Multistrike Moves & King's Rock
Statistical Odds of Effect Triggers & Writing Your Own Calculators
A common strategy in Pokémon games, both in competitive games and normal playthroughs, is attempting to "flinch" the opposing Pokémon and prevent them from moving this turn if they have not already. Some moves have an inherent or guaranteed chance of flinching opposing Pokémon, and some abilities give Pokémon a similar chance to flinch opposing Pokémon.
King's Rock in particular is a held item that provides every offensive move learned by a Pokémon that same ability. Per Pokémon Champions, "When the holder deals damage with its moves, there is a 10% chance that targets will flinch."
One potential strategy that can be used in tandem with the King's Rock is, simply, using it as many times as possible. Normally, each move would only hit the opposing Pokémon once. However, a series of moves in Pokémon games known as "multistrike" moves hit more than one time and, if combined with a King's Rock, reroll that 10% chance each time damage is inflicted.
Luckily, the odds on King's Rock are consistent. No matter if you're using a multistrike move in one turn or using a one-hit move over two turns, each attempt will always be a ten percent chance. However, when it comes to calculating the odds of flinching the opponent, these moves tend to grow more complicated.
This article seeks to analyze how these two factors influence each other and how to calculate the odds of them working in tandem with each other to flinch opposing Pokémon.
Table of Contents:
Odds of Success
In general, when working with random events, there are two options: success and failure. Either a random event does happen, or it does not happen. This can be further complicated an expanded on when adding multiple definitions of "success", but we'll discuss that more later.
To put it simply, the odds of success can be written as:
[odds of successful roll] = 100% - [odds of failing roll]
Most of the time, this "odds of successful roll" is directly given and can be written simply. In the case of King's Rock's guaranteed 10% with any generic move that makes contact with an opposing Pokémon,
10% = 100% - [odds of failing roll]
| 10% | 20% | 30% | 40% | 50% | 60% | 70% | 80% | 90% | 100% | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1st Hit |
As long as you roll within that blue cell (the ten percent), you succeed.
The reason this is simple is because there is only one definition of "success" – you do or you don't cause the opposing Pokémon to flinch. This already assumes a number of variables play exactly as you expect them to:
- The move successfully passes an accuracy check.
- The move successfully deals damage to the opposing Pokémon.
- The move only dealt damage to the opposing Pokémon a single time.
Continuing with this line of thought, what happens when you add more than one definition of success? Is it a simple 10% + 10% = 20% chance? No, it doesn't. Let's break down the possible rolls with a two-hit move.
| 10% | 20% | 30% | 40% | 50% | 60% | 70% | 80% | 90% | 100% | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1st Hit | ||||||||||
| 2nd Hit |
You only need to land in that column to succeed, right? How many chances out of those twenty boxes are a "success"? Is it only the two under 10%? If so, that would mean there are two out of twenty possible combinations that succeed.
Would this combination succeed?
| 10% | 20% | 30% | 40% | 50% | 60% | 70% | 80% | 90% | 100% | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1st Hit | ||||||||||
| 2nd Hit |
Or this combination?
| 10% | 20% | 30% | 40% | 50% | 60% | 70% | 80% | 90% | 100% | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1st Hit | ||||||||||
| 2nd Hit |
Or, equally possible,
| 10% | 20% | 30% | 40% | 50% | 60% | 70% | 80% | 90% | 100% | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1st Hit | ||||||||||
| 2nd Hit |
Out of the one-hundred different combinations of rolls that work in this roll, a total of nineteen would result in success: the first roll succeeding and the second roll failing (nine combinations), the second roll succeeding and the first roll failing (another nine combinations), and both rolls succeeding (one combination): 19% chance to succeed, not a simple 10%+10% chance like theorized earlier.
These combinations only grow more complicated to track the more rolls are made to be tracked. For three rolls total, two-hundred seventy-one out of one-thousand possible combinations would be defined as "success."
You could manually count them each time if you wanted, of course, but that takes a significant amount of time. Instead, if you look at the roll in reverse, the process becomes significantly easier to accomplish. Instead of finding every minute combination that can succeed and add those together, you can mathematically find the odds of failure and remove that from your whole.
[odds of successful roll] = 100% - [odds of failing roll]
Odds of Failure
Calculating the odds of failure rely on the same principles we started with in our earlier examples, except in reverse. Let's look at that table that simulated rolling on a 10% chance twice. Instead of highlighting the number you want to roll on to succeed, however, we will highlight the numbers you would want to avoid rolling on.
| 10% | 20% | 30% | 40% | 50% | 60% | 70% | 80% | 90% | 100% | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1st Hit | ||||||||||
| 2nd Hit |
In this instance, any combination of the two that lands in those first boxes is instead ignored, since we are only looking for rolls where you never succeed. While that results in a larger number, it's easier mathematically to account for these numbers. Unlike the earlier successful examples, you no longer have to account for combinations that do not always hit that same mark but result in the same roll.
Once this principle is applied, all that needs to be added to our earlier equation is a variable for how many rolls there are in the first place.
When calculating the odds of an event happening every time, all you have to do is multiply those values together (since that does not have to account for conflicting combinations that result in the same result). That will slightly adjust our chance of success formula now that we are explicitly checking multiple events at the same time.
[odds of successful roll] = 100% - { [odds of failing roll] × [odds of failing roll] × (...) }
Or, when simplified into an exponent,
[odds of successful roll] = 100% - [odds of failing roll][number of attempts]
Now we can specifically return back to the odds of success for King's Rock in particular. If King's Rock has a 10% chance to pass a single roll, it inversely has a 90% chance to fail at the same time. That equation can now be written as:
[odds of successful roll] = 100% - 90%[number of attempts]
Now, all you need to do is count how many moves you expect to land in each move and add that variable into your equation.
Multistrike Moves
Once you begin looking at multistrike moves, this either becomes much easier or much more annoying to account for. That's because not every multistrike move is calculated the same. On a general note, this is just another test that has to be made before the King's Rock roll is made.
[odds of successful roll] = 100% - { [accuracy check] × 90%[number of attempts] }
Here is how the accuracy of three different multistrike moves are calculated, assuming accuracy stats are not artificially increased or decreased:
Twin Beam
| Count | Odds |
|---|---|
| 0 Hits | 0% |
| 1 Hit | 0% |
| 2 Hits | 100% |
"Twin Beam" is guaranteed to hit twice (unless the first hit knocks out the Pokémon, but that's not taken into account when calculating if the move hits).
Rock Blast
| Count | Odds |
|---|---|
| 0 Hits | 10% |
| 1 Hit | 0% |
| 2 Hits | 35% |
| 3 Hits | 35% |
| 4 Hits | 15% |
| 5 Hits | 15% |
If "Rock Blast" hits, it has a pre-determined chance to hit 2, 3, 4, or 5 times. It does not roll consecutive accuracy checks.
Population Bomb
| Count | Odds |
|---|---|
| 0 Hits | 10% |
| 1 Hit | 90% |
| 2 Hits | 81% |
| 3 Hits | 72.9% |
| 4 Hits | 65.61% |
| 5 Hits | 59.05% |
| 6 Hits | 53.14% |
| 7 Hit | 47.83% |
| 8 Hits | 43.05% |
| 9 Hits | 38.74% |
| 10 Hits | 34.87% |
If "Population Bomb" hits, it rerolls a 90% accuracy check each time. If it passes the first accuracy check, it rolls a second accuracy check. If it passes the second accuracy check, it rolls a third. If it passes a third, it rolls a fourth. Etc. until an accuracy check fails or it hits ten times.
See why it can be difficult to account for this consistently?
Luckily for us, there is a simple solution: look at the moves you're looking at and compare how likely you are to reach the number of hits you need. For example, compare "Rock Blast" and "Population Bomb." King's Rock works the same way with the two regarding its checks, so compare how their accuracy compares. The most likely result is that your Pokémon hits either two or three times with "Rock Blast," whereas "Population Bomb" has just less than that chance for its highest number of hits. When it comes to selecting which move to favor,
- Determine if you already need a specific Pokémon (they probably can't run too many of these moves anyway)
- Determine if you need a certain move for typing reasons (Population Bomb is a Normal-type move that won't work at all against Ghosts, for example)
- Once you have the move you want to use, use that equation for each number of hits and memorize a rough range of how likely you are to crit as you play.
Multistrike moves and King's Rock Flinches are two different strategies that can greatly shift the momentum of the game. With Multistrike drastically increasing the power at your disposal and King's Rock preventing slower Pokémon from even making an impact on the field, the two in tandum could completely dominate parts of the game. If you're looking for a more consistent way to control the board, consider running one of these Pokémon on your team.