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Otherwise hope your opponent has no extenders and Ash the choke point.
Occasionally throw Nibiru at them.
You'll automatically win if your opponent rage quits from not being able to do anything.
...Wait that's just combo decks with extra steps.
On a surface level, probability looks like it is on your side. Consider a deck of 40 cards. Let's say you have 10 outs -- be they kaijus, handtraps, etc. The probability of you getting at least 2 outs with a 5-card hand is 27%. So around 1/4 games you will end up with 2 outs.
However, if you're hoping to win consistently, this is not likely the probability you want to see. If you played 100 games that means only around 25% of the time are you going to start with a set of outs you think is adequate. And that isn't even accounting for if you are going first or second, where second is the time you're looking for such a hand more often.
Further, there is the question of if your outs even matter. Drew Maxx C? It's Floo, so useless. Nib? Opponent gets a Baronne out early. Got an Ash? Your opponent is running outs as well, as if they have 2 Crossout and 2 CBTG they have a 35% chance of having 1 of those in opening hand assuming a 40 card deck, so you're SOL. Often times opening hands drawn from meta decks don't die to a single handtrap, if they did they wouldn't be meta. So if they 1-for-1 your out with one of their counter outs, you are not sitting pretty.
So, increase the out size then? To 15 perhaps and hope for 3 outs? That's just under 21% of a chance happening with 5 cards, for a 40 card deck. While such a hand may forge itself every now and again you open yourself up to far more bricking depending on your deck.
We can run numbers with different decks, proportions, etc, but at the end of the day we aren't arriving at any kind of definitive conclusion other than you're going to need to look at your deck and decide what outs it can take in, as well as the fact that more often then not probability just won't be on your side.
There is a reason "draw the out" is both an ironic and unironic meme.
However, also remember not every deck you face is going to be a Rose Tenyi or a Virtual World, so the amount of times you need to have sufficient outs at opening hand likely is not that large, and it's just the duels against these extremely combo heavy decks tend to sting a lot more in the head.
For example, any 1 cyberse monster can get you dpe+scythe lock, and if you draw enchantress or rite of aremesir you get adventure combo too.
So with 2 cards in hand, the rest can easily be hand traps without hurting you at all.
But if you spent that many cards in the first round, you are pretty vulnerable too (if you don't use Pot of Extravagance or Pot of Desires or your deck is so consistent that it can do a full combo with one card). One Skystriker player actually dropped 4 handtraps on me in the first and won the game
See this is why no Best of 3 is a bad thing.
You are absolutely correct. Assuming a 60 card deck, the probability your 5-card opening hand contains 2 of your 20 outs marks an improvement in chance from 27% to 34%. Moving from a 1/4 chance to a 1/3 chance.
However, there are two issues.
1. More outs does not mean always more counter power. Different outs do different things, and if you end up facing off against a deck like Floo where your drawn Maxx C and Kaiju are useless, you may be wishing you had a less cards so you had a chance to draw in maybe an Ash or an Imperm.
2. What decks can afford 60 cards? There are plenty of viable engines like Eldlich, DPE, and Adventure but what if a player wants to focus on a certain archetype? What if they do not want to play Cyberse or Phantom Knights? Can 60 card decks work with most playstyles? This is a genuine question since my experience in that front is limited, and it appears like a problem from my end.
Regardless, this whole probability debacle could be solved in almost its entirety with a... non-Bo1 format.
At least the first point is definitely sliced down. The game was designed for a side deck where you could swap cards to fit the situation. It would be far less of a frantic guessing game if people could rotate out cards to combat the deck they are against and adapt.
But of course, such is not the case, and as of now we have to work with what we got.
Ash, Lancea and what else? It seems they keep summoning not matter what you do.