Is Gigglegibber Gamblin' Fair?

by Jeff "Ethec" Woleslagle

I'm pretty suspicious of goblins. Especially ones that want me to gamble my money, and I have good reason. It all stems from a bad string of incidents early in lil' adventurer school involving my lunch money, a gaggle of goblins a few grades higher than me, and a bet involving me mooning the Queen Antonia statue (er, it was a younger looking statue at the time!). They kept the money and took a screenshot, and after countless lectures about respect and discipline, I find myself in cleric school! Imagine, a halfling templar. Bah, and I wanted to be a ranger (but nowadays, who doesn't!).

Anyway, like I said, I have a healthy disdain for goblins. I discovered a few hanging around these locations (thanks Glendral!):

  • Antonica - upstairs in the Frontier Farm.
  • Commonlands - the Crossroads.
  • Thundering Steppes and Nektulos Forest - on the docks.
  • Maj'dul - try your luck at the first row of merchants as you enter the city.
  • Sinking Sands - at the croc hunter camp northwest of the docks.

The gobbie wanted me to play the (/sigh) Gigglegibber Goblin Gamblin' Game. I asked the little overbaked greenie what exactly this game was, he/she/it screeched some unintelligible sounds in a grammatical style that would make Jar Jar Binks blush, and pointed to a book. I opened my mouth for a response, then thought better of it and read the book. "Ah," thought I upon reading, "a lottery of some sort."

Indeed it was. The book listed payouts for matching two through six numbers randomly chosen with a set of 6 pre-set numbers (ostensibly) server-wide. Think of the game as holding a 6-digit lottery ticket and being able to watch drawing after drawing for the cost of 10 silver a piece. The payours at the time I was playing: match 2 numbers for a 10 silver payout (it basically covers the cost to play), 3 for 50 silver, 4 for 2.5 gold, 5 for 25 gold, and 6 for 2.5 platinum with, again, a cost of 10 silver per play. Note that these payouts do not refund the buy-in, in gambling lingo for the match 2 payout it'd be "10 for 10" rather than "10 to 10" (in the latter, you'd win the cost to play back plus 10 silver for a total of 20 silver).

Who couldn't use some plat? Still, like Fred from "Scooby Doo," I had a bad feeling about this. Fighting the halfling urge to peeter away my cobalt fund (I have one of those kitchy jars on top of my microwave - "Armor Fund"), I decided to consult with my good friend (despite being a gnome) Skeezix. He's a sorceror training to be a wizard, and no doubt the Mages at the tower were putting them through the organ grinder known as "descriptive statistics." Which is kind of comical: my own training was simply a matter of being pointed at a fighter dummy and direct healing while a creative invective-hurling high elf drill sargent-type screamed at me to click FASTER!!, spittle flying, the dwarf next to me sobbing. An ugly scene by all accounts.

The more mathematical Skeezix'll take over at this point; he's kind of a pinhead so bear with him...

The Math We Thought We'd Never Need... (well, you still don't!)

Hello folks. Welcome to Skeezix's probabilistic summary of Gigglegibber gambling. First, some background on the game. The game randomly chooses 6 digits ranging from 1 to 36. If 2 or more of these numbers match the numbers the preset, server-wide numbers, you win! (see above for payouts). If 1 or fewer of these pre-set numbers turns up, you lose.

Despite the apparent simplicity of the model, there are other complex factors that a contestant must be aware of. First, while the machine appears to be akin to a casino-style slot machine, the "reels" (or wheels that turn displaying values, in this case, digits) appear to be just for show. Here's a sample "pull" (I've used my gnomish frappulator to capture the values as they pass the "bar" or viewing window). Note that this is one trial only and the numbers cascade into place one at a time, just like a slot machine:

Randomized on "Buy" click...
10
32
21
20
3
15
13
4
15
30
2
31
24
24
18
35
34
19
23
15
24
6
24
10
9
3
19
23
2
5
28
17
17
35
1
29
17
17
9
8
5
32
12
3
23
8
5
23
1
25
20
16
2
5
29
4
3
30
23
12
 
10
19
18
24
24
 
10
24
25
19
8
 
11
12
12
28
4
   
23
27
31
9
   
28
32
25
5
     
35
6
28
     
5
26
22
     
23
2
5
       
19
29
       
33
27
         
15
         
3
         
20

Ethec: If that's too complicated-looking, skip it. The gnome's just trying to show you that the numbers are randomly generated; the "slot-machine" animation is just for looks.

Skeezix: Quite right, and I must insist that you not interrupt my explanation again. I was just getting to that. (Ethec sneers)

Yes, you'll see that the individual "reels" or columns (as they are here) follow no discernable pattern. I ran this test on 4 other plays and there was no predictability or trace of commonality between the individual reels on different plays. This leads me to believe that the final six numbers of range 1-36 are chosen at random sometime during the pull. In this example, the result set is 29 11 28 23 33 20, which in no way coupled with the reward set: 19 12 16 7 24 27. In case you hadn't realized, the order is not important.

Not only are they random, but you'll never see the same number in the "result set" or the "reward set" twice. In statistics, we would say the numbers are randomly chosen "without replacement" - or that the 6 different "trials" are dependent on one another or "inseperable."

Ethec: He's trying to say that once 27 pops into, say, the first reel, you're won't see it in any other of the reels. Which makes the odds of winning suck worse.

Skeezix: Please! Yes, that's correct. It would be akin to rolling six 36-sided die, but once the first came to rest, the number displayed would be magically erased from the others, and then the second die's at-rest number would be erased from the last four, so on and so forth. While winners and losers are both knocked out of the realm of possibilities, a loss of a repeatable winner hurts the odds much more than the loss of a repeatable loser.

The no-replacement rule also makes figuring out the probabilities of winning any of the range of prizes difficult as well. Were repeats allowed, you'd have a straight 6 in 36 chance on every reel. As it stands, you have a 6 / 36 chance on the first reel, then if you "hit" a winning number, you'll have a 5 / 35 chance on the second reel. Should you lose on the first reel, you'll have a 6/35 chance on the second reel and so on. This is why your odds of hitting one number are substantially better than not hitting on any numbers.

Ethec: So how often do you hit on numbers, is that the only way you can get a date? Does it make things uncomfortable when you need to add the next day? /snicker

Skeezix: (/ignore Ethec) I hope you can see the complexity of this process- how many variables must be considered with each result. Never fear! The hypergeometric distribution comes to the rescue!

Ethec: Oh, tunare. He's not making this up either... please skip the particulars.

Skeezix: As I was saying, the hypergeometric distribution is incidently the same way most lotteries (except powerball lottos) in your world come up with the odds of winning. In your world, however, payouts differ based on a number of variables... who matched the same number of numbers, for example. In Norrath, payout amounts are fixed.

At your request, I'll proceed past the mathematics and present simply the results, though it pains me.

Ethec: Better you than us.

Skeezix: (/clears throat)

Skeezix's Research - Theoretical Odds of
Winning at Gigglegibber's Gamblin'

Hits (n)
Probability of "n" hits
Chance of winning is one in...
0
30%
3.3
1
44%
2.3
2
21%
4.7
3
4%
24
4
0.33%
298.5
5
0.0092%
10821.1
6
0.0000513%
1947792

/walks away

Ethec: Boy, what got into him... I'll buy him a lantern of pretty colors that farts and laughs, he'll be fine!

Turning Theory Into Monetary Loss

I returned to the goblin to do a little bit of "research" halfling-style. Nah, actually I was looking to take another step towards the "Dread Lord Goblin Destroyer" title should he be playing with dirty dice, so to speak. One hundred plays and I was 6 gold, 60 silver lighter (that's including the winnings). I also couldn't complain of being cheated... here's why.

Ethec's "Research" - 100 Actual Plays

Hits (n)

Theoretical % of "n" hits

Actual % of Hits
0
30%
36%
1
44%
36%
2
21%
25%
3
4%
2%
4
0.33%
0%
5
0.0092%
0%
6
0.0000513%
0%

The "variance" (as the boy genius would say) is caused by the low number of plays (100 is low in statistical terms - especially when working with these large numbers). We'd have much better luck at matching the theoretical probabilities if someone would bankroll me for thousands of plays (cash, check, or money order payable to "Ethec, Templar, Oggok Server" :) ).

So how much is Gigglegibber making on this gimmick for every one big hit? He's giggling all the way to the bank.

Hits (n)

Theoretical number of "n" hits before the big one

GG's Coin Gained / Lost
0
584,338
584p, 33g
1
853,590
853p, 59g
2
407,395
(407p, 40g)
3
77,599
(388p)
4
6,402
(160p)
5
178
(44p, 50g)
6
1
(2p, 5g)
Gigglegibber's Receipts
1,437p, 92g
Gigglegibber's Total Payout
(1,002p, 40g)
Gigglegibber's Net "Take"
435p, 52g

The /ooc Conclusion

Before the /rants start at that amazingly high figure (will you ever see 435p? I won't, unless inflation accelerates faster than a Station Exchange stuffed monkey backorder), I want y'all to consider a couple things: 1) its statistically "fair" - though I'm sure the devs will dork with the payout factors to make them more favorable to players soon, 2) you don't have to gamble, at all, ever... its purely voluntary,3) it was a free, fun update- relax and enjoy! and 4) we need money drains like this if the economy is going to stay healthy. Just consider how much a single plat is worth on Everquest nowadays, where items go for millions of plat. It's absurd, and it's a serious disincentive to returning players who are honest, workaday types.

Yep, the house makes a lot of money on gambling, on EQ2 and in real life. You need to realize this before you start gambling: you aren't going to be the one to defy the laws of probability, Neo. Sorry! However, that doesn't make it any less fun if done right. Everything in moderation, and perhaps fortune might smile upon you someday. As my stats teacher used to say, "If it can happen, it will happen, eventually." You just might walk up to the goblin someday, drop in your 10 silver, walk out with some plat, and be celebrated as the serverwide winner for the next 4 months!


Want to discuss? Did I biff on the statistics, you real life gnomes out there? Take me to task in the Interactive Guides forum!


To read the latest guides, news, and features you can visit our EverQuest II Game Page.

Last Updated: Mar 13, 2016

About The Author

Jeff joined the Ten Ton Hammer team in 2004 covering EverQuest II, and he's had his hands on just about every PC online and multiplayer game he could since.

Comments