Monte Carlo analysis of King’s Gauntlet

How much cheese do you need to succeed in the King’s Gauntlet?  Well, that depends…

Log summaries have given us a pretty good idea of how many potions are dropped per hunt on each tier.  From that you might be tempted to just multiply the cheese used by the drop rate and the potion conversion rate per tier to get an estimated # of eclipse caught.  But this has some flaws.  Since drops are rare and independent, the potion drops follow a Bernoulli distribution for each tier which looks different from a normal ‘bell-shaped’ distribution.  Also, a change of single pot drop, especially at high tiers, can have a huge effect on Eclipse Mouse catching.  Furthermore, wouldn’t it be great to see the whole range of possibilities for your run, rather than just a single average number of Eclipse expected?

A Monte Carlo simulation uses the estimated probabilities of events occurring and then does a simulated run thousands of times.  Applying this technique to the King’s Gauntlet of Mousehunt gives a set of simulations from which we can get an excellent estimate of the true distribution of possible runs, given a starting cheese amount and which tier you start converting with SuperBrie+.

Using MATLAB, I simulated 10,000 King’s Gauntlet run for each possible SB+ Tier conversion level, for multiple starting cheese amounts.  The results for 100 Brie as starting cheese are below.  The Y-axis indicates the cumulative proportion of runs that have equal or exceed the value of the X-axis.  For example, using SB+ conversion from Tier 2 pots and above, 54% of the time you will catch at least 1 Eclipse mouse with 100 starting Brie.  You will earn less than 1.9 million points half the time, and more than 1.9 million half the time.  And overall, you will lose 2.1 million or more in gold about half the time, assuming a SB+ cost of 5000 (+10% tax).

If you start with 1,000 Brie, here’s what your run distributions look like :

So now that we can see the range of possibilities for each strategy of SB+ conversion, we can answer the questions that are on every mousehunter’s mind.  Which tier should I switch to SB+ conversion on if I want to, on average, break even on profits in my hunting?  Converting Tier 5 pots and above with SB+ will let you break even across the entire run, on average.  Maximum average profit of 160,000 gold per 100 starting Brie is achieved when converting pots with SB+ only on tier 7 and 8, though starting on tier 6 is almost as good and will net you more eclipse. Starting with SB+ from the very beginning will be VERY expensive. You will lose about 2,000,000 per 100 starting Brie.  However, you will probably get an Eclipse even with only 100 starting cheese!

What about catching that Eclipse mouse?  How many cheese do you need to use to have a 50% chance of catching it?  What about a 90% chance?  If you SB+ convert from tier 5 onwards, you need to start with 265 Brie for a 50% chance and 880 for a 90% chance.

Of course, this data is only as good as our potion drop estimates, which are based on YOUR data.  Please consider saving copies of your logs and summarizing them with Nathan Yang’s tool found here.  You can submit your data to a massive mousehunt database by clicking here.

The estimates used for this simulation were:

If you are interested in the MATLAB code used to generate this data it can be found below :

mh_mousehunt

If you have further questions re: mousehunt please leave a comment.


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