Saturday, May 17, 2008

Mog Bonanza

Figured it was time to make a post and trying to win the Bonanza is more up my alley in terms of crunching numbers. My method for choosing numbers is part systematic, part random number generator. If you don't know about the Bonanza and how it works, try reading this first:
http://www.playonline.com/ff11us/guide/mogbon/index.html

My method is more along the lines of trying to win *something*, as something is better than nothing. First, lets explore the probabilities involving the Mog Bonanza.

Probability of Winning
For rank 5, it is rather simple. Only one digit has to match, so for 1 marble, you have a 1 in 10 shot at winning. For one character (10 marbles), you have 10 in 10 or 100% shot if you choose properly.
For rank 4, you have 2 digits to match, in the range of 00-99. So 1 marble has 1 in 100 chance. If you choose 1 character with different numbers, you have 1 in 10 chance.
This goes on and you get these probabilities:
Rank1 Marble
10 Marbles
50 Marbles
Rank 51/1010%10/10100%50/10500%
Rank 41/1001%10/10010%50/10050%
Rank 31/10000.1%1/1001%5/1005%
Rank 21/100000.01%1/10000.1%5/10000.5%
Rank 11/1000000.001%1/100000.01%5/100000.05%

I threw 5 character set on there for good measure. Now these probabilities are based on if you choose 5 different numbers for each rank. So you have to make sure it does not repeat for any of the rank.

Selecting My Numbers
I have 3 mules and 1 main. So to maximize my chances, I selected numbers which will enable me to win rank 5 on each of my character, and spread out my chances of winning rank 4 across all 4 characters, so I have no repeats of rank 4 numbers. To choose my numbers, I used this random number generator generating 4 digit numbers. The reason for 4 is that my last digit is predetermined so I have 0-9, each used once for every character. Each randomly generated number is tacked onto one of the single digits. Then I made sure that the last 2 digits (the rank 4 numbers) do not repeat across all numbers. Now since there are no repeating rank 4 numbers, that automatically means there are also no repeating rank 3, 2, 1 numbers. My final result is:
11663 32891 54037 67014 77034 91832
13568 35236 54335 68360 77897 93711
14450 39941 55724 69899 79457 95930
15322 41306 58592 72056 79577 98693
21079 42685 58933 73086 84369 99013
22255 46418 62978 75002 88571 99090
22264 48505 65789 75148

There are only 40 marbles, so my chances are less than the 50 marbles I listed above. So my probabilities are:
Rank 1- 0.04% Rank 2 - 0.4% Rank 3 - 4% Rank 2 - 40% Rank 1 - 400%

Impact on Server Economy
This was something I tried to discuss in my linkshell but nobody really seem to have an interest on it. The Census report from yesterday says there are 500,000 accounts. Across 32 servers, that is 15,625 accounts per server. Let's assume there are 3 mules per account and 1 main ( I have no idea if this is conservative or not, some people may level new characters just for this event, while others have 20+ gardening mules too). So that is 62,500 characters playing Bonanza per server (sounds reasonable considering ffxiah.com lists around 40,000 characters on Jeuno AH per server, and if you consider other mules on top of that and characters that quit as well). Each of which plays 10 marbles, for 625,000 marbles per server. With that many marbles, we can expect:
6 Rank 1 winners
62 Rank 2 winners
625 Rank 3 winners
6250 Rank 4 winners
625,00 Rank 5 winners

Rank 5 has no gil option, while Rank 4 has 3 or 4 items worth more than the 100,000 gil offered.
Now assuming all the Rank 1, 2, 3 winners choose gil (it is what I would do, not necessarily what others would though), that is: 600M+ 620M + 625M or 1.845 billion gil added to the server. That should be significant enough to cause some level of inflation, one that should not be taken lightly. So if you were smart, you'd put all your gils in items and watch as the Bonanza come and inflate the prices.

edit: I've forgotten one major thing about this: the costs of buying those marbles. At 625,000 marbles, 625M gil exits the system, so that leaves a net 1.22 billion gil added. Not quite as much but still a lot.

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