Is 30 cards always the optimum deck size?

[whatifidogetcaught?]

Nope. You won't have more bad draws; the chance of drawing each card type is the same. However, there is indeed a reason the 60-card version can be proven slightly different than the 30-card counterpart, but it is not luck. It is speed. In a 30-card deck, you draw 1/30th of your deck per draw, while in a 60-card deck you draw 1/60th of your deck per draw. Because of that, you draw twice as fast in a 30-card deck, so you deckout twice as fast. Its a double-edged sword...

By running the simulator, it is a .2 TTW difference. Pretty damn good if you want the perk of not decking out.

[ARTHANASIOS]

Don't forget that life deck has Dragons and Mitosis, which are much more useful in the upped version, since more turns pass and more quanta is generated. Anyway, the truth is 60-card decks based on rush are viable and reliable if you know what you want/need. Pretty underestimated and underplayed if you ask me. 60 card upped mono-life rush with plenty of stalling elements too. Hmm... I wonder how monoaether would've reacted against this...

[Absol]

Inb4 Glenn's 45-card creature rush.

But that life deck example is sure amusing.

[Marsu]

Of course you will have more bad draws. This can be easily proven by looking at the worst cases of draw from both decks respectively.
The worst draw you can have with the 30 card deck is "no pillar in 18 cards". the worst you can have with the 60 card deck is "no pillar in 36 cards". the second worse with the 30 card deck is "no pillar in 17 cards", and so on.
This adds up to way more bad draws for the 60 card deck, without any more "better draws", the only advantage being not decking out.

[ARTHANASIOS]

This adds up to way more bad draws for the 60 card deck, without any more "better draws", the only advantage being not decking out.

False, you forget the better draws of having more cards of the same kind. If you lose 3 Mitosis via Lobotomize, you have no more Mitosis in your 30-card deck, but you still have 3 more Mitosis in your 60-card deck. Same goes with Frogs, Cockatrices, Dragons etc.
Furthermore, this deck was just an example, food for thought. But overall, both decks have same drawing chances, the bad draws you mentioned are because of the smaller drawing power of 60-card decks. That means 3 turns without pillar in a 30-card deck means 6 turns without pillars in a 60-card deck. But if RNG is so mean not to let you draw a pillar for 3 turns in a 30-card deck, you have probably alredy lost, so there is not such a great difference of RNG unfairness in both situations imo.

[Marsu]

This could really easily be solved by simply using the deck test simulator. I somehow can't get it to work though.
Both decks against AI3 100 times would be interesting.

[CuCN]

wiidgc already put them through the simulator for level 1. Here are results for 1000 games in level 3:

Spoiler for 30 card deck:

Player
Wins: 817
Winrate: 81.7 %
Average TTW: 9.613219094247246
EMs: 113
EM rate: 13.83108935128519 %

Spoiler for 60 card deck:

Player
Wins: 480
Winrate: 48 %
Average TTW: 11.41875
EMs: 52
EM rate: 10.833333333333334 %

Not sure if the simulator is doing something strange or it really does have such a big impact on win rate. (I ran it through a couple more times with similar results)


Edit: there is something wrong with the deck shuffling in xenosim on Firefox. These numbers are not accurate.

[Regyptic]

^
This example is flawed though. It's simple statistics, you will have way more really bad draws with the 60 card version.

I still agree though that 30 isn't always best.

Nope. You won't have more bad draws; the chance of drawing each card type is the same. However, there is indeed a reason the 60-card version can be proven slightly different than the 30-card counterpart, but it is not luck. It is speed. In a 30-card deck, you draw 1/30th of your deck per draw, while in a 60-card deck you draw 1/60th of your deck per draw. Because of that, you draw twice as fast in a 30-card deck, so you deckout twice as fast. Its a double-edged sword...

I'm pretty sure you will have more bad draws. The chance of drawing any card is only the same initially. As soon as you start drawing cards the probabilities stop being the same. For example, here's a table of your probability of drawing a pillar in each of those decks given that you haven't drawn one after X draws.

X	30 Card	60 Card
0	14/30=46.7%	28/60=46.7%
1	14/29=48.3%	28/59=47.5%
2	14/28=50%	28/58=48.3%
3	14/27=51.9%	28/57=49.1%
4	14/26=53.8%	28/56=50%

If you're not convinced that the 30 card version will be more consistently better then here are the results of 10,000 games in the simulator between these 2 decks;

30-card Deck
Wins: 5323
Winrate: 53.23 %
Average TTW: 7.248919782077776
EMs: 3
EM rate: 0.05635919594213789 %

60-card Deck
Wins: 4677
Winrate: 46.77 %
Average TTW: 7.265768655120804
EMs: 1
EM rate: 0.021381227282446014 %

I've tried this with other doubled up rush decks and the 30 card deck generally seems to win around 52-54% of the time.

wiidgc already put them through the simulator for level 1. Here are results for 1000 games in level 3:

Spoiler for 30 card deck:

Player
Wins: 817
Winrate: 81.7 %
Average TTW: 9.613219094247246
EMs: 113
EM rate: 13.83108935128519 %

Spoiler for 60 card deck:

Player
Wins: 480
Winrate: 48 %
Average TTW: 11.41875
EMs: 52
EM rate: 10.833333333333334 %

Not sure if the simulator is doing something strange or it really does have such a big impact on win rate. (I ran it through a couple more times with similar results)

I tried this as well and got a similar result for the 30-card version but more like 77-78% win rate for the 60-card version which seems more reasonable. Have you double checked the deck code you were using?

[Marsu]

Where does the huge gap in the stats from CuCn and Regyptic come from though? 53,2% win really is not far from 50-50, while CuCn's stats suggest a totally different result.

[ARTHANASIOS]

Where does the huge gap in the stats from CuCn and Regyptic come from though? 53,2% win really is not far from 50-50, while CuCn's stats suggest a totally different result.

Imo, just don't trust the simulator. All honesty, if the simulator plays like the AI, it is going to be a really bad player, even for a pure rush deck.

The lower chance of drawing a certain card is because of the slowest drawing rate of the 60-card. This has both its advantages and disadvantages. But for a pure rush, a fat deck will be at least slightly slower for sure.

[CuCN]

I copied and pasted the codes from artha's post and the 60 card deck gets less than 50% against AI3 every time. I also tried them against each other and the 30 card version won 80% of the time.

Spoiler for The decks, just to make sure:

Hover over cards for details, click for permalink

Deck import code : [Select]

5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bt 5bt 5bt 5bu 5bu 5bu 5c0 5c0 5c0 5c7 5c7 5c8 5c8 5c8 5c9 5c9 5de 5de 5de 5de 5de 5de 5de 8pn

Hover over cards for details, click for permalink

Deck import code : [Select]

5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bt 5bt 5bt 5bt 5bt 5bt 5bu 5bu 5bu 5bu 5bu 5bu 5c0 5c0 5c0 5c0 5c0 5c0 5c7 5c7 5c7 5c7 5c8 5c8 5c8 5c8 5c8 5c8 5c9 5c9 5c9 5c9 5de 5de 5de 5de 5de 5de 5de 5de 5de 5de 5de 5de 5de 5de 8pn

[majofa]

Assuming Adrenaline is the key to winning fast:
The player with 30 cards has a better chance of drawing the first one.

60 cards	% to draw		30 cards	% to draw
4/60	6.667%		2/30	6.667%
4/59	6.780%		2/29	6.897%
4/58	6.897%		2/28	7.143%
4/57	7.018%		2/27	7.407%
4/56	7.143%		2/26	7.692%
4/55	7.273%		2/25	8.000%
4/54	7.407%		2/24	8.333%
4/53	7.547%		2/23	8.696%
4/52	7.692%		2/22	9.090%
4/51	7.843%		2/21	9.524%
4/50	8.000%		2/20	10.000%

The player with 60 cards has a better chance of drawing a second one.

60 cards	% to draw		30 cards	% to draw
4/60	6.667%		2/30	6.667%
3/59	5.085%		1/29	3.448%
3/58	5.172%		1/28	3.571%
3/57	5.263%		1/27	3.704%
3/56	5.357%		1/26	3.846%
3/55	5.455%		1/25	4.000%
3/54	5.556%		1/24	4.167%
3/53	5.660%		1/23	4.348%
3/52	5.769%		1/22	4.545%
3/51	5.882%		1/21	4.762%
3/50	6.000%		1/20	5.000%
3/49	6.122%		1/19	5.263%

The same percentages apply to Mitosis.

In a game that would often last less than 10 turns, the 30 card deck would defeat the 60 card deck the majority of the time.