Variance vs Strategy

[Crimhead]

How does the degree of variance in a game affect strategic depth?

There is a common bias against variance - the idea being that variance only serves to undermine strategy (the most carefully laid plans can fall apart with one bad "toss of the dice"). Others think that varinace can (sometimes) increase complication and actually enhance strategic depth. This is the position I plan to argue, and I would like to demonstrate it with two similar Magic cards:

VS

For the purpose of this discussion, we assume Therapy is being cast without knowledge of the opponents hand. Otherwise Therapy is just a strictly better Thoughtseize.

Most will agree Cabal Therapy is a more skill intensive card. With Thoughtseize the active player sees a handful of cards and must rank those cards via a threat assessment. With Therapy the player must assess the potential threat level of every relevant card the opponent might be holding, and weigh this against the probabilities (generally an estimate) that the opponent actually has that card. What's more the threat assessment itself is more complicated because the threat level of any given card is sometimes dependant on what other cards the opponent is holding - also a probability assessment.

But Cabal Therapy also introduces more variance than Thoughtseize. In fact it is because of this variance that Therapy is so much harder to play well! Sometimes playing around randomness and having to take risks in order to gain can actually add depth to strategic decision making. And Therapy is no exception. The above process is par for the course in decision theory problems.
https://en.m.wikipedia.org/wiki/Decision_theory

More thoughts:

Some would argue that Thoughtseize facilitates strategy more than Therapy does, as a good player is more likely to get a favourable outcome. I have two responses to this:

1. This isn't a fair comparison - Thoughtseize is (generally) a more powerful card, especially compared to blind casting Therapy (which is the comparison in question, otherwise Therapy does not bring variance or extra demand for skill). A better comparison is how these cards fare in the hands of players of various skill. Most competent players will Thoughtseize properly most of the time. A good player will usually chose the same card as a great player (when they don't, it will mostly be a borderline case where neither card is very much better than the other). With Therapy, there are a lot more variables and naming the right card is much harder for a merely good player.
   
   In other words, Thoughtseize will separate the good players from the bad players; while Therapy seperates good players from great players.
   
2. my second objection is that the extent to which a game rewards skilled play is not a true measure of strategic depth. The real test is how difficult it is to play optimally. Tic-tac-toe absolutely rewards skilled play! If you play that game correctly you will never lose and will beat all but the toughest opponents. But that doesn't give it depth! Depth comes from difficulty in determining the best line of play. Whether that line of play might randomly back-fire doesn't take anything away from the skill required to determine that line of play. It just means you don't always get credit for your brilliance.
   
   Imagine we play chess, but we add a rule that after a checkmate we roll a die and on a '6' the mated player is the winner. This addition of variance reduces the impact of skill in terms of the outcome, but it doesn't make the game any less deep. The skill set needed to play well is identical to that of regular chess. All the same strategic decisions still apply.

Obviously I'm saying variance necessarily adds depth! But it certainly can add depth by making optimal plays more elusive and harder to see.

[Echelon]

So... What do you hope to accomplish here..?

[Crimhead]

So... What do you hope to accomplish here..?

To generate discussion and/or debunk a myth. Also to move a conversation that was derailing another thread.
What does your comment hope to accomplish?

[Echelon]

To generate discussion and/or debunk a myth. Also to move a conversation that was derailing another thread.
What does your comment hope to accomplish?

To provide some insight on why one would feel the need to start this topic.

Mission accomplished.

[Crimhead]

I've had this debate a number of times in a number of contexts (usually comparing Chess to Bridge). I feel strongly that randomness (can) force us to consider more contingencies, and causes unique dilemmas. And I feel a lot of gamers are dismissive or oblivious to the depth this provides.

What motivated me to post was the recent revelation that Cabal Therapy was the perfect example of depth inducing variance. It's hard to compare Chess and Bridge because they're apples and oranges. But Therapy and Thoughtseize provide a more clear contrast.

[Lemnear]

If your matter is to wage variance (aka Splitting up playsets of cards into several similar ones but with more application) versus the strategic Depths the mentioned wider application brings, the examples are poorly Chosen.

Thoughtseize is a strategic card where you simply choose the most harmful card aka make quality picks, while Therapy is exclusively played for a) it's mind twist potential and/or b) if damage matters and/or c) if it's paired with other peek-effects.

You are talking about blind-naming with Therapy as a matter of gambling for a potentially bigger benefit, missing that failing to discard a card from your opponent usually is A GOOD SIGN and/or has strategic reasons (flashbacking or gaining knowledge of opposing playlines). You NEVER cast Therapy for quality tradeoffs like you would with Thoughtseize. Therefore I think the completely different strategic approach of both cards does not work out to mention both in the asumed context

I would gladly take feedback if I mistook you here, as the topic of Cabal Therapy is basically my Bread & Butter :)

[Crimhead]

You NEVER cast Therapy for quality tradeoffs like you would with Thoughtseize. Therefore I think the completely different strategic approach of both cards does not work out to mention both in the asumed context.

I've played the card mostly in Manaless Dredge and Elves. If Cabal Therapy hadn't been printed Elves most likely would be using Thoughtseize instead. And for the same purpose - to eliminate threatening cards from the opponent's hand that they cannot otherwise deal with.

Manaless Dredge mostly plays the card to get Zombies - but it also severs to protect your graveyard and/or stop a faster combo deck. Either way, once you've cast it and are faced with a choice, your objective is pretty much the same as it would be if the text read like Thoughtseize.

You are talking about blind-naming with Therapy as a matter of gambling for a potentially bigger benefit, missing that failing to discard a card from your opponent usually is A GOOD SIGN and/or has strategic reasons (flashbacking or gaining knowledge of opposing playlines).

Them not having the card is rarely better than them having it. If it has value in their yard I guess it's better they didn't have it in the first place rather than you make them discard it. The flip-side is that if they don't have it you just 1-for-0'd yourself (in other words, they have something else instead of the named card, and that might also be a problem card).

Yeah, if there is only one card your opponent can have to shut you down, there is no variance - you cast your discard spell and the coast will be clear. But if you name Relic of Progenitus and they show you a hand with Tormod's Crypt, it's a different story. Same thing if you name Chalice and see a Thorn. These are cards where Thoughtseize is easier to play correctly but more consistently rewards correct play. I don't see how this is not valid.

[rufus]

How does the degree of variance in a game affect strategic depth?

There is a common bias against variance - the idea being that variance only serves to undermine strategy (the most carefully laid plans can fall apart with one bad "toss of the dice"). Others think that varinace can (sometimes) increase complication and actually enhance strategic depth. This is the position I plan to argue, and I would like to demonstrate it with two similar Magic cards:

...

Variance is largely independent of complexity. There are high variance low complexity cards like Game of Chaos and high variance high complexity cards like Time Spiral.

Because of the zero-sum nature of Magic, strategic domination will automatically reduce variance - a 90-10 match-up is clearly a low variance affair. That means that there's an intrinsic anti-variance bias in the drive to win. So competitive decks that use a card like Cabal Therapy will be ones that have methods to mitigate the variance in the impact of the card.

[iamajellydonut]

What is this thread? Is it an April Fools or actually one of the most inane lectures to ever grace these forums?

[iatee]

Yeah, there's a reason why Jund plays Thoughtseize and not Cabal Therapy, and it's not because Jund players are worse. Jund can't afford to lose the value, whereas Pyro decks or pure combo decks have insurance policies (a. second Therapy b. you're just dead.)

If you're Storm, opponent has Chalice and Thorn in their deck and you Therapy them on the play, you name Chalice because Eldrazi decks dependably play 4 Chalice and don't dependably play 4 Thorn. If they eventually evolve into 4 Thorn builds, you name Chalice because it still wrecks you more. If they have Thorn, you didn't play poorly, you got unlucky. These have all been terrible examples to use for the Cabal Therapy because you're confusing getting unlucky with making the wrong decision.

The interesting and strategically deep Cabal Therapies are not when you have no information - in those cases the correct decision is often pretty straightforward. You're playing with a fair deck and you want to t1 Therapy them on the play? Name the most popular card in the format. You're playing a combo deck and you want to t1 Therapy - name the card that stops your combo.

Difficult Therapies happen when you have imperfect information (you know some of their hand but not all of it) or they Brainstorm in response. But especially in the Pyro/Probe era, the card probably doesn't deserve its reputation. Trying to read their hand and playing accordingly is something every deck does to some degree.

[Dice_Box]

What is this thread? Is it an April Fools or actually one of the most inane lectures to ever grace these forums?

It's birth comes from debate on Eldrazi. The topic is different though so there is no reason to stop conversation.

[Crimhead]

These have all been terrible examples to use for the Cabal Therapy because you're confusing getting unlucky with making the wrong decision.

Not at all. It was exactly my point that you could make the right play and get unlucky. I was responding to Lemnear who seemed to be rejectingvthe idea that playing Therapy introduces variance.

Yeah, there's a reason why Jund plays Thoughtseize and not Cabal Therapy, and it's not because Jund players are worse. Jund can't afford to lose the value, whereas Pyro decks or pure combo decks have insurance policies (a. second Therapy b. you're just dead.)

This is it exactly. Therapy on its own rewards skill less-so than Thoughtseize (hense Jund running the latter) despite Therapy being the more strategically demanding card to play well (on its own).
Hence strategic depth =/= a higher success rate for the more skilled player.

[iatee]

It's very rarely a more strategically demanding card, it just looks like it is.

[Richard Cheese]

Here's a pretty good article on luck vs. skill in gaming, and why some of the best games are a combination of both:

http://gamedevelopment.tutsplus.com/...k--gamedev-322

TL;DR - Something entirely luck-based like Snakes and Ladders doesn't hold the attention of players very long because there's not really any way to ever improve at the game. On the other hand, games that are almost completely skill-based like Chess or Go are fairly hostile to new players, to the point that a ranking system is practically a requirement.

Combining luck and skill can capture the best of both worlds - accessible to new players because they don't need to find the "right" opponents, but with an element of mastery to make it worth the investment of time and effort.

Another interesting point he makes is that randomization doesn't necessarily equal luck. It depends on frequency and level of impact. From the article:

Tetris is a perfect example of this: the whole game may seem luck-based, but because the player may be required to deal with hundreds of these random shapes throughout a playthrough, the game becomes skill-based.

Based on the last thread, it seems to me that some feel that meta gaming should not have an element of luck to it. It is fine for the format to have one or more decks that are 50% against the field, making them a 'safe' choice for any sizable event, or that even having a clear best deck is not a problem. Personally I disagree. I think the game is more fun when there's an element of luck outside just the cards you draw in a given game. I prefer a more rock-paper-scissors element of balance to the format, even if it means a random string of bad matchups could ruin my chances in a tournament. To me, the fewer viable decks in the format, and the more a clear leader emerges, the less the game rewards time spent considering card choices and trying to be innovative. When there is a clearly dominant deck with no truly bad matchups, that time is much better spent practicing with a list that's already proven.

I think that whether a given matchup is fun/interactive/skillful or not is a moot point, because it's entirely subjective and depends on which player's point of view you're taking. It also dismisses all the choices that were made (or could have been) before the game even started that could have affected the outcome. It does a disservice to a huge and important aspect of the game.

[Bobmans]

There are 3 differences for me that make Cabal Therapy superior to Thoughtseize.

1. The most precious resource in this game: life points.

2. Have you ever cast a Thoughtseize and see Two, 2 of the same freaking card? Well, some mind tricks with Therapy will snag them all.

3. Cabal Therapy gets a recast, hence flashback. In the right deck, this will break the symmetry on a very consistent level. Namely: Goblins, Elves, NicFit, Young Pyrodude, Lingering Souls and Monastery Mentor just to name a few.

All in all, Thoughtseize (nearly) always hits something, but Cabal Therapy has a high risk high reward. It requires not skill, but knowledge of the format and some recalculation on probability of what your opponent is doing and what he might be up to. It forces you to think about what your doing, what will affect your progress or what might disrupt it.

However, since the broad application (and flexibility) of Thoughtseize i mostly bring some in my board. I understand why Jund (for example) is not playing Therapy. Their creatures (with a random exception of Dark Confidant) are very precious.

[iamajellydonut]

1. The most precious resource in this game: life points.

Are we sure this isn't an April Fools' thread?

[Finn]

Right, Jelly. I wasn't going to say anything. But Bobmans, I think that in Legacy we are accustomed to throwing life away will-nilly. Also, I am not sure you meant it this way, but I don't think you can say that either of these cards are strictly superior. Finally, I hate putting Thoughtseize into my decks if I have blue. I want to use Gitaxian Probe to turbo boost my Therapies whenever possible. Snapcaster and Strix make this an even more attractive strategy. I consider using Thoughtseize as a failure on my part to be more creative.

[Bobmans]

Are we sure this isn't an April Fools' thread?

I didn't see a sarcasm sign.

[Lemnear]

I've played the card mostly in Manaless Dredge and Elves. If Cabal Therapy hadn't been printed Elves most likely would be using Thoughtseize instead. And for the same purpose - to eliminate threatening cards from the opponent's hand that they cannot otherwise deal with.

Manaless Dredge mostly plays the card to get Zombies - but it also severs to protect your graveyard and/or stop a faster combo deck. Either way, once you've cast it and are faced with a choice, your objective is pretty much the same as it would be if the text read like Thoughtseize.

You use discard in Elves to delay combo decks as the deck is already boss on the battlefield and stuff like Tarmogoyf aka Threats do not bother you much with Symbiote available. We hopefully do not need to talk about Therapys flashback to shred your opponent for the expense of a random manadork for example. Dredge & Elves are not different in their use of Therapy, but if Elves would be interrested in the classic value picking of "threats" they would play thoughtseize main and not in the sideboard as combo-hate. For dredge its mainly a tool to trigger Bridge from below and the discard is a secondary effect to aim at anything which might delays your opponent which I suspect being the reason why most Dredge players I faced simply name the first thing that comes into their mind without a second thought in game 1s

Them not having the card is rarely better than them having it. If it has value in their yard I guess it's better they didn't have it in the first place rather than you make them discard it. The flip-side is that if they don't have it you just 1-for-0'd yourself (in other words, they have something else instead of the named card, and that might also be a problem card).

How many Hardcounters in Legacy are played in maindecks beside FoW, Storm (for example) has to care about? That knowledge is the critical part of playing Therapy in the first place. Whats the deal with 1-for-0'ing if you win as a result? People make disadvantageous trades via FoW for close to two decades and I never heared the argument "what if your opponent has another spell you might want to counter?"

Yeah, if there is only one card your opponent can have to shut you down, there is no variance - you cast your discard spell and the coast will be clear. But if you name Relic of Progenitus and they show you a hand with Tormod's Crypt, it's a different story. Same thing if you name Chalice and see a Thorn. These are cards where Thoughtseize is easier to play correctly but more consistently rewards correct play. I don't see how this is not valid.

Its as valid as crafting a scenario of having Probe + Thoughseize versus two Delvers in opponents hand or casting a blind Thoughtseize just to see you are facing Burn.dec.

If you opt to ignore the opportunity cost of the 2 lifepoints of Thoughtseize and potential cardadvantage of Therapy and its flashback, I don't know if comparing the cards makes any sense at all. Its like we stick to the Thorn/Chalice topic and argue Thoughtseize versus Duress and act as if the non-creature clause doesn't matter at all, claiming that Thoughtseize is bad.

[iatee]

Based on the last thread, it seems to me that some feel that meta gaming should not have an element of luck to it. It is fine for the format to have one or more decks that are 50% against the field, making them a 'safe' choice for any sizable event, or that even having a clear best deck is not a problem. Personally I disagree. I think the game is more fun when there's an element of luck outside just the cards you draw in a given game. I prefer a more rock-paper-scissors element of balance to the format, even if it means a random string of bad matchups could ruin my chances in a tournament. To me, the fewer viable decks in the format, and the more a clear leader emerges, the less the game rewards time spent considering card choices and trying to be innovative. When there is a clearly dominant deck with no truly bad matchups, that time is much better spent practicing with a list that's already proven.

I think that whether a given matchup is fun/interactive/skillful or not is a moot point, because it's entirely subjective and depends on which player's point of view you're taking. It also dismisses all the choices that were made (or could have been) before the game even started that could have affected the outcome. It does a disservice to a huge and important aspect of the game.

Again, it's not whether there should be *no* luck to the metagame vs. playing rock-paper-scissors w/ cards with dragons on them.

Things go in one direction or another, lately things are going more in the direction of rock-paper-scissors magic. People who enjoy legacy precisely because of the depth of gameplay shouldn't be expected to be thrilled about it. Modern and vintage already provide these kind of environments.

People who like legacy because they love to brew with a wide card pool might be better off in a high variance format, but let's not pretend like nothing is being lost in this transition.