*by Mike Bourke*

We all leave our dice at home sometimes. If home happens to be where you are playing, that's not a big deal, but that is usually not the case. That's still not usually a major problem, as you can often borrow some from another player. Heck, at least one GM I know brings a couple of spare sets to games just in case of such an eventuality. If you're gaming in a store, you can also probably buy enough to get you through the day if you have to.

But on at least one occasion in my memory, everybody forgot their dice. This is more likely to occur with fewer players, as it needs fewer people to make the same mistake, but on the occurrence that I have experienced first-hand, there were seven players and one GM. I guess the stars were aligned "just right" on that particular day! What do you do then?

That was to be the main thrust of this article, when I first started writing it - a comparison between different dice substitute systems, because I had thought of a way to make Bingo draws an effective replacement for dice in a pinch. But as the text evolved, and one thought led to another, I came to a quite startling conclusion: using an online bingo site can actually make you a better GM.

I thought about revising the entire article, in line with this new direction, but concluded that it would be more useful to keep it as it was originally written; so only these opening remarks have been rewritten to accommodate the change in direction.

No random number generation system is perfect, but there are tolerable margins. In the bad old days, dice were manufactured from a softer plastic that eroded quickly along the edges; it was quite easy to blunt the edges along one face or set of faces to induce a bias.

The second generation of dice for RPGs were a considerable improvement, but it was still possible to weight the dice because the numbers were simply carved out in the moulds. It was common practice for players to fill these hollow numbers with liquid paper or epoxy or other such material to make the result more visible. By choosing materials with different densities, a slight bias could be introduced. It was also possible to place them in a vice and distort the shape a little, but these methods had vastly smaller effects on the accuracy of the results.

There was a perception at the time that computer-generated random numbers were more truly random, and for a time it was not uncommon for a computer-generated list of die rolls to be used instead of actually rolling dice. You could get a couple of hundred d6 rolls on a single sheet of printout quite easily, more than enough for three or more game sessions.

But not even computer-generated dice rolls are perfect, as I began to suspect after using a random number generator I wrote on my old Commodore-128, which seemed to have a "phobia" about generating extreme values in its in-built random number generator. When I wrote a program to test this perception I was able to confirm that the probability of a minimum or maximum result was significantly less than it should have been - so much so that die rolls even with a biased dice would have been preferable. (As a side-note, I did come up with a means of restoring the randomness to the in-built function: Multiply the psuedo-random number by 100 and throw away the part before the decimal point. Tests showed this to give a truly random distribution.)

Which brings me back to those alternative mechanisms to dice. One of the first issues of Roleplaying Tips that I read (issue #141) had various reader responses to a suggestion for replacing dice using random number tables. Other tips through the years both here and in other sources suggested using homemade chits when no dice were available - right down to the brute-force approach of cutting or tearing up a sheet of paper and writing the numbers 1-20 on the pieces, then folding them (like you do the stub of a raffle ticket) and placing them into a bag.

Immediately after I read about this idea I started wondering exactly how random they would be. If you used an folded piece of paper, the act of unfolding and refolding it could eventually make a result identifiable by feel. If the pieces weren't cut perfectly evenly, the same result could occur - it would be the equivalent of marking a card. If the numbers were of even slightly different sizes, one result would me more likely to come to hand than another.

Then there's the question of shuffling, which came to mind when someone suggested using playing cards instead of dice. We all accept a deck of cards that's been shuffled a couple of times as being randomised, but it has been proven mathematically that a deck needs to be riffle-shuffled no less than seven times to completely obliterate the pattern of results from a prior hand. Other methods of shuffling tend to be even less effective.

Which raises the question of how effectively randomised would a set of chits placed in a bag be? Surely, unless the bag was fairly large, the chits would tend to form stacks and preserve sequences of results in the order they were placed into the bag?

What is random, anyway? The human mind is lousy at perceiving randomness. We see patterns that aren't there, and tend to think that an even distribution of results is more random than one with clumps. Which is more random: 1,2,3,5,7,8,9,10 - or 1,3,3,5,7,9,10,10? Without being tipped off by the discussion we've been having, most people would have picked the first - but if you've rolled 6 numbers on a d10, there's a 60% chance that a 7th roll will produce a result you've already rolled, and only a 40% chance that it will be a different digit to the 6 that have preceded it. The chances of rolling 8d10 and not getting a single result repeated are more than 55-to-1 - against!

What's more, the human brain is lousy at creating randomness. When you study any large list of supposedly random numbers that have been deliberately created, you find that we under-represent 0's, 1's, 5's, 9's, and even numbers - and have a disproportionate number of numbers that end in 3 or 7. That's because these numbers feel more random when the list is being generated - but they actually aren't.

So, how does all this connect to Online Bingo?

Bingo, as a game, relies on the fact that if you draw often enough, and ignore those results that don't fit, eventually you will draw the required numbers to fit any defined pattern of results. Which pattern will fill first? How should you choose your numbers? Is there really an effective Bingo strategy? Articles about superstitions of players would suggest not, but at the same time, implies that choosing numbers that are commonly considered bad luck (like 13) might yield a result when you match the number and no-one else does. When you are competing with other people, human psychology always has to be taken into account; if all else is equal, any advantage you can identify should translate into long-term success.

If the results of the draw are genuinely random, or even close to it, then the perfect bingo card should also be random. There should be a more-or-less even distribution of results, with clumps, but with no perceivable pattern.

Which brings us back to replacements for die rolls. Because Bingo numbers don't repeat, once they are drawn, they aren't the same thing as a dice, so it would seem at first glance that they are of no help to us. However, if you play as many games simultaneously as the size of the dice - 6 for a d6, 8 for a d8, and so on - then you can get pretty close to true randomness. That's different games with separate draws, of course. For 2d6, you'd need twelve, and for d20, you'd need 20. In real life, that's impractical. But how about online?

What's more, the larger the die size, the more suitable this technique is. Consider a bingo game with 100 numbers (which never repeat, of course) - the odds of rolling the same result twice in a row on d% are pretty low - so much so that the margin of error is negligible. And the odds that the 1% higher or lower that would make a result the same as one that's already been drawn, and that this would happen to be at the exact point in the range of results to make the difference between success or failure is even smaller, to the point of being negligible for at least half the bingo results.

But to my mind, the most useful link between a successful Bingo player and roleplaying is that Bingo teaches us about the nature of randomness. A winning strategy at Bingo requires the ability to spot and reject patterns - and those same patterns are equivalent to a table of results from a biased die. Playing Bingo well makes it harder for players to cheat in an RPG.

And isn't THAT food for thought?