Mulligan ponderings

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Theo
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Mulligan ponderings

Post by Theo » Wed May 15, 2019 12:55 am

Here I'd like to share some of my ponderings and results of such ponderings on possible MECCG mulligan rules. Summary at bottom.

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I consider the following motivations/goals for good mulligan rules:

1) Reduce the number of wasted turns at the beginning of the game due to poor opening card distributions.
2) Don't dramatically increase the play time.
3) Keep the basics of deck building and game play the same.

#2 Basically means "keep it simple" and "encourage limited redraws". It feels like the easiest to evaluate for candidate rules, so I start my analysis there. But how to encourage limited redraws? I consider three main categories: hard cutoffs, increasing deficits, and qualifying conditions.

Hard cutoffs -- For example: "You can mulligan once." Any predetermined hard cutoffs would be prone to either (a) being too small and not giving players sufficient ability to avoid bad distributions (missing the point of criteria #1), or (b) being too large and motivating players to take mulligans with quite decent hands just to get some particular key card with the knowledge that they will probably not get a worse hand, impacting both criteria #2 from wasted time and #3 from allowing decks to rely more on getting particular cards early.

Increasing deficits -- For example: "Every time you mulligan, you draw one less card." A well chosen deficit will allow each player to balance their avoidance of poor starting hands while disincentivizing mulligans that are motivated purely by a desire for some particular opening card(s) (which should not be the point of a randomized deck game). More on this later.

Qualifying conditions -- For example: "You can mulligan if your current hand is all hazards or all resources/characters." Generally, these would be hard to implement without affecting (3); deck builds that tend to satisfy the qualifying conditions for mulligans could gain an advantage over deck builds that do not (bad for criteria #3). However, because deck building requirements stipulate that an equal number of hazards and resources must be included, qualifying conditions based on such distributions would be difficult to exploit.

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In this framework, consider, for example, the DC mulligan rules:
"Starting hand. If you have no resources normally worth any marshalling point(s) in your hand at the start of the game, you may reveal your hand to your opponent, shuffle all cards back into the play deck, and draw a new hand of 8 cards. This may be done once.
Clarification: resources with MP’s in parentheses are not considered worth MP’s."

How these match up to my mulligan criteria:
(1) Only minor help.
(2) Reasonable.
(3) Fails. The conditionality encourages deck alteration to use sparse/big resource MP over plentiful/small resource MP.

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Instead, inspired by the qualifying conditions category, consider the following mulligan rule (I'll call it "Turn Type Minimum X"):
"If you have less than X of the type of card that you are first playing as (hazard, or resource+character), you can reveal your hand distribution (doesn't need to be the cards by name), shuffle it into your deck, and draw a new hand."
If X is sufficiently small, this will occur rarely enough for the reshuffling to not burden the game, and mitigate risk of players fishing for their ideal opening hand. If X is sufficiently large, this will allow players to avoid opening hands that can't do much due entirely to an unlucky draw.

Choosing the right X is dependent on better understanding criteria #1. What exactly are the cases of "wasted turns at the beginning of the game due to poor opening card distributions." I imagine there could be a lot of debate on this point, and that I am probably on the more conservative side of that debate. For me, raw opportunities for playing cards are measurable; after that it is up to the players to construct their decks to be able to make use of those opportunities. So here are some examples where I would NOT say turns are wasted due to poor opening card distributions:
* resource player plays their entire hand, such as 4 critical preliminary stage resources plus 2 movement protection cards plus two sideboard accessing cards during their organization phase. This is not a wasted turn, but an ideal opening hand for some decks, and the mulligan rules should not support deck construction that allows this to be guaranteed.
* hazard player plays none of the 4 hazards from their opening hand because their playability requirements were not met. This may be a wasted turn, but I would argue that it is likely the fault of deck construction, not poor opening card distributions. The exception might be if these four hazards were among the only hazards in the deck that had playability requirements, and the player was just unlucky enough to draw all at once.

From this second example, I am inclined to separate out bad resource/hazard splits from bad distributions among plentiful cards of the player's first turn type. The "Turn Type Minimum" rule helps only with the former, but does so in, I think, a very fair way that only has limited ability for players to exploit through deck-construction choices (essentially just how many characters to include). So thinking only of turns wasted because of bad resource/hazard splits, which splits are reasonably unreasonable? My inclination is that only 0 or 1 cards of the type first played is definitely grounds for a likely wasted turn. Only 2 cards of the type first played is perhaps borderline; as long as the distribution of those two cards isn't bad, I think it is reasonable that you likely need not waste your first turn, even if the turn is not optimally employed. So conservatively, I'll stick to 2 for both resource and hazard players.
Turn Type Minimum 2 wrote: If you have less than 2 of the type of card that you are first playing as (hazard, or resource+character), you can reveal your hand distribution (doesn't need to be the cards by name), shuffle it into your deck, and draw a new hand.
Let's consider the statistics:
With a minimal characterless deck (33/30 resource+avatar/hazard split), the probability of starting with each of the following resource/hazard distributions are as follows (in parentheses are the probabilities if using max characters for a 43/30 resource/hazard split):
0/8: 0.00151 (0.000435)
1/7: 0.0173 (0.00651)
2/6: 0.0810 (0.0399)
3/5: 0.201 (0.131)
4/4: 0.290 (0.252)
5/3: 0.249 (0.291)
6/2: 0.124 (0.197)
7/1: 0.0331 (0.0719)
8/0: 0.00358 (0.0108)

As a rough generalization, if in a standard tournament the initial rounds have each player play 4 games, each player should expect between roughly a 1/4 and 1/3 chance that at some point during the tournament either they or their opponent will have a starting hand deemed "likely to be wasted" under this rule and eligible for this type of mulligan. I'm OK with the starting resource player expecting to be less eligible for this type of mulligan because they are getting the advantage from being first to seek MPs, and resource sides tend to have more potential for order requirements.

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Moving on to bad within-type distributions, I think it is beyond my scope to attempt to establish conditions under which hands from diverse deck strategies are imbalanced. Thus, my inclination would be to avoid another Qualifying Condition-based mulligans. As discussed above, in my opinion Hard Cutoff rules tend to be insufficiently effective or exploitable for certain deck constructions, so I will avoid them as well. This leaves Increasing Deficits, with the challenge of coming up with meaningful deficits.

I like the simplicity of MP penalties or bonuses for opponent, but because of the alternative The One Ring win conditions these are not always meaningful.

One major difference for MECCG (compared to other card games) is that card deficits are normally rectified after the first M/H phase, so this classic deficit example would not be very meaningful. Furthermore, in MECCG the resource player has some immediate control over deciding how quickly they will draw, albeit with some associated risks (by choosing sites to move to, and how many moving companies), so any draw-impacting deficit will need to consider that it could either advantage decks that move aggressively for more cards, or decks that squat, which starts interfering with mulligan criteria #3.

Longer hand size changes are also dangerous for criteria #3. Deck strategies with more interdependent cards tend to be impacted more heavily by hand size changes than those without; it is not my interest to support one end of this spectrum more than another.

Instead, what I've schemed up is a concept of "hand-locked cards". If number of cards in hand is taboo, I will instead focus on the USE of those cards. The idea is to designate certain cards in hand that are unusable by the controlling player for some number of turns. By unusable, I mean that they cannot be deliberately played or revealed/discarded, including for other card effects (Memories Recalled, Revealed to All Watchers, etc). Essentially, compared to just having a lower hand size, it allows the controlling player to know what cards will be usable in their hand when the deficit ends, while still "counting against them" for effects from their opponent (for example, Riddle Game).

The mechanics of these hand-locked cards I envision as follows:
* The number of locked cards is equal to the number of "discretionary" mulligans (not the earlier Turn Type Minimum mulligans), plus an extra for the first discretionary mulligan.
* The cards are placed into locked positions (visible to controlling player, not visible to opponents) at the start of the redraw; i.e. the player does not get to choose which cards are locked. The cards are considered in-hand for all purposes.
* Further mulligans will shuffle in any locked cards as well (in order to prevent subsequent mulligans from being motivated by fishing for cards that combo with the locked cards). Otherwise no effects by the controlling player can affect or benefit from locked cards.
* At the end of the Nth round (during the turn changeover after all players taking a turn), the next locked card becomes unlocked and part of the normal hand; i.e. the player does not get to choose which card to unlock.

So the effect of these discretionary mulligans is:
1: One round at a 6-card playable hand size with two more cards hand-locked, followed by one round at a 7-card playable hand size with one card hand-locked.
2: One round at 5, one round at 6, one round at 7.
3: One round at 4, one round at 5, one round at 6, one round at 7.
etc... Although the intent of these escalating penalties is to limit 99.9% of cases to two or fewer mulligans.

The penalties need to increase in initial hand effect (not just duration) to avoid getting to durations which players expect to be longer than the game length and so lack any meaningful penalty.

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Summary:
I think the combination of these two mulligans gives players adequate tools to avoid their worst bad luck cases resulting in wasted first turns while minimizing deck construction or play strategy impacts. I would also expect the number of mulligans per game to be less than one, minimizing delay impacts.
Turn Type Minimum 2 Mulligan wrote: If you have less than 2 of the type of card that you are first playing as (hazard, or resource+character), you can reveal your hand distribution (doesn't need to be the cards by name), shuffle it into your deck, and draw a new hand.
Discretionary Mulligan wrote: You may choose to take this mulligan, shuffling the cards in your hand into your deck and drawing a new hand. However, some number of cards in your hand are locked from you for some number of rounds.
* The number of locked cards is equal to the number of these mulligans, plus an extra for the first such mulligan.
* The cards are placed into locked positions (visible to controlling player, not visible to opponents) at the start of the redraw; i.e. the player does not get to choose which cards are locked. The cards are considered in-hand for all purposes.
* Further mulligans will shuffle in any locked cards as well (in order to prevent subsequent mulligans from being motivated by fishing for cards that combo with the locked cards). Otherwise no effects by the controlling player can affect or benefit from locked cards, including: play, revealing for benefit, choosing to discard.
* At the end of the Nth round (during the turn changeover after all players take a turn), your next locked card becomes unlocked and part of the normal hand; i.e. the player does not get to choose which card to unlock.
[edit: typo fix]
Last edited by Theo on Wed Jun 12, 2019 3:00 am, edited 1 time in total.
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CDavis7M
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Location: California

Re: Mulligan ponderings

Post by CDavis7M » Fri May 17, 2019 6:16 pm

Why Mulligan? It was chance that brought me that hand, if chance you call it.

DamienX207
Posts: 51
Joined: Thu Feb 09, 2017 6:53 pm

Re: Mulligan ponderings

Post by DamienX207 » Sat Jun 22, 2019 1:36 pm

Lol yes, Tolkien WAS a big fan of luck ...

But I really like this. My first thought was that less than 2 resources (i.e. 1 or 0) sounded like too few, but combined with the Discretionary option for *E.G.* getting stuck with 2 Escapes or some such, I think these complement each other well. Definitely better than the current CoE mulligan rule. Insert slow clap emoji from me!

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