Resource Attention to detail in RBY teambuilding

RBY is, has been and will remain (almost) the same since it's release in 1996.

With so much staticness, it allows changes in our perception and in ourselves to shine through.

These changes will usually be very subtle, as the meta is so close to optimal that there is little room for improvement. When suggesting a team or moveset for example, players and analysts, will add a contribution that perhaps amounts to one or two signature decisions, if that.

Today I want to share some bits of wisdom about how to maximize your expressivity when discussing sets and teams, while not derailing too much from standard sets.

To use as an example I shall seek for a pokemon which is in almost all teams, and which has almost always the same four moves, you know who I'm talking about. Let's consider Tauros in your team.

Of course, in informal talk we might just say "standard tauros" or just "tauros" and immediately convey the intended meaning. Furthermore this generation has no EV or IV expression (there is always an optimal DV spread which is maxing, but minimizing atks if special attacker).

That said, barring informal conversation, or team parsers with sensible defaults, we still need to define at least the attacks. I'll show an example of two different possible tauros which are technically the same, but semantically not:

A)
Tauros
- Body Slam
- Hyper Beam
- Earthquake
- Blizzard

versus

B)
Tauros
- Body Slam
- Hyper Beam
- Blizzard
- Earthquake

In the scenario A we place Earthquake first, while in scenario B we put Blizzard first. Order is important because it conveys how important we consider each move to be. The author of set A will be more concerned about covering gengar, and author B will be more concerned with covering Rhydon. I'd venture a guess that if you see set A, you are more likely to find a snorlax without earthquake, and if you see set B, you are more likely to find one or more electric types in that team.

A corollary of this, you might have noticed, is that there is expression everywhere, you may notice that in both cases I placed Body Slam before Hyper Beam, it's very different from:

C)
Tauros
- Hyper Beam
- Body Slam
- Earthquake
- Blizzard

In scenario C I may be thinking of tauros explicitly as a late game sweeper! While on B either I just thought standard tauros, or I'm valuing the possibility of spreading status vs a starmie.

Let's close off with a new set I've been trying

D)
Snorlax:
- Reflect
- Rest
- Body Slam
- Earthquake

A very standard, if not THE standard snorlax wall set. You will notice that I placed the defensive move first, which might tell you about how I use it. Usually stalling without revealing my moves, positioning for a PP advantage, and baiting opponent move and pokemon reveals.

Naturally, since the later two moves are revealed in later game we might propose additional moves:

E)
Snorlax:
- Reflect
- Rest
- Body Slam/Hyper Beam
- Earthquake/Self-Destruct

Here I showed you the 4 common moves I would consider, however, I believe that considering the narrow amount of possible sets, alternative notation is not as appropriate in gen 1 as it would be in future gens, where there is so much ground to cover that sets need to be joined together.

Consider:

F)
Tauros:
- Body Slam
- Hyper Beam
- Earthquake
- Blizzard/Rest

It would be a disservice to put such a radical idea such as rest tauros as an alternative of the standard set, it is its own set in its own right because it deserves as much space detailing the idea and how it plays. As it stands, in smogon there is only one tauros set anyways, and tauros is arguably the most common mon in the metagame. So we don't gain anything from collapsing multiple set analysis into one.

However back to E, the more moves we have, the more combinations we have, even with set E, there are 4 combinations of sets, each with its own merits and some unplayable. We may look into a more sensible but different way to simplify the combinations of sets, dropping the obsession with 4 moves.

G)
Snorlax
- Reflect
- Rest
- Body Slam/ Hyper Beam/ Earthquake / Self-Destruct

Here there is both a technical and a semantic difference, we are not only conveying information about how the mon is supposed to be played, but what the mon actually is.
A reader that reads that set might understand, and rightly so, that Body Slam and Hyper Beam are exclusive, while set G, expresses that any combination will do for the rest of the moves.
This has profound implications, assume that our opponent knows our style and teams because they play against us often. Then with our E Snorlax, as soon as we reveal earthquake, then the opponent would know that Hyper Beam is off the table, and that our other move is either Body Slam or self destruct.

Snorlax G solves this issue by making all alternative moves independent of each other, and dropping the 4th move allows us to convey this meaning.

Finally
H)
Snorlax
- Reflect (100%)
- Rest (100%)
- Body Slam (50%)
- Hyper Beam (50%)
- Earthquake (50%)
- Self-destruct (50%)

Now this has the same technical meaning and almost identical semantic meaning as G (it's just making explicit that the 4 last moves are equally likely, dispelling interpretations of preference due to order).
It may sound cumbersome to specify all probabilities, but consider that in actuality, we may favour some moves rather than others, especially if when we use mixed strategies in game theory analysis whether or not we seek Nash Equilibrium or play exploitively (subject for another post)

So actually

I)
Snorlax
- Reflect (100%)
- Rest (100%)
- Body Slam (75%)
- Earthquake (50%)
- Hyper Beam (50%)
- Self-Destruct (25%)

Would be a much stronger snorlax, as we can fine tune our probabilities and have an outsized impacts with moves that are either very strong, are shown late, or can only be used once, like self-destruct or sleep powder.

In later posts we will see that, the relationship between a moves strength and its frequency do not need to be proportional, it's very possible that the optimal strategy is that they are inverted, considering that the payout of a strong move is higher. Making sets like 75% earthquake/25% body slam snorlax, 25% psychic/75% double-edge exeggutor, or 25% thunderbolt jolteon not only viable but possibly preferrable. Think about it, in order to exploit a 25% thunderbolt jolteon, you would need to stay in with starmie, which risks a whole mon to an 0hko, reducing your frequency of a strong move will also make increase the Expected Value of actually using the move successfully when you have it, by avoiding being walled by multiple pokemon and having a chance to use it super effectively.



That would be all for today's post. I hope my perspectives from math, music and poker have enlightened the state of the game and that we can all move forward our understanding of game theory based on the One True Gen instead of keeping up with the latest cartridge released by Nintendo Corp.

Regards, Totomimi
 
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Quick proof of the claim regarding strong moves benefitting from lower frequencies.

Consider rock paper scissors, represented by payoff matrix

3 x 3 Payoff matrix A:

0 -1 2
1 0 -1
-2 1 0

Where the order is rock, paper, scissors of course.

The game is symettric so the payoff matrix of player B is

3 x 3 Payoff matrix B:

0 1 -2
-1 0 1
2 -1 0


EE = Extreme Equilibrium, EP = Expected Payoff
Decimal Output
EE 1 P1: (1) 0.33333 0.33333 0.33333 EP= 0.0 P2: (1) 0.33333 0.33333 0.33333 EP= 0.0
Rational Output
EE 1 P1: (1) 1/3 1/3 1/3 EP= 0 P2: (1) 1/3 1/3 1/3 EP= 0


Finally consider we add asymmetry to incentivize rock, such that the payoff is now

3 x 3 Payoff matrix A:
0 -1 4
1 0 -1
-4 1 0

EE = Extreme Equilibrium, EP = Expected Payoff
Decimal Output
EE 1 P1: (1) 0.250000 0.500000 0.250000 EP= 0.0 P2: (1) 0.250000 0.500000 0.250000 EP= 0.0
Rational Output
EE 1 P1: (1) 1/4 1/2 1/4 EP= 0 P2: (1) 1/4 1/2 1/4 EP= 0


We can see that the optimal strategy is to use paper half of the time for some reason. And using rock and scissors a quarter of the time each. this ensures we tie in the long run.

I make sense of it in that by overweighing scissor we defend against rock heavy strategies, and we only need to use rock a quarter of the time to enjoy it's benefits.

We can take this idea to eggy's sleep powder, snorlax self-destruct/Hyper beam, and even jolteon's tbolt, or eggy's psychic.

Source: https://cgi.csc.liv.ac.uk/~rahul/bimatrix_solver/
 
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