For Normal mode, levels advance when total captures (TC) + total living stones removed (TL) is greater than level * level * 10. So:
if ( TC+TL >= level * level * 10 ) level++;

The formula for Hard Mode & Single Color Mode is just:
if ( TC + TL >= level * 10 ) level ++;

…so it just takes a lot longer for your level to change in normal mode. You’ve probably also noticed that when you remove a particularly large group, you might jump lots of levels. The function that checks whether you’ve advanced a level is recursive, so it keeps calling itself until you are at the level you “should” be at, (hopefully that makes any sense).

There was some speculation earlier about score calculation. Here are the formulas:

Normal: level * score * score
Hard & single color: level * level * score * score

(But I will catch you one day!)

Any speculation on scoring calculations for Fast Mode?

Martin mentioned something about it being (c x c x l x l) where c = captures and l = level for normal mode.

As a father of a 1 & 1/2 year old, rewards and motivation are very relevant right now, so I appreciate your insights. (There will be no gold stickers in my household! …at least, not for tasks I want her to like. They might be helpful for getting her to do chores though.)

It strikes me that a book my wife and I are reading is probably relevant to this discussion, Nurture Shock: New Thinking About Children. It outlines a bunch of ways in which conventional thinking about child development and rearing have been discovered to be… if not wrong, then at least flawed in some way. I went and looked at the index, half expecting there to be a chapter that deals with this stuff. One of the later chapter titles suggest at least a tangential relationship, but I haven’t read that one yet. Anyway, it’s been well worth a read so far, and frequently comes up in conversation.

The joy for most dogs and most calm horses becomes far less about the reward itself and much more about creating behavior in the humans (“what can I do to get them to press that clicker button?” “what is the least I can do?” “What new thing can I do that will produce the *jackpot* (the extra-large reward given only for very special efforts)?”

With the horse in my video, two things were happening: I was using clicker-training (I.e. Gamification) to reinforce what *should* have been an intrinsically motivating behavior (as opposed to, say, a tedious task with no potential for intrinsically-rewarding feelings associated), AND this horse was not interested in the meta-game. He didn’t find joy in figuring out what I wanted him to do. So he quickly became less and less motivated (self-determination theory explains this quite well) with ultimately dangerous consequences.

Today, this horse is unrecognizable to those who knew him during that time. He is engaged and energized and spirited… all which happened when I stopped “rewarding” him for being engaged, energized, and spirited and used those principles of autonomy, mastery, and purpose. It has now been just over a year since I saw the “error of my gamification/Skinner box ways”, and the changes have been lasting and richer as time passes. He now is even more proud and willing than when I made that video.

I do still use extrinsic rewards for the things he would not otherwise EVER want to do, and those pose no problems. All upside, for him since there is no danger he will lose motivation. But I am extremely cautious using it for things which could/should be motivating.

I fear, deeply, for the ways in which extrinsic rewards are being applied to education in a well-meaning but ultimately dangerous attempt to “increase motivation and engagement for learning.” If it merely had a short-term boost and then eventually it stopped working and things returned to their pre-rewarded state, I’d have no cause for alarm. But it has the potential (demonstrated over decades in more than 100 different studies) to leave learners LESS motivated than they were before extrinsic reward structures were put in place. Just a few of the specific examples:

*kids given ribbons for drawings began to draw less than those not given rewards
* writers rewarded for poems began to write less sophisticated poems
* monkeys that enjoyed solving wooden puzzles began solving fewer puzzles (and making more errors) when a treat reward was given for solved puzzles

And on and on.

These results seem counter-intuitive, so it has been tough for people to recognize the harsh and lasting implication of applying extrinsic rewards *where there is or could be intrinsically rewarding activities*. Further, the fact that so many people and animals DO discover and enjoy a meta-game around extrinsic reward structures makes the problem even harder to spot: “but look how engaged and motivated they are?!” Yet if we look more deeply, we find the meta-game they are enjoying is producing engagement around the reward structure and not the thing-we-wanted-them-to-engaged-with. In many cases, this distinction simply does not matter. They are active and appear motivated, so who cares what’s driving it?”. But the difference can be staggering, because you end up with phoned-in behaviors for the thing you care about, masked by excitement around the meta-game.

Marketers in it for the short term, especially consultants, will get a lovely spike in engagement and sometimes a long-term meta-game spike. This makes everyone happy, sort of. But it produces no lasting effect of producing deep engagement, and in some cases can drive people to now care LESS than before about the actual thing you wished they cared about.

You can see it in the way marketers will often point to Nike+ as an example of success, forgetting the fact that people actively WANT to exercise more, and that for most people running is itself *not* an intrinsically rewarding activity. In other words, it feels good to HAVE run, but most never get the endorphin rush that makes it feel good in real time. So extrinsic motivation is pretty much all upside where exercise is related.

Oops, sorry for the novel-lenth comment…