Scratcher odds for prizes at different levels

[zwiswoo]

I tried to figure out the chances in a scratcher of getting prizes of different sorts. That is, the chance of seeing 1/2/3/4/5/6 items of the same sort. I think it comes out to:

1: 1.5%
2: 61.7%
3: 31.5%
4: 4.8%
5: 0.4%
6: 0.01%

I got those numbers by throwing random numbers and seeing what happened, assuming that all six item types (cash/respect/gun/melee/armor/vehicle) are equally likely to appear in a grid box, and that what happens in one box doesn't affect what happens in any other.

So basically you should expect to get a level 2 or 3 item a bit more than 90% of the time, and level 4 about once in twenty tries. You get five of the same sort once every ~250 tries, so maybe one a year. The odds of getting all six being the same are basically zip - you'd have to be scratching every day for more than a decade to have a reasonable expectation of getting a level six item.

Just to test the numbers, here's what I actually have for my scratchers (just looking at items...no idea what the deal is with cash or respect):

2: 24 (65%)
3: 11 (30%)
4: 2 (5%)

It's pretty similar...

[Dipstik]

... You made a simulation to find the odds of throwing six dice? Computers really do make kids dumb. The odds of throwing six of the same are (1/6)^5.

[Tommy Two Toes]

... You made a simulation to find the odds of throwing six dice?

Am I the only one old enough to remember playing Boggle?

Tangent: I traveled to Milwaukee once, and they Boggle this into a drinking game you can play at just about any bar.

[zwiswoo]

... You made a simulation to find the odds of throwing six dice? Computers really do make kids dumb. The odds of throwing six of the same are (1/6)^5.

Sure. All six different is also easy enough. But I think it's harder for two of the same (2,2,2 or 2,2,1,1 or 2,1,1,1,1) or three of the same (3,3, or 3,2,1 or 3,1,1,1) etc because there are more ways of doing the thing and you've to get them all. One annoying bit to note is that you want to count 1,2,3 as level 3 but not as level 2.

If you can give me a one line argument to the effect that level2's are twice as likely as level three's and 3's are six times likelier than 4's, now we're talking. Me, I prefer writing a ten liner than runs in five seconds to doing a homework problem...

[PawnXIIX]

We've figured this out but I'm glad to see people are still finding use in the random aspects of the game to write simulations. If you're looking for something to distract you for another 10 minutes write a simulation that uses random to give you scratcher items. When there is a tie for the highest number (ex. 2 money icons and 2 gun icons on the same scratcher) it just randomly picks one of the two or more and provides it. Just some ideas because I remember trying to find excuses to avoid my homework too :D