Template:Mixup/doc

	This template uses Lua:
	Module:Mixup

	This template uses TemplateStyles:
	Template:Mixup/style.css

This template displays the payoff table and first Nash equilibrium for a zero-sum, two player strategic game.

The game is defined in a .gbt file in the Mixup namespace. These files are used by the game theory software Gambit.

In other words, this template takes a well-defined mixup and shows the optimal strategy for both players, i.e. how often they should use each option. See the example for how to interpret this.

Usage

{{Mixup|Kazumi-fly-infinite.gbt}}

Example

Mixup:Kazumi-fly-infinite.gbt (download) ^{What is this?}

Kazumi FLY mixup in mirror after 1+2, ws3, and u/f+2 transitions on infinite stage.

	d	b	SWR	4
FLY.1	29	-31	-68	34
FLY.2	-75	-31	75	79
FLY.4,2	-80	36	36	39
FLY.1+2	24	2	-68	-68
FLY.3+4	64	-68	13	65

Nash equilibrium with payoff -4.79

FLY.4,2

0.39

FLY.1+2

0.33

FLY.3+4

0.28

d

0.35

b

0.44

SWR

0.21

Payoff for dominated options

FLY.1

-17.58

FLY.2

-24.48

4

-11.17

If the attacker does FLY.4,2 and the defender does standing guard, then the outcome is 36 damage in the attacker's favor. (The attack actually does 31 damage, but the okizeme is approximated to be worth about 5 damage.)

In the optimal strategy:

• The attacker uses FLY.4,2 ~39% of the time, FLY.1+2 ~33% of the time, and FLY.3+4 ~28% of the time.
• The defender uses crouching guard ~35% of the time, standing guard ~44% of the time, and SWR ~21% of the time.
• On average, the defender comes out ahead by 4.79 damage.
• The attacker's options FLY.1 and FLY.2 are never used, since they'd have a payoff of about -17.5 and -24.5 respectively. Similar for the defender's option 4.

If either player deviates from this strategy they can only worsen their payoff, so there's no way to force an opponent to change from it. However, it's possible for a player to get a better payoff by changing their strategy if their opponent is also not using this strategy, i.e. there might be a better way to exploit a weak opponent.

Limitations

A Nash equilibrium for a particular mixup is useful for getting a general idea for which options are better than others, but there are many limitations in the context of Tekken:

• Payoffs are defined in terms of damage, so any extra payoffs from frame advantage or okizeme need to be approximated.
• Life advantages aren't considered.
  • An outcome where both players trade damage is considered an even outcome, but it actually favors the player that's ahead.
  • A high risk option might be dominated because it has bad payoff on average, but if you're on 1 life, then taking 5 damage is the same as taking 80.
• Outcomes can vary a lot depending on execution.
  • In particular, whiff punishment is a big problem. The punisher used and whether it's fast enough can lead to dramatically different outcomes. In general, determine the attack from what caused the whiff (e.g. Kazumi would use 1,1,2 with sidestep and 3,2 with backdash) and if the whiff is very big then approximate how likely it is the player would react and punish optimally. Be realistic—optimal whiff punishment shouldn't be expected.