Interesting! I will definitely be sticking to single-card draw from now on.
Both methods have a "guaranteed 6-star drop" which occurs if you have already drawn a number of cards and have not received a six-star, and this is the part you want to exploit. The difference between the two methods is that when you pay for the 500-gem recruit, you go straight from card 1 to card 11. That "guarantee" only applies once, right at the eleventh card. With the single-card draw, your counter starts over every time you get a new six-star, instead of when you start a new 11 cards. I'll draw up an example, but it may not be very easy to understand.
Example For a given 33 drawn cards, imagine the sequence is 454465564454445455654454445445454. In other words, your first card is a 4 star, then a 5, then two 4's, then a 6, then two more 5's, etc. The same sequence, when split up based on your purchases, would look like like this:
(G = guaranteed 6-star, | = price equalizer)
-------------------------------------------G---------------G---------
Singular-draw: 4544655644|5444545665|4454445465|(454)
500gem-draw: 45446556445|44454556544|54445445456|
-----------------------------------------------------------------G----
Okay, so the chart is split up based on the amount of cards you'd get with 500 gems (with a | in between each 500 gems). With the single-draw method, you get 10 cards for every 500 gems. The first 10 are five 4*'s, three 5*'s, and two 6*'s. With multi-draw, you get 11 cards--same as the previous example, but with an extra 5*, in this case. So you get one card ahead by the second method. However, when you start the next 500 gems, the single-card method's guarantee-counter has already counted two cards (a pair of 4's), while the multi-card draw's counter resets to zero. As we proceed through the next stream of 4's and 5's, the counters continue to count up, until we hit our first "G" for singular-draw. See, it's been 9 cards since the single-card method gave a 6*, so the tenth card, underneath the G, is guaranteed a 6*. But since the very next card in the sequence happens by luck to also be a 6*, the multi-draw method's counter is disabled--and you don't get a guaranteed card for that method the way you did with the first method! As the sequence goes on, each method produces one more 6*, both through guarantees. In the end, the single-draw method gets three less cards (it can only get 30 cards for 1500 gems, where the 11-card draw can get 33), but for this sequence, they're just more 4's and 5's. The single-draw method gets five 6*'s from this method and the multi-draw only gets four.
Obviously this is just one out of billions of available sequences. The multi-draw method will always get more cards, so it will have more chances of producing a 6* by luck, and with the majority of sequences, you'd see no difference in the number of 6*'s drawn between one method and the other. However I'd rather gamble on the shorter, 10-card guarantee that only resets when you get a 6* (rather than every time you make a new draw) than on the longer, 11-card guarantee that only counts during specified iterations of 11 cards.
If my ramblings make sense to a single person on this forum, it will all have been worth it
