Cross-Rides, Break Rides, and Persona Blasts

Random Maths Article.

Basically, any Grade 3 Vanguard you run 4 of will be ridden by turn 4 about 57.2% of the time, nearly 3/5 of all your games, or 3/4 of all your games that you ride up into a Grade 3. Basically meaning that any players with midgame Vanguards, Break Ride Units, and Cross-Ride units should be well aware of this sort of junction. Along with this, the probability of Cross-Riding by turn 4 (or Break Riding by turn 4, but please don't eat damage just to do this) is 40.6%, nearly 2/5 of your total games and nearly half of all your games that you can ride up by turn 3. On this note, this also means that 40.6% of your games will have you sitting on that glorious Cross-Ride defense, netting you amazing card advantage in those fights. When also considering the other rides, the probability of Persona Blasting by turn 3 is only a measly 25%. This shoots up to 37.5% by turn 4, but it still may not sound so hot. I don't plan to go any further, mostly because my 1 damage per turn assumption sounds more and more ludicrous the further I go, but it should be well noted that just 1 more iteration should make it nearly a coinflip, and by the late game, should be generally high enough to deem 'consistent'. On the other hand, however, you'd have your Persona Blast ready by turn 4 about 65.6% of the games you already have ridden up to Grade 3, which is quite a bit from a closer point of view.

Probability of Riding a Grade 3 unit you run 4 of by turn 3 (14-11-8):

Grade 1:

181*390851/3*3*7*23*23*47*47

Grade 2:

3*3*5221939/23*23*43*47*47

Grade 3:

31225661/2*3*7*23*23*47*47

181*390851*5221939*31225661/7*23*23*47*47*23*23*43*47*47*2*3*7*23*23*47*47

Probability of Riding a Grade 3 unit you run 4 of by turn 3 (14-11-8)

11535415364931585453049/20172974972187814844802

About 57.2%

Probability of Cross-Riding by turn 4 (14-11-8)

3*11*41*43*301361/2*2*3*23*23*41*43*47*47

38239567407702622760879296579/94293407225899060411426679688

About 40.6%

Probability of Persona Blasting by turn 3 (14-11-8)

125366894186076470703736532/500546398317462150818999058

About 25.0%

Probability of Persona Blasting by turn 4

(43*11*37)/(47*23*47)

33306/50807

13*61*181*390851*5221939*31225661/7*23*23*47*47*23*23*43*47*47*23*23*47*47*23*47*47

9147584384390747264267857/24403055700284435924282267

About 37.5%