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A quick post this time. With the new PVP season that just started, we have a chance to recruit Elektra via lockboxes. She looks pretty cool (unremovable bleeding from every one of her moves? Not bad...). But what are your odds of getting her for free?

reminders & assumptions

I will be using the same assumptions and calculations as in this previous blog post.

But some quick reminders never hurt:

  • I assume that you will open boxes 10 by 10, all the time. It is the best way to get covers (click on the link above for the full discussion)
  • I assume that there is no "trick" that can influence the odds (waiting for big stacks of boxes, or on the contrary, never opening more than 10-20 per day, or spending 1G before opening a batch...). No one has ever convincingly demonstrated that these tricks work. Some are even convincingly disproved. Just ignore anyone who mentions such a trick unless he has convincing statistical evidence.
  • I assume you will play every day for 25 days (which will not be my case due to holidays for example...sniff) and get 5 victories (to earn a spin).

Calculations

How many boxes can you expect to get over the season?

  • 25 days x 5 boxes for your 5 wins = 125 boxes (with the days "a la Playdom", this might be a little more, actually, but let's be conservative)
  • tasks 1-3 = 40 boxes. Easy tasks, based purely on volume
  • 25 spins ~ 40 boxes. based on the roulette odds, we get about 1.55 boxes / spin

So, without gold, you should be looking at 205 boxes. As I said, PD days are generally understated, so let's assume 210 boxes.

According to reliable sources (my previous blog, linked above), 210 boxes give you 58% chance of getting the 8 covers.

Conclusion

If you get your 5 daily victories every single day, your chances actually look pretty good (58%), which still means that 42% of daily PVP players will have to fork out some hard-earned gold to get our favourite red-clad ninja assassin.

One last note about that: if you are in the unlucky 42%, getting the last cover can be very costly. It will take an average of 8 tries (which means 80G) and can take a lot more than that. I would not recommend trying unless you are willing to spend a lot of gold.

Good luck to you all!

Addendum: calculating your chances at any time in the tournament

Until now, the blog focused on your chances at the start of the tournament. 5 days in: how did you fare? What are your chances now? Well, have a look at the table below:


Nb of covers you already have
Days left 0 1 2 3 4 5 6 7
20 14.3% 19.6% 26.0% 33.9% 43.3% 54.4% 67.4% 82.5%
19 10.8% 15.6% 21.7% 29.4% 38.9% 50.4% 64.2% 80.6%
18 7.7% 11.9% 17.5% 24.9% 34.4% 46.2% 60.8% 78.6%
17 5.9% 9.8% 15.1% 22.2% 31.6% 43.6% 58.6% 77.3%
16 3.7% 6.8% 11.5% 18.0% 27.0% 39.1% 54.8% 74.8%
15 2.1% 4.4% 8.2% 14.1% 22.5% 34.4% 50.6% 72.1%
14 1.3% 3.1% 6.4% 11.8% 19.9% 31.6% 48.0% 70.4%
13 0.5% 1.7% 4.1% 8.5% 15.7% 26.9% 43.5% 67.2%
12 0.1% 0.7% 2.3% 5.6% 11.8% 22.2% 38.7% 63.7%
11 0.0% 0.4% 1.5% 4.2% 9.6% 19.4% 35.7% 61.4%
10 0.0% 0.1% 0.6% 2.3% 6.5% 15.0% 30.6% 57.3%
9 0.0% 0.0% 0.2% 1.1% 3.9% 10.9% 25.5% 52.7%
8 0.0% 0.0% 0.0% 0.6% 2.7% 8.6% 22.3% 49.8%
7 0.0% 0.0% 0.0% 0.1% 1.2% 5.4% 17.2% 44.4%
6 0.0% 0.0% 0.0% 0.0% 0.4% 2.9% 12.2% 38.5%
5 0.0% 0.0% 0.0% 0.0% 0.1% 1.7% 9.4% 34.6%
4 0.0% 0.0% 0.0% 0.0% 0.0% 0.5% 5.3% 27.6%
3 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 2.1% 19.9%
2 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.7% 14.9%
1 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 5.7%

How to read the table: the columns represent the nb of unique covers you already have. The rows are the numbers of days left in the tournament. The values in the table show your probability of getting Elektra for free.

Example: I have 5 covers at the time of writing, and there are about 20 days left. It means I have 54% chance of getting Elektra for free. In other words, I am basically on track (starting odds were 58%).

Assumptions and caveat:

I assume here that your tasks are done and that you already have the 40 boxes. If it is not the case, your chances are better than stated above (as you will get more boxes than I assumed for the rest of the tourney).

Be aware that the values in the table are averages and that on small samples like this, the standard deviation is probably quite high, especially as you get towards the end of the tournament. It is possible that the table shows a good chance of you getting the hero and that you end up with a ton of dupes. It's not a conspiracy against you by PD, it's just randomness.

Once again: good luck!

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