If you want to generate random numbers but don’t have any dice, all you need is two people (with at least one hand each.) Since you’ll usually want to do this in a RPG setting, we’ll call one the player, and one the GM.
On the count of three, both people hold up one to five fingers. The player then counts up from his number to the GM’s number. If the GM’s number is smaller than the player’s number, the players counts up to 5, then back around to 1 and then continues counting up. The count between the two numbers is the result. If players both choose the same number, the result is the maximum number of fingers, in this case 5. So, for example:
Player: 1, GM: 4, Result: 3
Player: 4, GM: 3, Result 4
Player: 2, GM: 2, Result 5
This should make every result from 1 to 5 equally likely.
Change the number of fingers, and you can simulate any die on the fly. Don’t have a d13? Well now you do! With dice bigger than a d10, I recommend both people shouting out the number at the same time. Not as clean, but it will work in a pinch.
This has some fun applications. If you use it to simulate a d6 twice, for example, you can add them together and generate the 2d6 bell curve. Play Apocalypse World without dice!
If you want 1s to be easy and 5s to be hard, do this: Each player holds up one to five fingers. Subtract the smaller number from the larger number to produce your result. If the numbers are equal, the result is that number. For example:
Player: 2, GM: 4, Result: 2
Player: 5, GM: 1, Result: 4
Player: 3, GM: 3, Result: 3
Using this method, there’s only one way to produce a 5, three ways to produce a 4, five ways to produce a 3, seven ways to produce a 2 and nine ways to produce a 1.
There’s some interesting things going on with this method, assuming that the player wants a high number and the GM wants a low number. For example, if the GM always showed a 3, then he could prevent the player from ever getting a 4 or 5 result. Once the player caught on to this, he might also start showing 3, which would leave them producing a result of 3 forever.
So what if we disrupt this balance by making a 3 result slightly better for the player? Let’s take a page from Apocalypse World and say that a 4+ result means a complete success for the player, a 3 means success at a cost, and a 1 or a 2 means failure. Now, if the GM always shows 3, and the player also starts showing 3, then the player will always succeed at a cost. If the GM wants to open up the possibility for failure, he’s going to have to also open up the possibility for complete success.
This might cause too much of a headache, though. I’d say Method One is more promising.