Nick Seeber's blog

Analysis of the iPhone game Drop7 with tips on advanced strategy

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I recently got the puzzle game Drop7 for my iPhone, and I've been playing it quite a lot for the last few weeks. 

Obviously I've also been trying to work out what the optimal strategy is for improving my score, but oddly there isn't really anything useful on the Internet. As such I thought I'd write something, hopefully it's be useful.

Of course this probably won't be interesting unless you've played Drop7 before, but if you have an iPhone I would urge you to try it out. It's very satisfying and incredibly addictive...

Drop7's gameplay is much easier to learn than to describe and I'm assuming that most people reading this will have played it before, so I'm not going to spend too much time describing the rules - but there are a few things to focus on that influence how you can score high points.

Briefly, Drop7 is a bit like a cross between Tetris and Sudoku. You have a 7 x 7 grid into which you have to drop circles numbered 1 to 7, and the aim of the game is to blow the circles up in a way that maximises your score before the game is over. There's no time limit, so you can spend as much time as you like contemplating your next move. You get points in two ways: firstly, when circles blow up, and secondly, a 7000-point level-increase bonus.

Circles will spontaneously explode if the number in them is equal to the number of circles in that continuous line (either horizontally or vertically, not diagonally). For example, in the picture above, if I dropped the grey circle into the right-hand column, the three #7s would all explode at once. As circles explode, "gravity" will pull circles above them down towards the bottom of the screen -- which may cause other circles to explode, and so on - causing chains of explosions.

Chains of explosions are rewarded very highly, with the scores increasing exponentially with each step: the first circle(s) to explode score 7, the circle(s) in the next step of the chain score 39, then 109, 224, 391, 617, 907, 1267, 1701, 2213, etc. Suffice it to say you will score vastly much more by setting up a sequence that results in four circles exploding one after the other (7+39+109+224=379) than by blowing up four circles simultaneously (7*4=28).

A complication is that you can't always see what the circle's number is before you drop it onto the screen -- some circles are greyed-out (like the one in the picture above). These greyed-out circles contain numbers like all the others, but they are only revealed by causing circles immediately next to them (left/right/above/below - not diagonally) to explode. An explosion next to a greyed-out circle weakens it, and a second explosion reveals a number.

Each time the level increases, a layer of greyed-out circles move on to the screen from the bottom, pushing all existing circles up the screen. This means that level increases usually cause explosions to happen, and you can use this to your advantage by setting up chains of explosions when you get near a level increase. If any circles get pushed out of the top of the screen, it's GAME OVER.

Progress through a level is indicated at the bottom of the screen, where you can see how many circles you have left until the end of the level. On each level you're given one less circle than the previous level. The first level has 30 circles, and each subsequent level has one less, until at level 25 it stabilises at 5 cirlces per level and doesn't go any further.

All this means that there are some constraints which will influence strategy. NOTE: throughout this post I'm going to refer exclusively to NORMAL mode - for Hardcore mode the best strategy is totally different (pure 'Chain-builder' incidentally, more info below).

Firstly, no matter how good you are, your game will almost certainly end around level 30. Given that the number of circles you can explode per level is limited, and each new level adds new seven greyed-out circles, it's very difficult to survive beyond level 27 (in my experience at least!). I think that the highest level I've got to was 28.

Secondly, circles are limited. The game starts you with 10 random circles and 30 more drop onto the screen, so by the end of level 1 you've been given 40 circles in total; by the end of level 2, 76 circles; etc. Assuming that you survive to level 28, you will have had 661 circles - and if you've filled the screen before 'Game Over' you will have exploded around 610 circles. Each one of those explosions is a chance to earn at least 7 points - the more you score from each explosion the higher your overall score will be.

Thirdly, the ratio of greyed-out circles per level rises during the game. This is because a quarter of the circles from the top of the screen are greyed out (according to my sample of 100!), plus there are seven greyed-put circles at each level, so the proportion of greyed-out circles per level rises from 25% in level 1 to 69% by level 25 (and beyond)! Each of them require two other (numbered) circles to explode to reveal their numbers, so the number of explosions you have to generate just to keep up with revealing the grey circles rises. Making the most of explosions is therefore more important as the ratio of grey circles rises later in the game.

Finally, the number of "spare" explosions peaks during the middle of the game. This is because you need to "spend" two explosions to get each grey revealed. Assuming that you use two numbered circles to reveal one grey circle* then once the ratio of greys starts rising towards the end of the game, you'll struggle more and more to keep up.

 

 

(*I realise that you can use one numbered circle to weaken up to 4 neighbouring greys - this is a key part of my 'Survivalist' strategy below).

Simplistically, then, there are two basic strategies - 'Survivalist' or 'Chain-builder' depending on where you want to get your points.

A 'Survivalist' minimises the number of circles on the screen and always explodes grey circles as quickly as possible, and gets high scores by relying on the 7000-point level increase bonus. This is a low-risk strategy and one that I've used to get a consistent score of 200,000+ per game.

Survivalist tips include:
- get rid of #1s as soon as you can. They're a nightmare if you don't blow them up immediately and can single-handedly scupper a good game.
- explode circles as soon as you can and reveal greys quickly - basically, try to keep the screen as empty as possible.
- if you find yourself with a #1 stuck at the bottom, check the circles around it and try stacking circles with the same number on top of each other - this will eventually free the one
- later in the game (after level 17 when you start being short of explosions and the ratio of greys rises more quickly), try to be more efficient and maximise the use of explosions to reveal grey circles. I pack greys around #3s, #4s and #5s - ideally you want to have four greys touching a number when it blows up, so you're as efficient with your explosions as possible.

A 'Chain-builder' sets up sequences of explosions that result in very high scores, but at the cost of not blowing up the increasing numbers of grey circles on the screen. It's much more of a high-risk strategy as an elegantly designed sequence can be ruined by a single unplanned explosion that defuses the sequence and leaves you with a screen full of grey circles and few points. However when it goes right, you can get huge scores - shown on the Global high-score list this morning.

Two things to note:

a - Since the maximum points from level-increases is about 210k (30 levels x 7,000 point bonus), these people are getting ~300-400k points per game from explosions - that's around 500-800 points per circle! (Note: They could also be getting points from completely clearing the screen multiple times (each time you remove all the circles from the screen you get a 70,000 point bonus) but I think that's quite unlikely as it's rare and there are people on the high score list with multiple entries - that doesn't happy by luck alone!). This means getting average chain lengths of 10, which is astonishing.

b - As you can see, my overall ranking is pretty poor - and following the survival strategy isn't going to help me any further. I need to start getting points from chains...! And working out how to design consistently long chains. One method I've seen described to build chains is to simply avoid any explosions (except for #1s) and then allow the level increase to wipe out your screen. I'm not sure about this as my efforts with this strategy have been quite unsuccesful, but I'd love to hear from anyone who has ideas about how to make the most of it.

From my analysis I believe that the optimum strategy is a hybrid of the two above - to build chains whenever possible early in the game (levels 5-20) and then moves to a pure survival mode for the remainder. Ideally you want to be going into levels in the late 20's with a pretty much empty screen that will let you fill up slowly over the next 6-7 levels - to make the most of the level increase bonus - making sure that you get every last circle in that you can!

I think that this strategy has a nice blend of riskyness - though it requires some experience to work out how congested you can allow your screen to get during the early levels before you hit the event horizon - beyond which you won't be able to recover, and will crash and burn within a couple of levels.

Good luck, and let me know how you get on - specifically, if you have any good Chain-builder tips for me :-)

I'll post updates if I make any progress... Next target is 300k!

Umair Haque's 'Generation M Manifesto'

Prompted by the G8 meeting in Italy, Umair Haque has penned the 'Generation M Manifesto'.

Dear Old People Who Run the World,

My generation would like to break up with you.

Everyday, I see a widening gap in how you and we understand the world — and what we want from it. I think we have irreconcilable differences.

You wanted big, fat, lazy "business." We want small, responsive, micro-scale commerce.

You turned politics into a dirty word. We want authentic, deep democracy — everywhere.

You wanted financial fundamentalism. We want an economics that makes sense for people — not just banks.

It's a thought-provoking read, I recommend reading the rest of it.

Negative visualisation & the rehearsal of worst-case outcomes

A Google I/O talk from the perennially thought-provoking Tim Ferris:

The messages I took from watching this 5-minute talk:

1. Negative visualisation – “What fears are stopping you achieving what you desire?”

- assuming  you took a bold move towards your ideal goal, list the potential areas for failure, and describe in detail the scary outcome
- for each outcome, rationally assess its

> probability   
> level of impact         
> longevity     

- visualise success, describe the desired outcomes in detail
- assess the probability, impact, and longevity of the successful outcomes
- weigh the outcomes, make a rational choice

2. Rehearse negative scenarios - "Is this really the condition that I feared?"

- face your fears and see if they are as bad as you imagine
- experience them first-hand to see if you could hack it
- inoculate yourself against fear by knowing that you would survive and thrive in the worst-case scenario

Next steps:

- Put this system into practice

- Read Seneca, Cato, Marcus Aurelius

Hell's Gate - 35 years of burning

A story to capture the imagination: Hell's Gate, Uzbekistan.

This place in Uzbekistan is called by locals “The Door to Hell”. It is situated near the small town of Darvaz. The story of this place lasts already for 35 years. Once the geologists were drilling for gas. Then suddenly during the drilling they have found an underground cavern, it was so big that all the drilling site with all the equipment and camps got deep deep under the ground.

None dared to go down there because the cavern was filled with gas. So they ignited it that no poisonous gas could come out of the hole, and since then, it’s burning, already for 35 years without any pause. Nobody knows how many tons of excellent gas has been burned for all those years but it just seems to be infinite there.

Stories like this make me want to travel!

Finding the most inaccessible place on earth

I enjoyed this New Scientist article about finding the most inaccessible place on earth:

The maps are based on a model which calculated how long it would take to travel to the nearest city of 50,000 or more people by land or water. The model combines information on terrain and access to road, rail and river networks. It also considers how factors like altitude, steepness of terrain and hold-ups like border crossings slow travel. Plotted onto a map, the results throw up surprises. First, less than 10% of the world's land is more than 48 hours of ground-based travel from the nearest city.

There are obviously lots of flaws in the logic - I think I would have made the size of the city larger (say 1 million+ inhabitants) which would have made the remoteness of some places starker. But as it is, the study is fascinating...

On a separate note, I like that the modern air routes (shown as pale blue lines on the map above) aren't too dissimilar to the undersea telegraph cables shown on this map from c. 1890s:

Like the convergent evolution of sharks and dolphins, sea and air routes have clearly adapted to the constraints of the environment...

Thoughts on values

Most companies have corporate values - in other words, characteristics that they believe distinguish their culture from others. Often these values are words like 'straightforward', 'honest', or 'simple'. Sometimes they are phrases that embody the rest of the culture - Google's, famously, is 'don't be evil'.

Why do companies do this? After all, inevitably someone in the organisation does something that violates one of their values, and the resulting backlash is worse than it would have been without the value being there. For example, when it was found that Google was censoring internet searches in China, there was a furore. This wasn't because they were the only search engine to do so (they weren't) but because the public held them to a far higher standard because of their commitment to doing no evil. No-one is surprised when we hear about the awful business practices of some tobacco companies, or fast food chains, or clothing manufacturers. I'm sure that they also have values, but they don't seem to carry any weight because the companies themselves ignore them.

So it's not the stated values of a company, it's the accountability to the values which the company expects from its employees. Drawing a line in the sand means nothing unless there is some consequence to crossing it. The corporate culture has to provide examples of the values being practiced by its employees, from the top down. As soon as there is an unchallenged action that isn't consistent with the values, the culture will begin to be eroded.

Where am I going with this? Well, I wanted to state my own values, which I expect to be held to by others. My line in the sand.

My values are:

- Courage - Integrity - Compassion - Self-discipline

I'll talk more about this soon.

-------------------------- Sent from my BlackBerry

Getting rid of privilege through greater transparency

Privilege is a word with an interesting etymology.

From the Latinate 'privi' and 'lege', we also obtain the English words 'private' and 'legislation', or law. So in its original meaning, privilege means 'private law' - a rule which applies differently to those in power than to those who are powerless. In Medieval England, a nobleman might have the privilege of hunting in Royal Forests, but a serf who did the same thing might have his hands cut off. That's privilege.

In the last few days, we've seen some MPs exploiting their positions of power to squeeze every last penny they can from their expense accounts. That they haven't been sacked for this abhorrent and unacceptable behaviour demonstrates that privilege remains. It may not look quite the same, but the priciple remains - different rules for the powerful few than for the powerless many.

The reason it's been this way is through lack of transparency. No-one would vote for venal and morally bankrupt individuals if their avarice was in plain sight - and they know it. MPs like Michael Martin (whose self-serving cronyism exemplifies the worst of political machinations) are doing all that they can to keep their expense claims hidden and private. Different rules. Privilege again.

So how do we introduce more transparency? We move towards a new mode of electronically-mediated government, where the norm is openness and visibility. We can use the power of social networks and collaboration (the blessings of Web 2.0, if you will) to solve the problems caused by lack of trust and transparency that plague government. It's what mySociety are doing and that's why Tom Steinberg is a hero of mine.

I'm looking forward to a day when all government is truly transparent, and where the actions of those in whom our trust is invested - the democratically elected leaders we are so lucky to have - are visible and accountable.

So where does that leave privilege?

I think we can live without it.

Debating Corporate Social Responsibility

The book group this evening (see last post) ended up discussing Corporate Social Responsibility and what it really means in practice.

It was interesting coming now from a company like BT (where CSR and acting 'inclusively' is a key part of our thinking and BT are seen as world-class in this respect) to one like Detica, who are now owned by BAE, one of the world's largest arms manufacturers.

The debate centered on whether CSR engagement is at an employee level or at a corporate level? Is it essentially branded volunteering, or more like pro-bono? Do companies do it to make their employees feel better or to increase reputation and thus Sales? Should CSR issues be linked to scorecards / reviews, or even to bonuses?

Of course there was no hard and fast conclusion, but it was a fascinating discussion, which raised some points I'll discuss with colleagues. And I'll try to attend the next book group!

Some facts that should change the world

This evening I'm attending a book group at my old company that I started when I worked there but has been carried on by a good friend and I'm glad to say is flourishing.

The scope was originally books that are pertinent to business consulting but not really the sort of thing you'd actually use as a textbook - examples being 'Emotional Intelligence' by Daniel Goleman or 'Influence' by Cialdini. These days there's a more varied mix but it's as interesting as ever, with the added bonus (for me) of being able to catch up with ex-colleagues.

The book this time is '50 Facts that should change the World', by Jessica Williams. By virtue of its structure - each 'Fact' is a self-contained chapter that can be read on its own - it's ideal reading material for a book group because it's possible to dip in and read as much or as little as you like without losing out. Or at least that's what I did.

Written by a journalist / TV producer, the facts range from globalisation 'horror stories' (there are lots of Starbucks shops in London; ten languages die every year) to privacy issues (number of CCTV cameras; aggregation of personal data) via human rights (slavery; female genital mutilation; torture) and sustainable living (greenhouse gases; 'throwaway culture').

Most of the issues I was broadly aware of, but there were a few around inequality and human rights that I wasn't aware of. In the table of contents I starred ten of the Facts that particularly surprised or shocked me and just read those chapters. They were:

8. Every cow in the EU is subsidised $2.50 per day, more than 75% of Africans live on.

9. In more than 70 countries, same-sex marriages are illegal; in nine countries, the penalty is death.

11. More than 12,000 women are killed in Russia each year as a result of domestic violence.

23. In Kenya, bribery payments make up a third of the average household budget.

32. Britons buy on average 50 items of clothing each year, most of which ends up being thrown away.

36. More people die from suicide than in all of the world's armed conflicts.

39. Two million girls and women are subjected to female genital mutilation each year.

42. One in six English teenagers believe that reality TV will make them famous.

44. There are 27 million slaves in the world today.

49. The US owes the United Nations more than $1 billion in unpaid dues.

Just appreciating these few Facts made quite a deep impression on me - they make for sobering reading, and put my very minor problems into perspective!

Now I just have to work out what I can do to change the world...

Nazi research and 18th century navigation: Phaeton magazine, Issue Two

Having registered with Scribd, I thought I'd have a play...

This is the second issue of a magazine I produced a couple of years ago for the London History of Science Society (which I founded with a friend). The society hasn't done much recently, but I expect it'll get revived at some point!

Anyway, if you've never seen it before, enjoy:

Phaeton magazine Issue 02

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