Wednesday, February 18, 2015

Hearthstone: Revising 'To Legend' Numbers

Sthenno pointed out that starting my simulation off at 0 stars isn't terribly realistic, especially now that I'm actually at legend this month. When the ladder resets for the next month you don't get set back to the very bottom of the ladder. Instead you get to start with a number of stars equal to the number of ranks you gained in the previous month. This means that I'll start off at 25 stars next season instead of at 0 and will therefore only need to gain 71 stars to hit legend.

Now, this isn't quite as good as it seems. The first 10 stars are practically free in that losses don't cost you stars down at that level. The last 26 stars are harder to get because the '3 wins in a row' bonus is removed at that point. So you're shaving off easy stars and still have the big slog at the end, but it should still make things a little faster. But how much faster?

I'm on my real computer now so I bumped the size of my spreadsheet up to a million runs, coded it to start with 25 stars, and set it running. Check the same things I checked last time, which was the minimum win percentage to guarantee legend in X games... (I checked both just the first 100k and all million and the numbers were the same.)

1700 games - was 52%, is now 52%
850 games - was 54%, is now 54%
567 games - was 56%, is now 55%

So not a whole lot of change, actually. But I'm now more wondering the inverse of what I'd been checking. With a given win percentage, what is the most games it took to hit legend? Average? I mostly care about the range around 50%, and anyone who didn't hit legend at all is counted as hitting it in 5000 games just because of the way I set things up. So averages close to 5k were mostly people who didn't hit legend at all.

45% - 1428 min, 4990 average
46% - 1035 min, 4922 average
47% - 809 min, 4522 average
48% - 718 min, 3482 average
49% - 606 min, 2228 average
50% - 502 min, 1418 average
51% - 459 min, 985 average
52% - 417 min, 733 average
53% - 353 min, 583 average
54% - 305 min, 484 average
55% - 280 min, 412 average
56% - 251 min, 360 average
57% - 241 min, 319 average
58% - 221 min, 286 average
59% - 206 min, 260 average
60% - 189 min, 238 average
61% - 174 min, 219 average
62% - 164 min, 203 average

Basically it really feels like 54% win rate is a good target. Find the fastest deck that wins about that much and you're good to go. Slowing down to eke out a slightly higher win rate isn't likely to be worth it. Speeding up by losing more often than that is probably too big a hit to your actual speed to legend, especially if you're far away from the minimum values.

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