To Momo Or Not To Momo? The Math Behind Deck Searches

The Math Behind Deck Searches In One Piece Card Game

“To Momo or not to Momo”, that was the question. But as I considered what Momo would do in Red/Green Law decks, I realized my question was broader than just this one card in this one deck.

In this guest article from Quinn of the Romance Don Podcast, we’ll take a look at some of the maths behind the game. More specifically – how many of a specific type of card should you run in a deck to make including a “search for” card worth it? Let’s dive in!

The question I really wanted an answer to was: “how many ‘hits’ does my deck need to run for me to be happy running one of these conditional draw effects?” For me “happy” means 80% of the time or more I draw a card. You might be happy with 70%, this is not meant to be prescriptive, play whatever makes you happy.

Note: I’ve heard people refer to these cards as “tutors”. I am not going to do that. For me, coming from a Magic the Gathering background, “tutors” are cards that let you search your entire deck for a card, they are often used to reliably find 1ofs or combo pieces.

These cards only let you look for X cards of a specific type. So they feel less like a tutor and more like a conditional draw spell where sometimes you get a choice in what you take but often you are just happy to draw a card.

The searcher cards from OP-01 and Starter Decks 1-4 – Click image to enlarge, click name to view full details

Right now, there isn’t a wide range of cards available for every “type”. That means you have to think hard about what “types” to include in your deck based on their use. So when I talk about these I am looking at what is my probability of getting to draw a card off of them


In order to test this I wrote a python code to simulate a deck. The deck contained 4 copies of the card with the effect (E), some number of cards that could be “hit” (H), and the rest of the deck is “misses” (M).

I wanted to see what the likelihood of drawing a card off of one of these was when it was drawn at the beginning, played, and activated as soon as possible (not recommended in actual play). So I set my program to draw 6 cards since the earliest you can activate many of these cards is after you’ve drawn 1 card (either turn 2 on play or turn 1 on draw). 

Now technically this assumption isn’t perfect. Nami can be played turn 1 on the play (5 cards in hand) and some of the other cards looked at can’t be played until later. This really won’t skew the numbers too much. If you think this is an oversight let me know and I will rerun the numbers.

The program looked at the opening 6 cards. If one of those 6 cards contained a card with the effect it would “use it” and look at the next N cards (depending on what the effect says). If the next set contained an “H” then it was a “hit” and otherwise, it was a “miss”.

Note: Most cards available are “Look at 5 cards” but some cards spoiled from the next few releases look at other numbers.

There is probably some sophisticated probability analysis that could be done to get a more accurate result, but brute forcing it with computing power was a lot easier for me. I included my code at the end if anyone wants to double-check or if you just want to play with it and do your own analysis.

The Results

Effects that look at 5 cards need at least 13 hits in the deck to hit 80% of the time.
Effects that look at 4 cards need at least 16 hits in the deck to hit 80% of the time.
Effects that look at 3 cards need at least 20 hits in the deck to hit 80% of the time.
Effects that look at 2 cards need at least 27 hits in the deck to hit 80% of the time.

Probability of Drawing A Card Based on How Many Cards You See

So keep this in mind when you are building decks with multiple card types and when making changes. If you cut down on a certain type you might want to double-check if running these searcher cards is still worth it for you.

And as for the question of “To Momo or not to Momo” the answer is you probably shouldn’t. It is hard to get to that 13-hit threshold without running cards like Yamato which I don’t think are worth it. 

Editor’s Note: My latest Kid deck runs 15 Land of Wano cards, including two Momos. So it just slides in as over 80% – though it still bricks!

The code used to run these simulations is included for those who want to double-check or do their own analysis.

import random
def generate_list():
   global h_count
   global e_count
   global b_count
   make_lst = ['H'] * h_count + ['E'] * e_count + ['B'] * b_count
   return make_lst
def evaluate_list():
   global hits
   global misses
   global lst
   hits = 0
   misses = 0
   i = 0
   while i < 10000:
       first_six = lst[:6]

       if 'E' in first_six:
           i += 1
           next_set = lst[6:6 + LookAt]
           if 'H' in next_set:
               hits += 1
               misses += 1
   return hits, misses
# H is the number of hits in the deck, E is the # Cards with the effect that don't count themselves, and B is 'bricks'
h_count = 4
e_count = 4
LookAt = 0
for LookAt in range(2, 6):
   print("\n# of hits : probability when you can view", LookAt, "cards")
   for h_count in range(40):
       b_count = 50 - h_count - e_count
       lst = generate_list()
       hits, misses = evaluate_list()
       odds = hits / (hits + misses)
       print(h_count, odds)

Hi! My name is Quinn but I go by “AvianFang” in most online places. I am a level 1 OnePieceTCG Judge and have been an avid player of TCGs for over a decade and a half.

Magic the Gathering was my bread and butter for almost all of that time, though I dabbled in Hearthstone and other games here and there.

My professional backgrounds are in mechanical engineering and education. My goal is to use this somewhat unique perspective to offer insight and to help improve our community.

You can find me on Twitter @RomanceDonCast and listen to my podcast on Spotify here.

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