Math People...What are these odds?

[MojoGM]

here's what Djeta said:

"First we rolled the same initiative (roll 1). Then the same attack (roll 2). Then we did that again (roll 3). Then we noticed it was weird so we each rolled a random roll to see what would happen (roll 4). We both got a 10. Then we both rolled the same initiative again (we both got natural ONES that time) (roll 5)."

hmm... don't know what happened to the last one, but Djeta said in her initial post that it was 6 rolls.

There were two initiative rolls, two attack rolls, a random roll (the 10), and the last initiative roll (the natural 1). That ended our streak.

 

[Iron Sheep]

What's the odds of this happening to an enworlder? and hence the odds of us seeing something like the above posted? Seriously, does anyone care to make an estimate of this?

Well, as a very rough estimate, a player probably rolls at least 50 d20's in a session (4 combats of about 5 rounds, plus a few skill checks), more if they play a higher level character with multiple attacks. Playing once a week for 2 years (which I think was the typical life of a campaign according to wizards' research), we have about 5200 d20 rolls in a campaign.

So the chance of Djeta and MojoDM rolling the same sequence of 6 rolls during a campaign is roughly

1 - (1 - 1/20^6)^5200 = 0.0000812466997...

or roughly one in 100 000, as a ballpark estimate.

If you have 4 other players (including the DM, and you want to allow for the possibility of rolling with any of them, the odds become:

1 - (1 - 1/20^6)^(5200*4) = 0.000324947...

If you then allow for this to happen to any ENWorlder, there are probably about 1000 people who post at least infrequently (and if that number is off, then we also have to allow for the fact that many ENWorlders probably play in multiple campaigns), so the odds that someone who might post has this happen to them in a 2 year campaign is roughly:

1 - (1-1/20.0**6)**(5200*4*1000) = 0.2774726475996...

or 27.7%. If you allow for everyone who has an account, then the number becomes:

1 - (1-1/20.0**6)**(5200*4*10000) = 0.96122579...

or roughly 96% likely.

In other words, this was probably going to happen to someone here sooner or later. Particularly given that I was conservative in my estimates. If you think any number I gave is off, you can calculate the changed probability by substituting it in the formula.

As an aside, this estimate says that ENWorlder account holders and the people they play with, as a group, roll somewhere around 250 million d20s in a two year period.

Corran

 

[Seule]

Well, the odds of rolling the same numbe are 1 in 20. You did that three times, for a 1 in 8000 before noticing. I'm sure everyone here has rolled 8000 times over their career, so that's nothing unusual, bound to happen eventually.
Then you started rolling to see how long it would keep up. At this point it was no longer something you'd just noticed, and the chances of the next 3 rolls matching were 1 in 8000 again. That's pretty long odds. However, again, how many times have people noticed something like this, tested it, and it didn't continue? Probably at least 1000 times over the course of everyone of the boards. That's just an estimate, but a conservative one, and it leaves a 1 in 8 chance for it to happen eventually. Be proud that you were the ones it happened to, but it's well within statistical probability.
Overall, 1 in 64,000,000 of it happening on demand, but remember any time two people roll dice and they don't match, that's one of the 64,000,000 non-matching attempts.

Note: If my math is off, that doesn't invalidate my basic point.

--Seule

 

[Uruush]

I rarely buy a lottery ticket because I understand odds relatively well. When I do, it's a lark, to support our schools, and as a conversation starter with whomever I'm buying them with. I invariably pick the numbers 1,2,3,4,5,6. If I do ever win, I want to be the guy who wins with those numbers so I can use my press interview to get in a sound bite about odds, and how all those people who are buying dozens of lottery tickets a paycheck with money they can't afford to lose to *please* stop.