[Rant, Primer, Summons] 2019 Summons x1 versus x10 - now with Taxi Driver simile

[Rant, Primer, Summons] 2019 Summons x1 versus x10 now with Taxi driver simile

Summons x1

For a while, blue 4* Grimm was considered the best blue 4*. Grimm is one of the Ramming Pulverizer trio. I also needed him for my original Wu Kong Cascade Squad ( one of the most over powered rainbow 4* hero teams in Empires ).

I got Grimm on my very first Elemental blue summons.

Hansel is a unique, fast mana speed, hero with a special skill defense and mana control.

I got Hansel on my very first Grimm Forest pull of that month ( I had failed other times ).

Several times I have gotten a hero I want/ need in the first 3- 4 summons.

Summons x10

If I had done a Summons x10 for Grimm, I would have had a strong chance of getting Grimm plus nine blue 3* heroes - including 2- 4x Gunnar.

If I had done a Summons x10 for Hansel, I would have had a strong chance of getting Hansel plus nine 3* heroes - probably including Gunnar.

When I get a hero I want in the first 3- 4x summons, I only get 2- 3x additional 3* heroes.

If I had done a Summons x10, I would have had a strong chance of getting 6- 7x 3* heroes or double to triple the 3* heroes - probably including Gunnar - I would have gotten doing Summons x1.

Gem discount

Unless Summons x10 offers a significant discount ( personally I would want a 50% discount ), Summons x1 can save you a huge amount of gems that you can use on other summons.

If you get the hero you want/ need in the first 1- 4x summons, you save Edit: 1400g to 2300g for the next summons you want to do. These numbers are even higher for Atlantis summons.

Even if you have bad luck and need to use 8x summons, the odds of getting the hero you want with Summons x1 eight times ( 2400g ) versus Summons x10 ( 2600g ) are very similar.

Players who love Summons x10, and I have to agree

The real advantage with Summons x10 are my teammates who spend thousands of USD on HotM. Summons x10 lets them quickly do 30x to 90x summons. Ironically, they are the ones who care the least about the gem discount.


Getting 2- 4 Gunnar from Elemental Blue, or 2- 4 Bane from Elemental Yellow
Using the Cascade squad, alternate roster for the squad ( due to color stacking or hero roster ).

Emblems and the Cascade squad
(Classic 4* heroes and emblems or Gryphonknight's emblem spending plan EXPOSED )

Hansel/ Proteus/ Merlin/ Gretel discussion
Bundle sales example- Buy One Get One Free

On the contrary, BOGOs can be much more profitable for stores than a half-price sale. To see why, assume that you value your first pizza of the night at $15.01 and the second at $5.01 and let’s say it costs the store $2 to make each pizza. If the pizza store has a buy-one-get-one-free offer at $20 then you will buy two pizzas and the store will have profits of $16 ($20-$2-$2). But if the store sells pizzas for half price, $10 each, you will buy just one pizza and the store will have profits of just $8 ($10-$2). The BOGO doubles the store’s profits! ( linky, linky)

Carefully designed BOGOs increase profits because they let the firm price more flexibly, what economists unfortunately call “price discrimination.” At $20, the BOGO is equivalent to charging $15 for the first pizza and $5 for the second. Notice that these prices are ideal for the firm since they are the maximum the consumer will pay – any more and the consumer won’t buy.


I agree, unless you want multiple heroes from the same event. In which case I accept that I’m probably not going to get any of them lol, but I know I’m willing to try 10×. Going after 1 specific hero has never once worked for me no matter how I try (fair enough since 10pulls is the maximum I’m willing to “bet” with such low odds) But I’ve gotten some great heroes along the way that I didn’t know I wanted until I got them :smiley:

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This applies only if you are interested in drawing one 4* hero in the entire summons and absolutely nothing else.

For a 5*, the odds of drawing a particular hero are so low (lets say 0.4% - and this is being quite generous for the majority of summons), that, statistically speaking, you would need 250 pulls to get that one hero you need. Doing single pulls, you would waste 400 gems for every ten, equating to 10,000 wasted gems.

At the end of all those pulls, what you save from your strategy would be 2300 gems at best (if a single pulls results in the hero you need vs. spending 2600 on a 10x). The average saved gems using single pulls would be only 1100.

Even using the HOTM at 1.3% odds, its not close. Statistically, 77 pulls are needed. Lets use 70. This equates to 2800 wasted gems (7*400), to save 1100 (or at best, a chance to save 2300).


To my mind, it depends on what your objective is. If you intend to spend until you draw the HOTM, then 10-pulls (or 30-pulls) are the lowest expected cost to achieve.

But it is also very true that the additional benefit per dollar spent diminishes as you spend more dollars. Here’s a graph of the 5* percentage per dollar spent at the Atlantis portal:

If you don’t mind not getting a 5*, you’re much better off to only do a few pulls. That’s where the peak benefit per dollar lies.

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In the first portion you speak to the cost per 3*, 4*, and 5* hero. I want to speak to that.

You said:

Stars Cost
3* $5
4* $80
5* $240

According to my math, these figures are way off… unless you’re speaking of non-american dollars or doing some fairly wonky math. I suspect that you’re not following the precise percentages stated in the summon portal, but rather doing the required number of summons for a guaranteed pull… which is heavily weighted because the stated figures are the average number of pulls across all of E&P, whereas the guaranteed figure is a definite outlier.

The best non-deal price for gems is 10,000 for $100, which equates to $0.01 per gem. The price of gems from the most popular non-deal store offer is 2,800 for $30, which equates to $0.0107 per gem, or just over one penny per gem. Let’s use $0.01 per gem as a nice round figure.

3 Star Hero Math:
A 3* hero from the Epic Hero Summon has a 72% chance of appearing… but in reality, since you’re guaranteed at least a 3* hero, it’s basically one pull is equal to a 3* hero. Thus, the cost of a 3* hero is $3.00, since it’s 300 gems at $0.01 per gem.

4 Star Hero Math:
A 4* hero from the Epic Hero Summon has a 26.5% chance. This is approximately one-in-four summons. Since it costs 300 gems per summon, the cost of a 4* hero is equal to the cost of 4 summons, or $12.00.

5 Star Hero Math:
A 5* hero from the Epic Hero Summon has a piddly 1.5% chance. That said, the HotM also has a 1.3% chance to arrive with each and every pull. This means that there is a 2.8% chance to pull a 5* hero since all HotM are 5* heroes. With the base 1.5% the odds are one-in-67 pulls, and the cost would be $201. If you include the odds for the HotM then the odds are one-in-40, making the cost $120.

The Real Cost To Summon:

Stars Cost
3* $5
4* $12
5* $120-$200

The cost of the 5* hero depends on your willingness to accept the HotM as a valuable 5* hero, which I suspect is only true for the first, maybe the second, one that you receive in that particular month.

I just wanted to make some corrections to the math. You’ll find that all summons have approximately the same odds, but it should be noted that Challenge Events and Atlantis have even better 5* odds, at 2.5% PLUS the 1.3% chance for the HotM, making the odds of getting a 5* from those even higher than the above, which would drive down the cost of getting a 5* hero yet further.

Note: I do not believe that 5* heroes are cheap, and rather consider them to be exorbitantly expensive. I even asked a question of SGG in the AMA thread because of this disparity that makes one 5* hero cost more than an entire traditional game. Very not cool. :frowning:


Nice catch. Peer review at its finest!

Looks like $7.5, $18 and $180 were the numbers I was targeting. I will edit later.

Was writing four topics at once ( Color stacking explained using Trainer Heroes is interesting ), and somewhere messed up my ratios.


I agree summoning heroes suck! I get the gems, I save them up , and when I use them I get crap!! I like this game, but I really don’t see me playing much longer if I can’t get better heroes!!


How I’ve missed this post for this long is beyond me. I’d thought I had read almost all of your informative, well thought out writing. Thank you for the heads up @Gryphonknight.

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