RBY OU Help for non-reflect Alakazam vs Tauros matchup

First case: Both pokemon are without status, Tauros is around 51-82% HP (dies to crit Psychic or two non-crits), and Alakazam has enough HP to survive a non-crit Hyper beam from Tauros. Should the Alakazam use Psychic or Thunder wave?

And a second case, non-statused Alakazam who is in range of dying to Tauros's Body Slam is facing a paralyzed Tauros, should the Alakazam player ever in any case try to use Recover?

These are quite a common situations and often I'm quite clueless on what is the best play. Sometimes it's an easy choice, like if the Alakazam player has a Starmie then facing low HP non-paralyzed Tauros is better, and if he has a Dragonite then facing high HP paralyzed Tauros is better. But often it's not so easy for me.

 

First case I’d definitely click psychic as you’re giving him multiple chances to para and crit his way through if you click twave.
Second case it seems optimal to go with recover if you can survive a hyper beam. If not then I’d go with psychic as you’re a crit/drop away from winning if he paralyzes or misses the hbeam.
These are just quick estimations though and I’m not sure if they’re the correct moves to go for mathematically.

 

When you're against Tauros, the right thing to do is to pray.

Gg ohhhh

 

No mindgames here - Tauros' optimal play is Body Slam whatever you do. If you use Psychic, Tauros wins if you don't crit and it either crits or paralyses (34.5%, not counting 255s). If you use Thunder Wave, Tauros wins if it doesn't FP and crits or if it doesn't FP and doesn't crit and doesn't para and then you don't crit and it doesn't FP the next turn or a couple more options involving it paralysing with Body Slam, but just the first two options already come to 40% so it's pretty obviously the option Alakazam doesn't want.

I'm not sure. If you aren't high enough to avoid a KO from Hyper Beam after Recovering and Tauros is chipped into crit Psychic range, definitely don't Recover. Otherwise it's a little murkier.

 

In your first situation, I think one way to go is list the number of ways Alakazam wins in a 'probability tree'. I'll round the probabilities so I have 4 decimals (I ignore the 255's, it's not off by much since the 255 go both ways too and I want to avoid clumsy conditional stuff). Let's look at the situation where Alakazam has full HP first. Hopefully I didn't make any mistakes!

• Psychic crits: 0.234;
• Psychic does not crit, and Body Slam doesn't crit nor inflict PAR: 0.766 * 0.785 * 0.7;
• Psychic does not crit, and Body Slam does crit but doesn't inflict PAR: 0.766 * 0.215 * 0.7 * 35/39;
• Psychic does not crit, and Body Slam doesn't crit but does inflict PAR: 0.766 * 0.785 * 0.3 * 0.1 * 0.75.

Note that in the third bullet, there is a 35/39 chance that crit Body Slam does not OHKO. In the last bullet, Alakazam will have to dodge Hyper Beam (which is always the best move for Tauros, since even when the first Body Slam gets a max roll, the second one has (by far) less than 90% chance to KO anyway, even factoring in the crit rate) AND avoid the full paralysis, hence the last two multiplications. Formally the tree options don't end here because Tauros can miss Hyper Beam while Alakazam is fully paralyzed and then miss AGAIN, etc, (turning the situation into a limit if PP is neglected) but I'll neglect those highly improbable cases for simplicity and they don't change the sum of these probabilities much, at least not to make your decisions. So finally, Alakazam has about a 77% chance to win the 1v1 with this strategy, rounding a bit on purpose. Note that this probability is so high because Tauros is in your specified range.

Will post the probability of winning when using Thunder Wave after this, but need to do some Markov Chaining for that . I am convinced that Psychic is the way to go if you want to optimize chances of winning, however. The reason to use Thunder Wave is traditionally only when you can reliable revenge kill Tauros after, and don't per se need Alakazam anymore.

 

Okay, I finished the Markov stuff. Again, neglect 255 misses . I defined 13 states as follows:

1. Alakazam and Tauros both healthy (for Tauros this means in the damage range like you specified);
2. Alakazam healthy and Tauros paralyzed but no damage;
3. Alakazam healthy and Tauros paralyzed and hit by non-crit Psychic;
4. Alakazam wins;
5. Alakazam unparalyzed, hit by non-crit Body Slam and Tauros paralyzed but no damage;
6. Alakazam paralyzed, hit by non-crit Body Slam and Tauros paralyzed but no damage;
7. Alakazam unparalyzed, hit by crit Body Slam and Tauros paralyzed but no damage;
8. Alakazam paralyzed, hit by crit Body Slam and Tauros paralyzed but no damage;
9. Alakazam unparalyzed, hit by non-crit Body Slam and Tauros paralyzed and hit by non-crit Psychic;
10. Alakazam paralyzed, hit by non-crit Body Slam and Tauros paralyzed and hit by non-crit Psychic;
11. Alakazam unparalyzed, hit by crit Body Slam and Tauros paralyzed and hit by non-crit Psychic;
12. Alakazam paralyzed, hit by crit Body Slam and Tauros paralyzed and hit by non-crit Psychic;
13. Tauros wins

Those are all the situations that can occur with our assumptions. I have assumed Tauros always uses Hyper Beam against Alakazam when it's hit by a non-crit Body Slam, and of course that it uses Body Slam to finish off Alakazam that's hit by a crit Body Slam before. I will spare you the calculations of the Markov matrix (unless you like to see them of course), and the first row of the matrix A^n for large n (you don't even need to use a very large n, because the average battle here only takes 1, 2, or 3 turns) has 55,5% in Alakazam's favor and 44,5% in Tauros' favor. So that's pretty bad for Alakazam compared to using Psychic; it's like needing to hit Sing.

For your reference, here is the transition matrix I used (note that this doesn't incorporate Recover usage yet; the strategy for Tauros is to use Body Slam or Hyper Beam):



And if you're interested in the probabilities when entering in another Stage than Stage 1, here's the matrix to the 32nd power, from which the probabilites can be read (for stage N, look in row N):

 

Actaeon has out-m9med me.