Which Dominos Pizza Size is the Best Value for Money?

 

My parents accompanied my brother on a trip up North and I was home alone over the weekends. Since our helper was on leave every Sunday, I could not exploit her to cook lunch for me and had to settle lunch for myself. It has been some time since I had pizza so I was thinking why not order some pizza for myself? And what better pizza to order than Domino's pizza itself? 

Sorry Pizza Hut lovers, Domino's is simply the superior brand of pizza and we can agree to disagree.

So which Pizza Size should I order?

I was scrolling the page and they had so many offers up in place. They ranged from regular pizzas all the way to XXL pizza. 

I was googling which pizza size to purchase but the AI generated answer only mentioned the difference in sizes but did not take into consideration the monetary value of the pizza. 

And in this case, the cost per square inch is a critical ingredient in our calculations. Now there are a few boundaries for this experiment:

1. I am ordering only for myself so I will be comparing only portions that one person can finish
2. Don't judge that I think I can finish two regular pizzas by myself
3. If I cannot finish the pizza I will just chug it into the fridge for future meals

Now that being said, we first need to investigate the size of each pizza. And luckily enough, we can easily find out the size of each pizza from the menu.

After which, we will find out the cheapest deal for each of these pizzas available for one single pizza lover. And these were the deals that we select for our calculation.

We then crunched some numbers and here are the results below:

And lo and behold, it was actually the more economical to order an extra large pizza for yourself! 

In fact, I was surprised to find out that ordering one large pizza is more economical compared to ordering 2 regular pizzas. This means that the deal dominos has been pushing out regularly on their home page was actually the least economical one for you!

Of course some naysayers will say "Your calculation isn't accurate, what about including the delivery fees?". And for you losers, I've included an additional column to calculate the overall cost per square inch:

So the moral of the story is if you are ordering a pizza for yourself, just order the xtra large one and you can have it for two meals! Now don't mind me as I enjoy my Xtra Large pizzas by myself...

Joking la, I got this photo from someone's blog. I ended up eating McGriddles instead.

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.

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!