOTO combinations have to be created and thus the possibility of more people having an equal share in the top Prize Groups. We have seen from the TOTO $12 Million Hong Bao Draw that it is possible to have a few winning combination iTOTO bets for the top Prize Groups.
At the individual level, it still holds true that you are taking lower risks (smaller costs) to enjoy the same probability (as System 12) of winning big, yet at a proportionately lower prize amounts as well.
On the other side of the page, people somehow want the “power to decide their preferred numbers” for the draw. You can do that with System bets but not with iTOTO, though essentially, there is no difference between manually chosen and system chosen numbers.
To Singapore Pools, a System 12 winner and a group iTOTO (28 units) winner is one and the same. Singapore Pools has a slight edge in my opinion for iTOTO.
For some reasons, there are people who do not manage to collect their prize money, whether it is due to losing or misplacing their physical tickets, or even forgetting about it. Having more winners for the same prize amount increases the chances that someone will not collect their prize money.
Some people also wondered: For iTOTO tickets which do not sell out all 28 units e.g. only 18 units are sold, are prize money divided into 18 instead of 28 units? The answer is No. In fact, such situation is advantageous to Singapore Pools; Singapore Pools distribute out 18 winning shares but keep 10 winning shares in their coffers.
Lottery is part and parcel of many Singaporean families. Being “exposed to gambling” from young — us cousins in the family used to hang around our grandparents’ place every weekends and “tikam tikam” or guess numbers for their weekly bets. We picked individual numbers out of a jar for TOTO and 4D, sometimes we win most of the times we didn’t.
Most writings I encountered so far don’t go beyond the obvious — cost and odds of bet types or prize amounts. Playing the Devil’s Advocate, I thought it would be interesting to offer some of my own thoughts on top of the good work by predecessors on why higher bet types are prohibitive yet offer the best chance of positive returns over a long run.
This post in no way encourages gambling. Betting is still a game of luck and probabilities. TOTO is a gamble with huge variance. You could lose hundreds, or thousands of dollars if you make many huge and frequent bets. It is a sure-lose way of throwing away money as the probability of winning anything is 1.85%. Even going for exams without studying will get you more than average 2 points overall.
However, is this prejudice without looking much more in-depth into the gamble itself? The point of getting into a gamble anyhow, is to opt for the bet with the highest probabilities based on the maximum risk that you can take. Predecessors have unseated this prejudice as well with exploratory analysis and simulation.
| TOTO is fairer than it seems: there is a way to maximise expected winnings with enough capital. And I don’t mean buying up all of the different combinations. |
Simple enough, 6 (min) to 12 (max) numbers are picked between 1 — 49, through the various bet types:
| Bet type | Number of Ordinary entries | Cost |
| Quickpick / Ordinary | 1 | $1 |
| System 7 | 7 | $7 |
| System 8 | 28 | $28 |
| System 9 | 84 | $84 |
| System 10 | 210 | $210 |
| System 11 | 462 | $462 |
| System 12 | 924 | $924 |
| iTOTO | 924 | $33 |
| System Roll | 44 | $44 |
The prize amounts for the various prize groups are derived from Singapore Pools website.
Generally, betters are highly interested in efforts required to reap the rewards versus the costs of attaining it. A higher bet type will have more ‘ordinary’ chances, thus better odds and higher probability. It’s all co-related.
Odds and probability for Ordinary bet are mathematically derived. For System 7 to 12, they are derived from Monte Carlo simulation . 50 million TOTO games was simulated to figure out the probabilities of achieving matching combinations with each bet type.
A bettor has a 1-in-54 chance of winning any prize for an Ordinary bet and down to a 1-in-7 chance for System 12 bet over the long run.
In short, there is no sure-win strategy. Ignore all the high-low, odd-even, sum-of-numbers, frequency-of-numbers strategies out there. Each draw is independent from the next draw; any number drawn is independent from each other as well. Lucky numbers, popular numbers etc., they do not mean anything really. Trends arise after a long run and can be explained by statistics.
Taking data for the past 1254 games (Game 2341 to 3594), we have come up with some statistics to examine.
Odd/Even numbers combinations
Each number has an equal 1/49 chance of being drawn from the start. Similarly with 25 odd and 24 even numbers, there’s an almost equal chance of an odd/even number drawn with a very slight probability that odd number has a higher chance of being drawn.
Therefore we observe that having equal number of odd/even numbers drawn is the highest (37.6%). Having a odd/even combination of 2-4, 3-3 and 4-2 becomes statistically higher at 81%.
Without going into the high-low range or high-mid-low or even each number range grouping (1-9, 10-19, 20-29 etc), we find that it will statistically tend towards equal distribution.
Same number appear from the last draw (not same combination of numbers)
At the end of 1 draw (6 tries), the probability of a particular number being drawn is 0.1292 [1/49 x 1/48 x 1/47 x 1/46 x 1/45 x 1/44]. The probability of the particular number being drawn at the next draw as well is 0.01669 [0.1292 x 0.1292]. Since there are 49 numbers to draw, the probability of any number being drawn in the next draw is much higher.
We observe that having 0 or 1 number appearing from the last draw is roughly the same. Having 0 or 1 number appearing from last draw is statistically high at 85%. In reality, we know as well that it is more improbable for 2 or more same numbers to appear from the previous draw.
Similarly, one can plot the same numbers that had appeared within the past 2, 3 or 4 draws to notice the trend with enough data.
Is the set of (1,2,3,4,5 & 6) impossible to take place? Out of 13,983,816 combinations, all numbers or even combinations has equal chances of appearing; we just haven’t had enough actual games yet.
Here, we are more interested in examining results of probabilities stimulations.
A fair gamble is one where you have a 50-50 chance of winning $1 with an expected payoff of zero. If you were to gamble in countless numbers of fair gamble, you make nothing in the long run.
| Expected Payoff = (50%×$1) + (50%×−$1) = $0 |
A better-than-fair gamble is one where you have a higher chance of winning $1 with an positive expected payoff (due to higher probability). Say a 55-45 chance of winning $1. It could also be one whereby you win more dollars than you lose in a rarer chance, leading to a positive expected payoff as well (due to higher payoff). Over the long run, you will earn money.
| Expected Payoff (due to higher probability) = (55%×$1) + (45%×−$1) = $0.10 |
| Expected Payoff (due to higher payoff) = (40%×$2) + (60%×−$1) = $0.20 |
TOTO is a better-than-fair gamble, regardless of the individuals’ bet type or prize pool size.
HUH? Now by this time, people will be scratching their heads. How can TOTO be a fair gamble? It is 1 out of 13,983,816 to win the jackpot and 1 out of 54 to win any group prizes with an ordinary bet. With the most expensive System 12 bet, the odds are brought down to 1 out of 17,857 for the jackpot and 1 out of 7 for any group prizes. No way is this 50-50 or even better, and everyone is bound to lose over the long run.
I thought it will be interesting to look at the overall picture and then delve deeper.
Just like a casino, we would expect that Singapore Pools is making much MORE money than it is giving out if TOTO was not a fair gamble. Is Singapore Pools making a huge profit all this while?
As a background, 54.5% of TOTO sales in each draw is for distribution of prizes in the Groups 1 — 4 which may be won for each draw. The rest of the TOTO sales is reserved for Groups 5 — 7.
| Prize group | Numbers matched | Prize amount |
| 1 | 6 nums | 38% of prize pool (Minimum Guaranteed of $1,000,000) |
| 2 | 5 nums + 1 add | 8% of prize pool |
| 3 | 5 nums | 5.5% of prize pool |
| 4 | 4 nums + 1 add | 3% of prize pool |
| Total | 54.5% of prize pool |
The prizes for the higher groups 1 — 4 are fixed as a percentage. The number of winners does not matter as the group prizes will be shared equally among the winners in the same prize group.
| Prize group | Numbers matched | Prize amount |
| 5 | 4 nums | no. of winners X $50 |
| 6 | 3 nums + 1 add | no. of winners X $25 |
| 7 | 3 nums | no. of winners X $10 |
| Total | 45.5% of prize pool |
While the prizes for the lower groups 5 — 7 are fixed dollar amounts, the number of winners does matters as all winners get the same dollar amounts in the same prize group.
Singapore Pools makes money only if total payout for the lower groups 5 — 7 is less than 45.5% of total sales.
Interestingly, Singapore Pools has made almost nothing when looking at data from October 2016 onwards. The overall sales is negated by overall winnings from the betters. From this simple analysis, we can infer that TOTO is a fair gamble. By fair, we do not mean that the game is fair to you but as a single party (betters) to single party (Singapore Pools) comparison, both parties have an almost equal win in absolute dollars.
Prize Groups 1 — 4 are allocated 54.5% of the prize pool or total sales of TOTO. Generally, the larger the prize pool, the larger the winnings. All bet types encountered a positive net expected value but over the long run. In other words, a better-than-fair gamble regardless of the bet types.
The only issue is that people naturally “give up” after not winning for some time. We don’t see players participating in all TOTO games over a prolonged period of time.
The compulsive gambler too does not follow a religious system in their betting — they bet however big they want or “tikam tikam” over a few different bet types. They upped their bets after winning something, which sometimes turn their winnings into bigger losses instead.
Hence, I would agree that short-term players end up contributing to the prize pool for other lucky or determined players to win. These said players do not play enough to break even or profit through a massive win. It would take thousands of games and possibly thousands of dollars in costs to win the big Prize Groups 1 — 4. Even in 10 years of our lifetime, only 1040 games are played.
To cut the long story short, predecessor had done 1,000 simulations of 1,040 TOTO games each for each bet type to identify possible outcomes.
The outcome could be summarised in the below table
The outcome range shows the maximum and minimum net balances from the simulations; you should be willing to be down as low as the minimum balance and expect at most, the maximum balance during a 10-year TOTO regime.
By betting on only System 9 for 10 years, I should be prepared both mind and soul to lose as much as $75,076 and make at most $4.0 million. As the median, I would expect to earn approximately $175,359 over ups and downs.
System 7 and System 8 turned out to have negative median outcomes instead, largely due to the low probability of hitting any big wins.
The above simulations were strict in a few criteria: no snowballing or cascading of prize monies, no sharing of prizes. In reality, these few factors do change the flavor in the expectations further.
Statistics however do not determine trends. Take a coin with Head/Tail sides. By taking 1 million simulations for example, we find that the outcome is roughly 50% for both Head/Tail. This does not determine however that one side cannot happen for a long time before the other side happens e.g. 20 Heads appear before 1 Tail.
| A sample coin flip: THHHHHHHHHHHHHHHHHHHHTTTHTHT |
The simulations for TOTO above is carried out for thousands of games. Over 10 years, only 1040 actual games are carried out — not quite a lot of games if you were to ask me. There is nothing against stopping you from losing tens of games before winning a small Prize Group, or even hundreds of games before winning a large Prize Group.
Yet, it does not change the fact that TOTO could be a better-than-fair gamble as the rare payoffs are sufficiently large (to compensate for the probability of winning them) and the smaller payoffs are sufficiently common. It also depends on the bet type you intend to stick to (for a long time) and your time frame.
Over the short run, TOTO is a losing bet for most of us who do not stick around for enough games to land a large win. Over the long run, TOTO becomes a winning bet, though it will take a very long time to realise a net positive expected value. Statistics is in your face to either gamble on the more expensive bet types (System 10-12) for a very long time or not bother at all.
It sounds ridiculous but rational at the same time. The only thing holding us back is our available capital. That is why you do not hear of many people even playing System 10 consistently over a long period of time.
Could we have it any worse?
Credits to the writer of TOTO: An Irrational, Rational Approach to Singapore’s Second Biggest Lottery for stimulating my thoughts.
In Singapore, like any other countries, every motor vehicle must have a vehicle registration number (VRN) to operate on the road. Each VRN is unique and like no other — it does not repeat and cannot be reused once discarded.
Most motorists use the VRN automatically assigned by LTA when buying a new vehicle. There is no charge for an assigned VRN. You could also bid (from LTA) for a new VRN or retain a VRN from an older vehicle. Your third option is to purchase and transfer a VRN from the open market.
A VRN generally consists of 3 parts: the prefix, the numbers and the suffix. Take ‘SJH1842U‘ for example. SJH is the prefix, 1842 form the numbers and U is the suffix derived from the checksum of the prefix and numbers.
Private car VRN began in the early 1900s, with a single prefix S for denoting Singapore. There are only 9999 numbers in each series. As the years went on, 2-letters prefix had to be introduced in 1913, E/EA introduced in 1972 before going back to S with 3-letter prefix in 1984.
At the time of writing, we are currently on SMU prefix.
| Prefix | Year | Prefix | Year |
| S | 1906 | SQ | 1954 |
| SB | 1913 | SR | 1955 |
| SC | 1920 | SS | 1957 |
| SD | 1927 | ST | 1959 |
| SE | 1933 | SU | 1961 |
| SF | 1937 | SV | 1963 |
| SK | 1943 | SW | 1965 |
| SL | 1946 | SX | 1967 |
| SM | 1949 | SY | 1969 |
| SN | 1951 | E | 1972 |
| SP | 1953 |
If you are observant whilst on the road, you may have observed cars who have 2- or 1-letter number plates. These number plates are known as vintage plates, with the last of the series EZ beginning in 1984.
One of the most satisfying thing as a driver on the road is to notice nice numbers on another vehicle, even better if it is a vintage plate. It really hits-it-home if the number plate is “more expensive” than the car itself that it is affixed to.
The market value for a single-S car registration number is priced around $300,000.
S32H at a public auction in Feb 2016 sold for $335,000. A similar S45X is offered for sale at $388,000 for sale on sgCarMart at that time. The auction or sales of vintage VRN is not new. Even now, older VRN are still highly priced and sought after.
The bidding for new VRN from LTA is good revenue for the government. Some $600,000 to $1 million in revenue is collected from 1,000 and 1,200 received bids for each series. The highest bid amount received so far has been $118,000 in 1995. All revenue is payable to the government’s Consolidated Fund.
Not all single-digits are equal — numbers 1, 3, 7, 8 and 9 usually attract the highest bids.
1 remains the most popular, with its significance is to be the “number one”. Equally nice-looking single-digits in a ‘normal’ series go for at least $10,000.
For the Chinese, they attribute numbers to fengshui.
The number represents ‘double’ or ‘双’, which may also means a pair or doubles bring blessings.
三 has similar sounding to 生, which means “life” or “to give birth” in Chinese. 生 has a positive connotation.
四 has similar sounding to 死 (sǐ), which means “death” in Chinese.
五 has similar sounding to 无 (wú), which means “not” or “without” in Chinese.
六 has similar sounding to 流 (liú), which means “flow” in Chinese. A popular Chinese idiom, 六六大顺 (liù liù dà shùn), denoting things will run smoothly.
Lucky Seven has seen the number 7 as a lucky number from the western culture. 七 has similar sounding to 起 (qǐ), which means the “start” or “rise”, and also 气 (qì), which means “vital energy”.
八 has similar sounding to 發 (fa), which means “wealth”, “fortune”, and “prosper” in Chinese. 8 is the luckiest number in Chinese culture. Multiples of eight are approved, 88 for example bears a resemblance to 囍 (shuāng xǐ), or “double happiness”.
九 has similar sounding to 久 (jiǔ), which means “long lasting” and “eternity” in Chinese.
Sometimes, we find novelty plates on the road, and these gets tongues wagging due to their being checky.
It really depends on how deep your wallets are. Yet, it need not break a hole in your pocket. Bidding for nice number plates is still a possibility with each series that come out from LTA.
For vintage plates, there are also those which are more affordable yet still don’t sound too bad.
Each VRN number is unique from one another. Once discarded, the same combination can never be reused. The supply of old or vintage VRN continues to fall over the years as people scrap their cars and give up their VRN.
The rich or those with expensive rides tend to go for a fancy VRN. The market demand is there for nice number combinations, single-digits and vintage VRN.
Generally if you have an old car running in the family, have a look whether it has a nice combination of the above. It is also not uncommon for number plates to be passed down from one car to another as the family retains the VRN.
Who knows if you have another S32H for the future?
It is the end of September with all mandatory contributions in for the month.
OA to SA transfer for the month of September is also completed. SA balance currently stands at $109,200.42, slightly more than half of 2020 FRS or 60.3% of the journey.
Theory of Constraints 