Wednesday, January 1, 2025

Would You Win More $$ If Toto Dropped to 5 Numbers?

 


If you haven't been living under a rock recently, you would've came across the new year draw featuring a massive 8.2 million prize pool. It was supposed to be just 5 million but since the past 2 draws had no group 1 winner, the prize pool has snowballed to be worth more than 10 HDB flats. 

Given that Toto has featured the drawing of 5 numbers during it's inception back in the 1960s, I was thinking whether it would be better for both consumer and operators if we adjust it to draw 5 numbers but from a bigger pool of numbers. But before we delve into that, for the unculturedinitiated...

Just What is Toto?

Toto is a popular lottery game in Singapore operated by Singapore Pools. Players choose at least six numbers from 1 to 49. During the draw, six main numbers and one additional "bonus" number are drawn. To win, players need to match at least three of their chosen numbers with the drawn numbers.

Key Rules:

  • Minimum Bet: $1 per set of six numbers.
  • Winning Combinations: There are multiple prize tiers, with the jackpot (Group 1) going to those who match all six numbers. Lower prizes are awarded for matching 3 to 5 numbers, with or without the bonus number.
  • System Entries: Players can increase their chances by betting on more than six numbers in one ticket, forming multiple combinations.
  • Draw Days: Held every Monday and Thursday, with special draws occasionally.
That's the general gist of the Toto and it's rules that I asked ChatGPT to type out. You may access the full list of rules here.


So What Are The Odds of Winning?

TLDR: It's 1 in 14 million

For those who have been listening to their E-Maths lesson, you would probably be able to easily calculate the odds. But for those who haven't been paying attention to their Maths teacher back then (shame on you), here's some math so bear with me for the moment.

In general, the mathematics behind hitting the Group 1 Jackpot in Toto (matching all 6 numbers) relies on the concept of combinations. Here's the visual representation of the combination formula:


And now for some quick maths, we just need to substitute n for 49 and r for 6. It would look something like this:


Now if you type this into your phone calculator, you would be able to compute 10,068,347,520/720 = 13,983,816. You are not mistaken, your odds of winning Group 1 in Toto is 1 in 14 million. So my advice to you is to stop donating to building the next national stadium. But for those 没买没希望 degens, thanks for contributing back to our society o7

If you are interested, I went ahead to calculate the odds of winning each prize group below:
  1. Group 1 (Jackpot): Match all 6 numbers

    • Odds: 1 in 13,983,816
  2. Group 2: Match 5 numbers + the Bonus number

    • Odds: 1 in 2,330,636
  3. Group 3: Match 5 numbers

    • Odds: 1 in 55,491
  4. Group 4: Match 4 numbers + the Bonus number

    • Odds: 1 in 22,197
  5. Group 5: Match 4 numbers

    • Odds: 1 in 1,083
  6. Group 6: Match 3 numbers + the Bonus number

    • Odds: 1 in 812
  7. Group 7: Match 3 numbers

    • Odds: 1 in 61

Overall Odds:

  • The overall odds of winning any prize in Toto are approximately 1 in 54.

Now What If We Dropped Toto To Just 5 Numbers?

I know what you are thinking. If we drop to just picking 5 number obviously the odds will increase right? Of course, but if we were to continue along with our experiments of dropping the number of balls being picked (yes, we still pick out the number balls manually), then we would also have to adjust the total number of balls inside the machine.



In fact, this was just a random shower thought that sprouted out so I went ahead to google whether there were lotteries out there that selected 5 numbers for the jackpot. Apparently, most gaming operators out there have the same idea in mind where a jackpot required 6 matches. 

The Euro Millions and Lotto from the UK's National Lottery

The game that is closest to Singapore's Toto when dropped to just 5 numbers would be the Euro Millions Hot Picks where choose 5 numbers from 1 to 50 and need to match 5 numbers for the jackpot so your odds is just 1 in 2,118,760. 

Before you close this window, you need to remember that this game needs to be fair for both the operator and participant. Pools can't be operating at a loss right, if not how to generate 10 billion of revenue in 2024?




As such, we would want to increase the number of balls being picked to be the same as those of the UK national lottery's Lotto. The Lotto allows player to pick six numbers from 1 to 59 where you need to match all 6 for the jackpot. We will be taking the same approach in our modified version of our Toto featuring 5 numbers picked.

So What Are The Odds of Winning Toto with 5 Numbers Drawn?

TLDR: Don't have cos I want you to read finish (takes effort to write one hor)

If you remember our combination formula earlier (as seen below), then you would know that we just need to substitute certain numbers to figure out the odds of the updated Toto


Here's the updated game configuration:
  1. Number Pool: 1 to 59
  2. Numbers to Match for Jackpot: 5
Now to calculate the odds, we just need to substitute n with 59 and r with 5. Here's a visual representation of the calculation:

And the final results is that the odds of hitting the jackpot is 1 in 5 million.

Since the odds are better, naturally there will be more Singaporeans being enabled to throw more money for that little piece of hope while in theory would lead to more revenue for Singapore Pools. 

So why has Pools not improved the odds over the years? We need to remember the original mission of the organisation which can be seen from the screengrab I've taken from the press release back in 2007 from Sports SG.




Pools doesn't operate as an organisation to maximise earnings but rather is an outlet for people to buy a little piece of hope. In fact, they have contributed more than $2 billion to nation building (together with others from the Tote Board Group). So next time you walk by an outlet while going back to office from lunch, feel free to make that $2 donation to our nation building.

And there we have it, the odds of our adjusted Toto game with 59 numbers and 5 balls drawn would increase our odds of hitting the jackpot from 1 in 14 million to 1 in 5 million.

P.S Initially there was a simulation section where I used python to see how many tickets it would take before I get a winning ticket under the original Toto rules. However, after running for more than 30 mins there was no winning ticket generated so I went to google and realised that it would take too long to generate 14 million iterations so I promptly closed the programme.

Friday, March 24, 2023

Anime Trading Cards: Can You Actually Make Money From Opening One Piece Booster Packs?


I am sure you have came across articles like this as you browse the internet. These high quality Charizard cards have been sold for more than $400,000. And in fact, this isn't even the most expensive card ever sold. Yes imagine a Pokemon card being able to fund your BTO - now isn't that an amazing feat?

As such, a light bulb lit over my head during the new year as I hassled and pestered my friend Hengfu into going to a card shop and buying the whole box of booster packs to see if we can make a quick profit.


After a hefty discussion, Hengfu suggested that we head down to this card shop to open some cards. At first I wanted to open Pokemon cards but he said that the chances of us getting good cards were low so why not try out One Piece cards. If you have followed (stalked) me closely on my instagram stories, we actually opened 5 packs each at Kuala Lumpur back in December for fun and Hengfu was the only one that had any good draws.

But back then we opened the series 1 cards and now we were attempting to open series 2 cards instead. So you may be wondering what's the difference? The general gist is that the cards you are getting from each series will be different which means the rare goodies you are getting will be different.


For illustration purposes, Shanks (alternate art) will be the card that you want to get from series 1 and is priced at around 2k back when I was opening the packs.


And for series 2 you have my favourite Ace (Foil, super parallel) at a whopping 1.3k. Pretty amazing right? 

But What Are The Odds?

Before we go about opening the boxes let us also understand the odds of getting these ultra super rare cards so we can sort of guess our expected value gotten from each pack opening. Here's a MVP answer from a reddit user:


Here's a summary of the odds in text format:

A case has 12 booster boxes and is guaranteed to have:

  • 4 boxes with a standard Secret Rare (most likely 2 Shanks and 2 Yamato) and no parallel art card (*unless it is manga Shanks), and 3 Super Rares.
    • I say standard Secret Rare because (most) parallel Secret Rares will appear in place of a parallel art card in one of the other 8 boxes.
    • *Unlike other parallel art cards, manga Shanks seems to appear in place of one of the 2 guaranteed Secret Rare boxes with a Shanks.
  • 2 boxes with an alt Leader, a parallel art card (of any rarity except manga SEC Shanks), and 3 Super Rares.
  • 6 boxes with a parallel art card (of any rarity except manga SEC Shanks) and 4 Super Rares.

All booster boxes will fall under these 3 categories.

Alright now that we understood the odds, we went ahead to the shop and got 1 box of cards at $50. Yes this meant that we will have 24 packs between both of us and each of us get to open 12 packs leading to a total of 144 cards. So out of this 144 cards I am looking out for Mr Ace.


Let There Be Cards


So two guys seated at a random corner of Dhoby Ghaut interchange started opening the One Piece card packs and let the games begin.


We started taking turns opening the cards and the first pack I opened I got this anime grill from out of nowhere.


I then attempted to sell Hengfu this on the spot for $20 and he rejected my offer. Shame on him not knowing a good deal when he's being offered one. The next few packs that we opened didn't really have any good cards with Hengfu constantly complaining on his poor luck while me spamming “见证奇迹的时刻”


It was amazing how after opening more than half the packs we didn't see any good cards at all. This was when we had a change of luck and the packs I opened started to have some amazing drops.


I first got this totally cool looking Luffy card..


Before getting an even more amazing Ah Gong Whitebeard next


I ended my draw with a more cartoony version of Luffy.

In the meantime, I was harassing Hengfu throughout. Cue my constant LAI LIAO LAI LIAO LAI LAIO....


Before Hengfu realising that he got some garbage cards. But at the end he was able to get two interesting draws of Marco and Aokiji. At first I was mocking him for getting these trash draws until I googled the value...


This lucky dude broke even with just 1 card. And meanwhile here's how much his Aokiji card was worth:


Yup, he gotten $32 worth of cards from just 2 draws. Truly amazing luck right there. I even asked him for 6 numbers so I can buy Toto later.

So Did I Make A Profit?


And to answer that question, I went on carousell to determine a fair value of the rare cards that I gotten.

Luckily a user out there was having a fire sale on his cards and I was able to find out the values of my draws:



The above picture is a rough estimate of the value of the cards that you can draw from OP-2 (kudos to carousell user @blossomcup)

And here's a summary of my draws that were worth anything:

Cool Foil Ah Gong Whitebeard - $6
Burning Luffy - $3
Foil Kozuki Oden - $6
Random Anime Grill - $3

Total - $18

So I made a loss of $7 from opening these card packs while Hengfu made a profit of $7.

To be honest, I expected an even greater loss and being able to get $50 from spending $50 from a card in total value was actually rather decent.


The Verdict


Even though we were able to breakeven, this does not mean that you should go about opening random one piece boxes. There is still effort in selling your cards and also there may be a decay in value if you do not protect your cards properly with card sleeves.

But all in all, it was a fun activity to pass time and being a One Piece fan myself, I will definitely be keeping these Luffy cards until the end of time. And one last video of me annoying Hengfu for the road.


Thanks for reading and stay safe everyone!

Wednesday, October 19, 2022

A Walk to Forget: Bishan to Kallang


Are you guys excited for the yearly Nasile-mak post? I know I promised to update the blog more regularly to pen down my thoughts and views about life in general but I couldn't find an interesting to talk about unless you guys are into getting rugged by Crypto lenders.

So the back story about this 'Walk to Forget' started back in September where I met up with the boys Reynold and Limpin to feast on some Middle Eastern cuisine. We went to a quite famous (and also expensive) restaurant at Kampong Glam called Cappadocia.


I definitely didn't take the photo above and I should have known that it was going to be expensive when you see the restaurant name in 4 different languages on their shop banner. 


Anyways the food was great and we really had quite a good meal there so kudos to them and check them out here: https://cappasg.com/nw/ (Sorry no affiliate code for you to use)

You must be thinking why am I not flaming them? Because this is the new revamped Nasile-mak where we only share positive vibes and thoughts. I cannot simply just come out and say that their Turkish Coffee was so small I could've finished it in one mouth right. That would just be plain rude and we should refrain from such behavior in an already toxic online environment.

Anyways, we started talking about how we have a lack of physical activities in our life and we were pretty much living a sedentary life. I know we have an army regular amongst the midst of us and could easily pull off a 11 mins 2.4km run. But take note that this guy used to be able to run it in just less than 8 minutes. 

Yes you don't need to re-read the previous statement, this guy used to run 2.4km in 8 minutes.

And a few kebabs later we all agreed that we should probably do some physical activity together for the sake of a long life so we can actually enjoy our CPF money. We spoke about urban trekking as covered by Esquire where we just walk from one point in the city to another. The concept is pretty cool and the distance isn't that far where anyone could do it easily while absorbing in the sights and sounds.

A snippet of an urban trekking route


But Reynold pointed out that it may be quite difficult for complete newbies like me which I agreed so we decided to walk the park connector instead. We suggested a couple of routes and being the lazy bums we are Rey decide to suggest somewhere near his house and proposed us walking from Bishan all the way to Kallang. I thought that he was just kidding but there was actually a park connector that ran all the way from Bishan to Kallang.


Above is a snippet of the route and when you zoom in, you will be able to see how there were green lines that were park connectors. And aiyo I not asking you to zoom in on the image above hor, I have provided a nice recording of how it looks like below.


The distance on Google Maps was 7.6km in total and we all felt that it was doable. So we marked the faithful date on our calendar and extended the invite out to Shameer, Zuhair and Vivi. Howeverone of them was pretending to be busy on the day itself and avoided replying us 🌚


Okay la he replied us in the end but he was busy "working".



So fast forward to the faithful date of 1st October where we finally started on...

A Walk to Remember Forget

We all agreed to meet at Bishan Mcdonalds at 9am and to nobody's surprise, nobody was early. I was pretty sure I was last to reach as Limpin was already standing outside Macs waiting impatiently and flaming us. Reynold was once again up to his shenanigans as he wanted to pee before the walk. The small bladder man emerged from the shop shortly and told us that he could not relieve his business as the queue for the toilet was too long. I was quite sure he just got kicked out as he looked like a non-paying customer trying to take advantage of the store's facilities.



We started our walk as the occifer briefed us on today's plans. He told us that we will be mainly following the park connector but we will need to first make an emergency pit stop for a toilet break soon. We told him to do his business just within some random bushes of Bishan park and he accused us of  头脑进水. This was rather rude response on his end to our superb and constructive feedback. This is why Singaporeans very hard to work with. Give them some suggestions and they shit on your idea smh.



On the way to the stadium we found Reynold's lookalike. As it was a weekend morning, the park connector was filled with people jogging and walking their dogs. We were quite lucky as the clouds were out so the sun didn't directly shine upon us. It made the walk really enjoyable as we gradually reached the starting point of our trek.



As we stood at the traffic light, we could also see that there were many cyclists along this path.


Interestingly, the path wasn't divided to walking and cycling path and both kind of commuters were haphazardously riding and walking trying to avoid each other. It became a game of pacman where you avoid getting eaten by those on the bike. It was then when our dear mr small bladder said that we should make a tourist stop at Bishan stadium.



I haven't been to the stadium for a long time and it reminded me of how Home United has rebranded into the Lion City Sailors. They even sealed up the seats to prevent kaypoh people like me from sitting on it.


Surprisingly, there weren't many people in the stadium track and I assume that people probably preferred the park connector with a changing scenery. But jokes on them as if they run 3km and enjoy 3km of scenery, they would have to walk 3km back in the opposite direction don't they?


And after relieving himself, Mr Heng reminded us to hydrate ourselves as it's going to be a long walk. I just reminded him that if he drinks more water we probably will need to have a second dehydration break along the way. We went back on track and continued on our walk along the Bishan MRT depot. It amazed me at how big the whole depot was as the scenery wasn't really changing with the depot stretching across the entire pathway that we were walking on.


Halfway through we spotted a few people attempting to do something along the river. They seemed to be rather enjoying whatever activity they were doing and I wish I could say it was the same for me after Limpin cracked his fourth lame joke of the day as we continued our walk.


We took our first break along the Kallang River and mr siao on Reynold decided that it would be good to just have a short 10 minutes rest. What he failed to inform us was that our 10 minutes started 5 minutes ago as just after a short 5 minutes he was ushering us to continue walking so that we can ride on the momentum. And at that moment, the only thing I wanted to ride was probably a grab to Kallang.

A Path Walked by Many



We were gradually making progress as we were nearing Braddell. This was when we met our first obstacle. 


As seen from the image above, the usual path that normal humans would take be to walk along the park connector. However, being the army man he is Reynold suggested another path along that I drew in red. I told him that I have just finished my yearly reservist and I had enough of the jungle for the year. However, I suspect that Limpin may have 头脑进水 as he agreed with Reynold's suggestion of a yolo walk through the grass.


Got path to walk don't want to walk

That pretty much summed up our decision on walking through a random grass patch versus along the nice pristine concrete path connector. In case you didn't watch the video above, I have uploaded the gif version of it below.


It was quite funny also because there was indeed a pathway that the students from St Andrews probably used on a daily basis as they walked to school. 


As you can see there's a clear dirt path that has been walked by many. It made me wonder how many batches of students have walked along the same path and jump the school gates to avoid the discipline master when they were late. 

You can also clearly see the bridge that connected both the secondary school and junior college campus of St Andrews. It would really have been an amazing 6 years of those students' lives.


After walking past St Andrews, we were met with a slightly small issue. Because we deviated from the path, what we saw was an expressway blocking our path. That's right, we weren't following the path on Google Maps from now on and just based on our pure gut instincts. On hindsight, that probably wasn't the best idea 🌚


We were on the other side of St Andrews when we spotted a path that we could take to go under the expressway.


We weren't really talking much at this point, not because of tiredness but rather the sound of car rushing past us was just overwhelming. But this just goes to show how the design of the park connectors was rather efficient too as it allow users to cross expressways. As you can see in the photo above, the park connector routes were marked with red dotted lines on both sides. So if you are ever lost, just follow the dotted red lines and you will probably reach civilisation. 


And after crossing the expressway and a short distance away, we reached Jalan Besar. We could see the welcome banner with 5 smiling faces welcoming us after our trek from Kallang. It was at this point where we deviated again from the path as Reynold started saying that he was hungry. 


As we settled down for our second and final rest stop of the day, we were presented with a dilemma. Do we stop for a short food break at a place and continue our walk, or do we trudge forward and just finish our walk before eating at the hawker center? What do you think? Did you think that we were weaklings who would succumb to hunger and not push forward for our final goal which is the upper boon keng food centre?

Mak, Han Ren. Reynold and his house. Photo. 29 in x 36.25 in.

To Walk or Not to Walk?

Being the sensible people we were, we decided to have the walk before the meal instead of walking after the meal. We continued our walk to remember and even though it was almost 11am, the weather was still really good. 


If you're keen eyed, you can see that it was still shady and the cloudy weather was really great for walking. As we were nearing the Kolam Ayer bridge, we spotted a nice vegetable by the community and I was asking the guys if we wanted to pluck some chilli for our lunch later. The other two boys just ignored my comment and walked along as if they couldn't hear me. I was thinking why were they ignoring me until I spotted that glorious pussy.


Limpin was the first to play with the pussy and he was really entranced by it. I was just surprised the cat didn't give Limpin a scratch to remember by.


And right here we can see the pussy hunter in his natural environment as he stalks his prey. He first let the tabby sniffs his hand to make him get familiar with his scent before going in for the pet. The cat was smart and sensed danger as he ran away from the hunter.

Things were going too smoothly and that's where unfortunate incident number two happened - part of the park connector was under construction. This meant that we had to make a detour to reach our target (pretty sure we walked more than 8km in total).


We walked along some shady private property that was fenced up as we could see Geylang West Community club just right ahead. Our legs were getting wobbly and we were simply overjoyed when we caught a glimpse of the food center.


And suddenly their weariness was gone as they picked up the pace to enjoy our well deserved lunch.



And that was the end of our 8km route march. We settled down for lunch and none of us wanted to get up to order our food. We can see that Reynold was really hungry as he devoured whatever noodles he ordered and went ahead to buy another plate of carrot cake. He asked to share with us but I was sure he demolished 3/4 of the plate by himself.


I was googling what was famous in the food court and tried the Char Kway Teow. Unfortunately, it wasn't as good as I thought it would be probably from the wok being not hot enough since it was still morning. If I had ordered in the afternoon the ingredient would probably be fried to perfection.

Thoughts

And there you have it lads, the completion of the walk from Bishan to Kallang. My personal thoughts was that after completing this physical activity, I really felt a sense of accomplishment. This was no competition but I felt like I won a battle against myself. I would be lying if I said I didn't feel tired during this walk. Even though it was just 8km it was still a 2 hour walk in our concrete jungle so it was rather challenging. As I mentioned earlier, this walk was just a precursor towards walking more urban treks in our CBD area. 

It was really fun so do stay tuned to Nasile-mak for our future escapades!