|
8 months ago ::
Oct 10, 2012 - 10:00PM
#51
|
Date Joined:
Sep 23, 2011
|
I made a humanish shuffler. Every human shuffles differently, so obviously results are going to vary, but I made what I thought felt human. First the deck is cut based on:
Length of Deck / 2 + [Deck Size / -8 → Deck Size / 8]
Where [X → Y] is a random number between X and Y.
This means that if you have a 60 card deck you could end up with one of the piles having around 37-38 of the cards and the other only having around 22-23 of the cards with the ugliest possible cut. Then the piles are intertwined based on:
[0 → 1] + (.08 * (P1 Size - P2 Size)) ^ 3 > .5
If the statement is true a card from the left pile is dropped, otherwise a card from the right pile is dropped.
This means that if 3 more cards are in one pile the probabilities of dropping are still incredibly close. If there are 6 more cards in one pile then that pile has around a 3/5 chance of droping. When a pile has 10 more cards it is garunteed to drop. In 1000 trial simulations I got the following results, where Stacked means the deck had all the lands on top, Weaved means the lands were weaved perfectly with the spells, M means the max land clump among all trials, A means the average of the max land clump in each trial, and LC // SC means Land Clump // Spell Clump. Stacked; 12 Shuffles
MLC: 9
ALC: 3.81
MSC: 14
ASC: 5.582 Stacked; 5 Shuffles
MLC: 9
ALC: 3.808
MSC: 13
ASC: 5.549 Weaved; 12 Shuffles
MLC: 9
ALC: 3.745
MSC: 13
ASC: 5.535 Weaved; 5 Shuffles
MLC: 8
ALC: 3.695
MSC: 13
ASC: 5.533 Random
MLC: 10
ALC: 3.825
MSC: 15
ASC: 5.581 If you want any other stats, or what me to change up the shuffling formula then I can do so. But the data seems to imply that rifle shuffling, even if only five rifle shuffles, distributes lands and spells pretty well, and does screw you over slightly less than random shuffling. Though this could just be data evening out, perhaps there's a different stat I should provide? Like probability of having a >3 land clump or a >5 spell clump? That might be more relevant to the discussion.
|
|
|
|
8 months ago ::
Oct 11, 2012 - 4:59AM
#52
|
Date Joined:
Jun 15, 2009
|
I was originally suggesting shuffling them by hand, but ... good initiative, it's much easier to run thousands of trials using this method. As for the shuffling algorithm, one thing I would change to better approximate the cut would be to make it a normal distribution, centered at the center of the deck. A player might cut the deck at different points, but as you move from the center it becomes increasingly less likely. I would also run the simulation for 8 shuffles, since this is the number of times I think most players riffle shuffle after interleaving. The ALC and ASC is probably the most descriptive, but another good statistic to gather is the percentage of resulting starting hands that contain 0,1,6 or 7 lands vs the number that contain 2,3 or 4. Another statistic to gather would be the percentage of time a person keeping their starting hand would make their first 3 land drops, as well as the percentage of time a person keeping their starting hand would be mana flooded after drawing their first 17 cards.
|
|
|
|
8 months ago ::
Oct 11, 2012 - 7:41AM
#53
|
Date Joined:
Sep 23, 2011
|
Alright. Changed up the algorithm to cut the deck precisely in half.
These are the results after 10,000 trials. "Drawgoods" are opening hands where you have at least 2 lands and 2 spells, by your third draw you have 3 lands and 3 spells, and by your sixth draw you have 4 lands and 5 spells. Stacked; 8 Shuffles
ALC: 3.81 (+.02)
ASC: 5.55 (+.01)
Drawgoods: 80.52% (+.48%)
Throws: 11.63% (-.89%)
3rd Draw Fails: 3.95%
6th Draw Fails: 3.9% Stacked; 12 Shuffles
ALC: 3.79 (+0)
ASC: 5.56 (+.02)
Drawgoods: 80.65% (+.61%)
Throws: 12.08% (-.44%)
3rd Draw Fails: 3.87%
6th Draw Fails: 3.4% Weaved; 8 Shuffles
ALC: 3.80 (+.01)
ASC: 5.55 (+.01)
Drawgoods: 81.15% (+1.11%)
Throws: 11.15% (-1.37%)
3rd Draw Fails: 3.92%
6th Draw Fails: 3.78% Weaved; 12 Shuffles
ALC: 3.81 (+.02)
ASC: 5.57 (+.03)
Drawgoods: 79.75% (-.29%)
Throws: 12.43% (-.09%)
3rd Draw Fails: 4.14%
6th Draw Fails: 3.68% Random
ALC: 3.79
ASC: 5.54
Drawgoods: 80.04%
Throws: 12.52%
3rd Draw Fails: 3.78%
6th Draw Fails: 3.66% I increased the number of trials to a million to reduce the margin of error and test 8 shuffle weaved decks against random decks. I got 80.28% drawgoods (12.17% throws) with the random deck and 80.69% drawgoods (11.87% throws) with the weaved deck. This suggests that weaving without shuffling much gives you favorable odds that are slight but noticeable over the long term, I expected that.
|
|
|
|
8 months ago ::
Oct 11, 2012 - 8:52AM
#54
|
Date Joined:
Aug 11, 2008
|
i really wish people would stop whining about this.
Amen.
Those who fear the darkness have never seen what the light can do.
I've seen angels fall from blinding heights.
But you yourself are nothing so divine.
Just next in line.
|
|
|
|
8 months ago ::
Oct 11, 2012 - 4:04PM
#55
|
|
|
No. I got 5th on a 5-1 record at a pre-release "tournament" where the house rules allowed for friendly mulligans. My final opponent had numerous opportunities to fish for his game-winning combo, which he did and used against me every game.
It was ridiculously unfair and sapped all fun I had away from the tournament. This kind of "mulligan" shifts the game into combo decks and drains the craft of consistency and the skills of playing against randomness out of the game.
Just to make this clear and put it on the record: PLEASE mail Wizards' Organized Play when you experience this sort of thing! Prerelease product is specifically meant to go to organized prerelease tournaments, any organized tournament has a set of rules that it's obliged to follow, and those rules include the standard M:tG floor rules; they most certainly don't include 'house mulligan' rules even if it's for a good cause, much less when those rules are sprung on unexpecting participants. It's in everyone's best interests in the long run to have these events run properly, and if Wizards doesn't know about it then they can't clamp down on organizers who mis-run events.
|
|
|
|
8 months ago ::
Oct 11, 2012 - 4:21PM
#56
|
|
|
Nice try silentbobus, but we all recognize your alt.
1000th post November 26, 2010. Where Islands gets his decks: Spoiler:
Show
It was revealed to me in a dream. All the cards were in my dream except for three slots which I plugged in as Vault Skirge.
FULL DISCLOSURE: The dream was post AVR so there was a copy of Slayer's Stronghold. I decided to keep it pre AVR in my post here.
EDIT: I just remembered. The Skirges might have been 2x Whipflare and 1x something else, probably War and Peace.
EDIT2: Currently 4-0 in my first four games with this. My opponents have been very angry. I fought off a Wurmcoil from Grixis for six turns before I found my second Dispatch. Jeez, I can do a lot of damage.
EDIT3: Streak broken. Lost to an unexpected Overrun.  Cracking a Shrine for 10 wasn't enough.
How Kedi tests his decks: Spoiler:
Show
also, I've been playtesting this deck in my sleep today
that kinda freaked me out
Sleeping on Halloween: Spoiler:
Show
Halloween is a conspiracy by crossdressers and furries.
 Thanks to Kipz for the sig. Make a contract with me to become a magical girl!
|
|
|
