Author Archives: david

Playing beeminder on hard mode by adding backpressure

So as you might have gathered I really like beeminder. A proper advocacy post will follow at some point, but for now this is just a report on a new experiment I’m going to be performing with it.

One of the things I don’t like about beeminder is the eep days. That is, days where you’re about to fall off and need to do some panicked activity to prevent you from doing so. In principle they’re fine – they provide good motivation and remind you of your duties as a good anti-procrastinator – but there are two main problems I have with them:

They tend to bunch together. Generally if I’m getting eep days it’s because I’m falling behind on ability to meet my goals, usually do to energy or time constraints, so I can get several goals eeping at once or in short succession.
They tend to reoccur. The problem is that goals are necessarily set at a reasonable daily rate, so necessarily if I just do a reasonable daily rate on an eep day it will reoccur tomorrow.

It should be relatively easy to prevent eep days from occurring. You just work a bit extra when you have the energy to do so to build up a buffer, then resume a normal rate and you’ve got this nice comfort zone.

Of course, it doesn’t work out that way. I naturally procrastinate until things become pressing and the buffer gradually dwindles away and the eep days happen.

Hmm. What I need is some sort of tool to stop procrastinating. Say, a way to be reminded of it and penalised for it.

Do you know of such a thing?

Oh, right. There’s this thing called beeminder. I could beemind my beeminding.

So I wrote a simple script to add a smooth backpressure to beeminder. The way it works is that I have a “Do less” goal (I’m really enjoying the do less goals) which tracks how many goals I have with less than a week left till I fall off the road each day. This goal is set to allow me 7 due-goal-days a week, so I can safely have one goal which is approaching due but if I have two then I will exceed my allowed rate and rapidly head towards failing my pledge.

I currently have two goals which are coming due (read more non-fiction and go to the gym more), so I’d better hurry up and get one or both of those sorted if I don’t want to derail.

Edit: Note that I’ve changed this to only apply to “hustler” (do more) type goals, as I found it didn’t work well with “do less” goals.

Richman Scrabble: A play report

A while ago I proposed Richman Scrabble. Nearly a year later I’ve finally got around to playing it, with my flatmates Dave and Rae.

The specific rules we played:

Richman scrabble as described in the link, with the take a penny leave a penny rule for change left after splitting. Each starting with 30 tokens (chosen to be “a bit less than a bingo”).
Currency was supposed to be secret, but we didn’t have a good way of hiding it so you generally had a rough idea of how much people had even if you didn’t know the exact count.
Bidding happened when everyone agreed they were ready with no time limits.
In the event of a tie, the winner is randomly resolved (we use a die). The second price is of course the tied bid (so if two people are tied for 8, a random one of them wins and pays 8).
No dictionary research, no word lists, etc. “Sudden death” challenging – anyone can challenge a word at no cost, you lose your turn if your word isn’t valid. Validity is determined by SOWPODS.

The game went pretty well. By which I don’t just mean “I won”, though I did. Rae had a 22 point lead on me, but I had a 31 currency token lead on them, so that made the difference for me winning. So, obviously I think that adding the currency to your score at the end is a good thing.

Dave was quite far behind on points but managed to claim the lion’s share of the currency tokens, which brought him very close to victory. If he’d known the word “pice” (which, of course, is “a former monetary unit of India and Pakistan, equal to one quarter of an anna”) he’d have pulled ahead at the last minute and won.

Over all I think the bidding for turn mechanism worked pretty well. I did find myself fairly often forgetting the second price rule, but between us we remembered it. I thought it had a pretty positive effect on the bidding.

The strategy I settled on was basically to bid 2/3rds of the score I’d get by playing plus an “urgency bonus” for tactical considerations around really wanting to play (e.g. if I was desperate to get rid of a bunch of tiles I would overbid compared to the cost of the word I’d get).

One thing that was interesting and I don’t know if it’s legitimately how this style of game plays out or just the result of us all being slightly drunk and a bit out of our depth with the new rules is that the scores were really low. I normally aim for a par of about 20 points before it’s worth playing (a strategy hit on by my brother which I shamelessly stole), but I only got 20 points twice in the game – most of my scores were closer to the 15 point mark.

I’m not entirely sure why this was. I was trying for 20 point pars I think, but it didn’t seem as easy to achieve. Possible due to less letter churn when your hand is bad – normally if you have a rubbish hand you’re going to have a turn anyway and that will force you to get rid of some letters. Other possible theories are that you’ve less incentive to mess up the board for other people because you could just play twice in a row. I’m not sure. I’d have to play more games to know whether this is a real effect or not. Right now I think I’d put my money on it just being a result of unfamiliarity.

Dave, who is totally fluent but not a native English speaker, reported that he felt the game put him at a bit of a disadvantage because he’s much better at Scrabble strategy than he is at the words, and this seemed to emphasise the words more. This sounds more like a feature than a bug though, as I suspect (particularly with the above caveats) that once we’ve adjusted to the new style of play this version will be full of strategy, but hopefully one that results in a slightly less frustrating game than normal scrabble (one of my bugbears is that optimal scrabble play makes the game less fun).

The only thing that I felt hurt the game a bit was the lack of letter churn. I think it might be interesting to play a variant where before the bidding people can freely swap out tiles from their hand. I don’t know if that would be an improvement, but it might be worth trying.

All told, I think the bidding for turn mechanism is a good one and will probably be playing around with it as a concept a bit more.

A mod for a large class of board games

Have you noticed how there’s an external factor that is largely decided for social rather than tactical reasons and massively influences the tactics and strategy of a large number of games you play?

No? Are you sure? You probably have. Most people who play board games regularly will have commented on it at least once.

This factor is of course where you’re sitting. More accurately, the order in which you’re sitting.

We noticed this most recently playing citadels – I was acting as a spoiler between two players who are normally more evenly matched but one was now consistently winning by a large margin. We’re not sure this is a seating order effect (though we were sitting in the same order each time), but it seems a plausible culprit. I’ve definitely noticed a strong seating order effect in the past when playing scrabble – what the player before you is willing to pass on makes a massive difference. If you have two equally matched players and one inexperienced player, the one who comes after the inexperienced player gets a huge advantage.

I have an idea for how to offset this. I don’t know how well it would work, but it should be pretty easy to try: You randomize the order of play each turn.

The exact mechanism of doing this depends a bit on the game in question. e.g. citadels has a different turn structure from scrabble. Most games are more like scrabble than citadels and can use that variant unmodified.

The basic tool is the same though: A set of cards, one for each player. When you need to decide turn order, you shuffle them and deal them out face up. Play proceeds in that order.

(For Citadels, play starts with the King as usual, but the characters are then passed around in player-card order rather than seating order).

For something like scrabble where people are actually taking turns you’d instead want to deal out the cards, play in that order, then when you get to the end shuffle and deal again.

The scrabble one does change the character of the game somewhat because you no longer have a fixed number of plays occurring between each of your turns (though it averages out) – potentially you can even get to play twice in a row. For Citadels I think this should matter much less.

Other variants:

Play the cards face down so you don’t know who comes after you
(For the scrabble version) Play with two sets of player cards. Deal both out face up, one after the other. When you complete the first one, shuffle it and deal it on the end of the other one. This means that you always know when your next turn is going to be so it’s a little more predictable.
(Also for the scrabble version) Have a deck with multiple copies of each player card. Shuffle these all together and draw from the top to determine whose turn it is. This changes the game a lot more, and makes it much more random. It might be interesting but it’s probably not going to be that good (see also Richman Scrabble).

I haven’t tried any of these yet. I’ll report back on if they’re any good if I do.

Gnocchi with Courgettes and Sundried tomatoes

Here is a recipe very much composed by my previous algorithm, albeit the “what’s in the kitchen” variant rather than the “what should I buy?” variant.

It’s also influenced by the “I am feeling super lazy therefore I’m going to throw technology at the problem” style of cooking, using both the food processor and the pressure cooker. You could probably prepare it without the pressure cooker, you can certainly prepare it without the food processor.

Ingredients

100g dry sundried tomatoes
1 small red onion
1 head of garlic
4 medium sized courgettes
About 50g salted butter
500g gnocchi
200g feta cheese
“some” black pepper

Note: I used the sundried tomatoes directly from dry. This worked pretty well but I forgot that they have a lot of salt in them if you do that. If you have less salt tolerance than me you may wish to soak them a bit before you do this to leech out some of the salt. If you do it from dry then definitely do not add any salt to this dish.

Instructions

Step 1:

Peel but do not chop the head of garlic. Finely chop the onion. Coarsely chop the sundried tomatoes (I used the food processor, you could just use scissors). Add these with just enough water to dampen the sundried tomatoes (so they don’t burn) and the butter to the pressure cooker. Bring it up to pressure and then cook for an additional 5 minutes.

Step 2:

Meanwhile, grate the courgettes (again, I used the food processor, you could just use a normal grater).

Once the previous step is complete, add the gnocchi and grated courgette to the mi, crumble the feta into it and grate some black pepper on top. Mix well. Now bring the pressure cooker back up to pressure and cook for another 5 minutes.

Step 3:

Eat.

Notes

The flavours all work really well together. It’s a bit too salty for me (and I love salt), so I think next time I will definitely partially pre-soak the sundried tomatoes just to ditch a bit of the salt, but I think it’s otherwise almost perfect. I might try adding some capers next time for a bit of sharpness, but it’s probably not necessary.

In terms of quantity: This will look like it’s not a lot of food, but it’s very dense. It served three of us (and we were quite hungry) and we were very full at the end. It’s probably a 4 person meal if you add a side salad to make it look a bit less small – it’s certainly filling enough.

In terms of doing this without a pressure cooker: My guess would be that the best way to do it is to mince the garlic, fry it with the onions in the butter, then add the sundried tomatoes (which you should definitely pre-soak or use an already soft variety) after that. You may also want to pre-cook the gnocchi. It will be a somewhat different dish – it’s very hard to do garlic like a pressure cooker does garlic – but it will likely still be very tasty.

Another example of a compact convex set

At the end of my last post on compact convex sets I claimed that every point in one was a countable sum of extreme points. I later realised that I’d made a stronger claim than the theory did, and thus that it was probably false. As such I owe all 5 of you who read my maths posts a counter-example.

One reason it took a little figuring out is that I’m pretty sure the result is true for normed spaces. I haven’t worked out the details, but basically I think you can use a sequence of finite sums approximating it to within \(2^{-n}) to build a countable sum equalling it exactly. I may bother to figure out the details, but I’m about 90% sure they will work.

However the claim is false for locally convex (Hausdorff) topological vector spaces. Here’s an example:

Let \(V = \mathbb{R}^{2^{\aleph_0}}\) with the product topology. The basic open sets in this are convex, so it’s a locally convex topological vector space.

Let \(A\) be the set of non-negative vectors such that for all \(a, b\), \(x_a + x_b \leq 1\). That is, we’ve “cut off the corners” of the unit cube. This is a closed subset of the cube \([0, 1]^{2^{\aleph_0}}\), which is compact because of Tychonoff’s theorem, therefore is itself compact. It’s an intersection of convex sets, so is also convex.

The extreme points of this are then the origin and all the unit vectors \(e_a\). Therefore any countable sum of extreme points can only be non-zero on countable many coordinates (because convergence is pointwise). But the vector which is uniformly \(\frac{1}{4}\) everywhere is a member of \(A\) which is non-zero at uncountably many coordinates, and thus cannot be a countable sum of the extreme points.