What’s up boys and girls, it’s T-Time! Sorry that I have been gone, I plan to drop multiple articles shortly, I’ve just had a lot on my plate lately. I have decided to take a break from Deck Doctor for just a moment in order to submit an article that has been weighing on my mind for nearly a year now. I have always wanted to type this article up, but have never really gotten around to doing it. Drawing cards, building decks, and even the odds of topping events can be analyzed using mathematical formulas considering the fact that they are all discrete random functions. Finding random variables means finding a representative numerical outcome for an uncertain event, such as opening with Shark/Magician or even topping an event. The random variables are discrete, which means that they random variables produce outcomes coming from a counting process. I hope that this article is helpful, but take into consideration all of the possible variables such as sleeves and weight of cards, shuffling styles, and the hundreds of possible variables for play testing in my “odds of topping an event” example. Without further ado, let us get started with a deck building example.
The number of cards you should have in your deck has always been brought to question. For a moment let us look at how the number of cards in your deck would affect the odds of you opening with 1 or more of a card that you play 3 (ex. Miracle Fusion) of, or opening with a staple that you only play 1 of (ex. Heavy Storm).
40 card deck drawing Miracle Fusion: 39.4%
40 card deck drawing Heavy Storm: 15%
41 card deck drawing Miracle Fusion: 38.6%
41 card deck drawing Heavy Storm: 14.6%
42 card deck drawing Miracle Fusion: 37.8%
42 card deck drawing Heavy Storm: 14.3%
45 card deck drawing Miracle Fusion: 35.6%
45 card deck drawing Heavy Storm: 13.3%
50 card deck drawing Miracle Fusion: 32.4%
50 card deck drawing Heavy Storm: 12%
Conclusion: Adding cards to your deck doesn’t decrease the odds of you drawing a specific card much at all. Maybe this can put a damper on the idea that every deck must contain no more than 40-41 cards. Also consider the fact that adding a card that you don’t play to a 40 card deck increase the odds of you drawing it from 0 to 14.6% and decreases your odds of drawing other cards only marginally. Remember that the next time you consider dropping an important card for something else. Plus it gives you more options in and out for your side deck.
With that established, if you were playing 40 cards, how do the odds change if you were to cut a card that you would normally play 3 of affect you drawing 1 or more of them in your opening hand?
Playing 3 Miracle Fusions: 39.4%
Playing 2 Miracle Fusions: 28.1%
Playing 1 Miracle Fusion: 15%
Conclusion: As I stated above, it is probably better to just add a crucial card than to cut another crucial card for it. Just remember what you want to draw and what you don’t. Every card you put in your deck should be a card you don’t mind having in your hand.
So you have been testing for the latest YCS or Regional. You have been testing against the decks you expect to play and against players who are of the caliber of those whom you will play at such events independently (it is known that there are better players at YCS’s and worse ones at Regionals, so the testing should be independent). The average Regional player you are going against should be somebody who consistently tops locals and has one or several regional tops in the past. The average YCS player should be someone who frequently tops Regionals and has one or more YCS tops in the past. In the most ideal situations, the average win percentage that you hold against them and those decks will translate to the event, so let’s assume that it does. Let’s also assume that the regional will have 8 rounds and you can only top with a 7-1 or better record. Let’s assume the YCS will have 10 rounds and that you can only top with an 8-2 or better record. What are the odds of topping if my playtest win/loss ratio is 50%.
Regional: 5.1%
YCS: 6.8%
What if it is 66.6% (2/3)?
Regional: 17%
YCS: 22.9%
What if it is 75%?
Regional: 25.6%
YCS: 33.8%
Conclusion: Okay… This is nowhere near pin-point accurate, but it should maybe give you a gauge for how well you should be doing in play testing. It should also show you that even some of the BEST players in the world who can beat another good YCS player (someone who has topped) 3 out of 4 times is more likely to not top than to top. Actually, it is likely that he will only top 1 out of every 3 events. There are so many variables involved that this is far from accurate, but this is probably as close of a gauge to how well you are play testing as you are going to get.
Let’s say that you are playing something with 2 Destiny Hero Malicious or Reborn Tengu in it. You want to know the odds of drawing them both together. In a 40 card deck, the odds of opening with x amount of them is as follows:
0: 72%
1: 26%
2: 2%
Conclusion: I guess drawing multiple Malicious really is a terrible beat, huh? Don’t forget that playing draw cards will increase the odds of this happening. Also remember that as you thin your deck and hold on to these cards, the more cards you draw and the odds increase dramatically for ending up with two.
Let’s assume that you are playing Starlight Road and are running it specifically because you want to stop your opponent’s Heavy Storm. Here are some odds, assuming you are only playing 1 Starlight Road and both you and your opponent are playing 40 card decks.
Odds of your opponent having Heavy Storm: 15%
Odds of your opponent having Heavy Storm and you having Starlight Road: 2.25%
Conclusion: This would lead you to believe that Starlight Road really isn’t all its cracked up to be. On the other hand, remember that there are many more cards that destroy multiple cards such as Mirror Force, Dark Hole, and Torrential Tribute. For those of you who have Heavy Storm, remember that your opponent setting two or more cards doesn’t necessarily mean they have Starlight Road, so go ahead and do your rain dance, they are likely bluffing.
If you were playing 6 gauge Gadgets in a 40 card deck, what are the odds that you open with…
0: 35%
1: 43.4%
2: 18.1%
3: 3.1%
4: .2%
5: .005%
6: .00003%
Conclusion: During a 10 round tournament, you are likely to open with 3 or more gadgets at least once. Those numbers are very comforting and make 6 gauge gadgets a very safe deck. They lack the explosiveness of the 9 gauge, which can run Ultimate Offering, Double Summon, and Call of the Haunted much more effectively, but they are certainly a safe bet.
If you were playing 9 gauge Gadgets in a 40 card deck, what are the odds what you open with…
0: 19.2%
1: 39.8%
2: 29.5%
3: 9.8%
4: 1.5%
5: .1%
6: .002%
Conclusion: During a 10 round tournament, you are likely to open with 3 or more gadgets between 2-5 times. That may seem scary, but it really isn’t as bad as you would assume considering you would be playing between 20-30 games. Also, the odds of you drawing a Gearframe with that or having a Machina Fortress make drawing multiple not so bad. The same goes for your opponent opening with Effect Veiler, which they are relatively likely to have in their deck if it is game 2-3.
Let’s turn our focus to Wind-Ups. Assuming you are playing 3 Magicians and 3 Sharks in a 40 card deck, what are the odds of you opening with…
1 Wind-Up Magician and 1 Wind-Up Shark: 11.6%
1 Wind-Up Magician or Tour Guide and 1 Wind-Up Shark: 14.4%
At Least 1 Tour Guide or Wind-Up Magician and at least 1 Wind-Up Shark: 20%
Conclusion: The odds of you opening up with the big Shock Master combo aren’t overwhelming, but with being able to draw it 20% of the time, be prepared for it to happen to you every other Wind-Up match. Luckily for the deck, it has 3 Wind-Up Rabbits and 3 Wind-Up Factories that will allow the deck to quickly get to the cards it needs to go off. Plus with 3 Wind-Up Rats, there are plenty of late game options.
Let us assume that you are playing hand traps (Veiler/Maxx C) in a 40 card deck and you want to open with one of them in the first 5 cards (since generally, you would want them turn 1 in defense of Magician/Shark etc.). What are the odds of you opening up with one of those if you play…
1 Hand Trap: 12.5%
2 Hand Traps: 22.4%
3 Hand Traps: 30.1%
4 Hand Traps: 35.8%
5 Hand Traps: 39.8%
6 Hand Traps: 42.3%
Conclusion: I would want to play no more than 4 of them, considering the fact that the odds of you drawing multiple increase so dramatically. Plus once you get past 4, the odds of you opening up with one only increased by 4%. The more you play the increase in the odds of you drawing them becomes smaller, though it is an increase none the less. You just have to decide on how desperately you want to open with one against the odds of you opening with multiple. Also, don’t forget that Wind-Ups will only have the Shock Master combo first turn 20% of the time, so don’t get carried away with your hand traps.
In my final conclusion, again remember that none of this is exact. Remember that I am trying to give a numerical value to an uncertain event and that you could very well go through an entire tournament without drawing Heavy Storm once! I hope that this article was helpful and fun and if you have any further questions on this please leave them below and I will try my best to respond. If you enjoyed this article and want to see me do another one of the like, let me know!
Thunderpants
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