I've toyed with the idea of not using a fair RNG for games for this reason. People expect die rolls to converge to the average distribution much much faster than they actually do. So perhaps you can make a RNG program that does exactly that and does what the user expects, even if mathematically ridiculous.
For example, if 20 is rolled then the probability of 20 being rolled again is halved (so it has a 1/40 chance) while the probability of its inverse is doubled (so probability of 1 is 1/10). This dramatically reduces the chance of the three 20s in a row scenario and would very quickly regress to the mean, just like people expect. Added flair for affecting the probabilties of all possible values subtly (so that after rolling a 20, a 2 becomes more likely and a 19 less likely).
I'm sure I can't be the only person to think of this.
Say the player loses a 75% roll, then attempts another identical 75% roll. The game will actually give you better odds for the second roll. I think it's silly -- the game basically lies to you about your odds on the second attempt.
It may be deceitful, but it makes for a better game. Seeing your five hit attack miss five times at 5% miss chance per attack will induce true frustration. Battle for Wesnoth doesn't care. It will be honest, and you will scream in anger.
> Seeing your five hit attack miss five times at 5% miss
> chance per attack will induce true frustration.
I was curious, so I worked out the chances of this happening. For a given five hit attack the chance is 0.00003125%, or 1 in 3.2 million. So yes, I imagine it is very frustrating, but it happens incredibly rarely.
Shuffling is different from selecting at random. I had an MP3 player that would use random selection instead of shuffling all tracks and it would annoy the hell out of me to hear the same songs twice in a row. I don't know if this is what iTunes used to do but if so then those people were right to complain.
It is. iTunes would play a song, and randomly select the next one (it would do random play, rather than shuffle).
Nowadays it generates a shuffled playlist and goes along, and people whine because it doesn't reshuffle automatically (you have to disable and enable shuffle to reshuffle).
An other option is to use random sampling, and to re-sample after you're done with the current set (possibly excluding any song of the previous sample)
iTunes used a shuffle that always resulted in the same order as long as there was the same number of songs on the device. (Or perhaps just shuffling with a tiny PRNG that used the number of songs as seed.)
You're right that would probably lead to better user satisfaction, but I'm not going to implement something like this. I refer you to the answer I've given herokusaki below. Basically, the site is not about straight-up die rolling. It supports a myriad of different rule systems. On top of that, it doesn't keep track of users, so it's not possible to tinker with results based on user state. I have no real intention of changing that either ;)
I've thought about the same for Settlers of Catan, which I think is too random if you use dice, disrupting people's ability to do more than basic strategy.
I know there exist "dice" packs of cards, which contain the correct distribution of rolls. If you shuffle a few of those together, you'll probably get a nicer game.
That sounds like a nice idea, actually. I hate those rounds where 11 or 2 occur more often than 6 or 8. I know it can happen, but it can make the game rather annoying at times.
I actually think that makes the games more fun. Especially so when you have a larger game so that there are people on those tiles.
For me, it makes the game feel less "solvable" by basic analysis. Sure, statistically certain observations will hold. For the game you are in, though, you have to be ready to adjust your strategy based on what has happened. (Clearly not in anticipation of future rolls, but more based on the resources you have managed to get, not the ones you wanted.)
Admittedly, we already tend to take the number planning a bit out of the game by initially turning them on the other side and you can only reveal the numbers to hexes you have built at (for the inital round of placing settlements/streets they are revealed after everyone has placed both). Makes for a nice variant where exploration holds surprises, or you can expand to hexes that are already known.
One of the nice features of the Settler of Catan assistant for the iPhone is that it will roll the dice for you, and it keeps a chart of the results. Thus one has data to back up the complaint that "Your 3 is out producing my 6!"
I've had to do this when training research monkeys in a former life, particularly when there is only one or two parameters being varied. They would learn the 'patterns' far too quickly. After seven heads in a row, they'd stop paying attention and always choose heads for some time afterwards.
The solution we settled on was block randomization. But that's probably not what you'd want for a human game as they could potentially figure out the end of each block (and what value remains). But it worked wonderfully for us.
People are born with bad intuitions about how randomness works -- it's not learned. For whatever reason, our brains are wired to make uniformity feel random and randomness feel ordered.
It's why we see stars in the sky, which are more or less distributed randomly in the star field, yet they don't appear random: they appear to form constellations.
It's basically impossible to correct this bad intuition. People educated in the statistics and mathematics of random numbers have to consciously learn what real randomness looks like and override their intuition.
But try as you might, the night sky will still form constellations. And dice rolls will still, frustratingly and confusingly, fall into streaks more often than you'd expect.
There are a lot of systems in the brain. It's theoretically possible that one of them will be untrainably spitting out the same flawed predictions, but we can certainly learn how to respond appropriately to those sensations.
IMO the problem can be best explained with a classroom experiment, almost like a magic trick. It is a built in human intuition which is at odds with the reality of randomness.
Split your class into 2. Give half A the players dice and a piece of paper. Give other half B just a piece of paper. Half B plays with imaginary dice, Half A with real dice. Everyone records 20 games of a piece of paper. You hand in the papers and the demonstrator (or maybe a new one that hasn't been in the class, for extra theatrics) looks at the papers. He will accurately place them into separate piles.
The trick is that fake randomness and real randomness are different enough that they are distinguishable with a high level of accuracy. Real dice will roll the same number in a row far more often than fake dice. The more games you play, the more accurately they can be distinguished.
You can look at the formulas to figure out the odds of rolling the same number 4 times in 100 rolls, but it doesn't drive home the message that your intuition is broken until you see intuition being beaten consistently and reliably by a better tool. It's fun too.
For example, if 20 is rolled then the probability of 20 being rolled again is halved (so it has a 1/40 chance) while the probability of its inverse is doubled (so probability of 1 is 1/10). This dramatically reduces the chance of the three 20s in a row scenario and would very quickly regress to the mean, just like people expect. Added flair for affecting the probabilties of all possible values subtly (so that after rolling a 20, a 2 becomes more likely and a 19 less likely).
I'm sure I can't be the only person to think of this.