This is a guide for speedrunning the Monkey Kombat section of the game. You must first be familiar with how Monkey Kombat works and basic strategy for beating Jojo in order to make sense of this guide. I will use the letters A,O,E and C to refer to Ack, Oop, Eek and Chee.
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Guessing plays In your run, there will be 10 different plays taking you between stances. These are not decided entirely randomly. Firstly, all plays consist of three different cries. Unlike in diving, where Marco can sometimes duplicate moves, plays like AOO or CEC will never be valid in Monkey Kombat. Of the 10 plays, 6 of them will always be the 6 plays which begin with A (AOE, AOC, AEO, AEC, ACO and ACE). This leaves only 4 other possible plays. OAE is most probably one of the other plays, and OAC is very likely to be another. It seems that the remaining plays are selected randomly, and can be any of the other options (though, for whatever reason, are unlikely to be COE or COA). This gives us a reasonable strategy early on - we can save before our turn, and guess an A-starting play (which is not currently used for something). If it is a foul, or takes us to a losing position, we reload and guess another. By doing this, we can have perfect play from the start. It removes the need to draw to learn information. Update: I am aware of one run (but only one) where not all 6 Ack-starters were present. The full "rules" here are not known, but it is almost certain that all 6 Ack-starters are indeed present in your run.
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Which monkeys There are four types of monkeys. They are, in order from weakest to strongest, timid, smelly, strapping and brawny. Which monkeys spawn are dependant on which monkey was just fought, and whether you won or lost. Winning fights, and fighting stronger monkeys, causes stronger monkeys to spawn. In order to be accepted to fight Jojo, you must beat at least the strapping monkey. In order to spawn the strapping monkey, you just need to win a fight (the easiest being timid monkey). At the start of your run, only timid and smelly monkeys will spawn. This means that (assuming all fights are won) the shortest path to victory is timid -> strapping -> Jojo. Your health bar is dictated by the monkey you just beat (or lost to). At the start, you have 8 health. Beating the timid, smelly and strapping monkeys gives you 10, 13 and 15 health respectively. Note that this has no impact on the Jojo fight, so the only possible issue with the timid -> strapping -> Jojo route is that you only have 10 health for the strapping monkey fight. For this reason, you may want to see if you prefer smelly -> strapping -> Jojo, which will provide a safer fight against the strapping monkey, but is slower as the smelly monkey fight takes longer than the timid monkey fight.
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Pentagram method The biggest time save here concerns how you record the information and work out what move to perform. The pentagram method is, once mastered, very quick for both of these. I am generally able to give my response as soon as the game permits input. Before starting your run, draw a pentagram. The five points represent the five stances - write AA, BB, CC, DM and GG by these points, in a clockwise fashion from the top. Notice that the pentagram represents all possible connections between different stances - the circle around the outside takes us from AA to BB to CC to DM to GG back to AA, and the star connects AA to CC and DM, BB to DM and GG, and so on. If you learn about one stance beating another, then add a little > or < to the line between those stances, turning it into an arrow. The stance which wins "points" to the stance which loses. For example, if you find out that GG beats BB, you would add > to the middle of the horizontal line, turning it into an arrow from left to right. This way, you can easily answer questions like "what beats CC?" - look at the four lines connected to CC, any arrows inwards are from stances beating CC. We can also easily use the fact that every stance wins and loses to two other stances to our advantage. On the pentagram, this translates to "whenever you see two arrows inwards to a stance, the other two must be outwards, and vice versa". When you learn about which plays move between stances, write them next to the arrow (or middle of the line if there's no arrow yet). This way, you immediately know what play is needed to move between any two stances - it is the play written next to the line between those stances. During a fight, keep track of where both you and the monkey are on the pentagram. Look for arrows pointing into the monkey's stance to tell you the stances which beat it, and look for the play between your stance and the target stance. Early on, this process will not always be possible and you will need to save and guess. After the first few plays, however, this will be the process on every move. Once you get the hang of it it is very fast.
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Jojo Jojo is programmed to let you make one mistake. The game will set up a position where you are both on one banana, at which point Jojo draws, and you finish the fight with a win. Firstly, this means when you're on one banana, it's best to beat Jojo from a stance where you don't know the play taking you from that stance to Jojo's - it forces Jojo to play that move and teach you it. Secondly, this fight is sped up by getting to one banana as quickly as possible (the game will make your penultimate move deal 7 banana's of damage to compensate). So the best strategy is to play "Chee Chee Chee" as your very first move, taking three lots of damage in a row, before playing only winning moves. This saves around 20 seconds over perfect play.
Good luck!
I have made a video commentating on these strategies as I used them in my 53:06 run here: I hope this is helpful :)
21st April 2022 update: Picking through the code of the game, we have been able to work out why the "Ack"-starter phenomenon occurs. It is not actually guaranteed that any "Ack"-starter is present, but it is extremely likely. The moves that are most likely to appear, in order from most likely to least likely, are: AOE, AOC, AEO, AEC, ACO, ACE, OAE, OAC, OEA, OEC After these 10, every other move is equally likely to appear. Moves should be guessed in this order, from left to right. An additional outcome from this, which is much less extreme, is a bias in terms of what beats what. The strongest bias is towards DM>AA>BB, but these relations will only happen 2/3 of the time, so aren't worth betting on. The "most likely" full pattern is: AA beats BB & CC BB beats CC & DM CC beats DM & GG DM beats GG & AA GG beats AA & BB
We are making a very minor update to the timing rules. Instead of time starting on selecting New Game, time will begin on first input.