Strength VS Inconsistency

[tsabo_tavoc]

I am not sure if the topic has been discussed in other threads, some wild ideas came to me and they looked as:

1. Leave aside card interactions, compare Lightning Bolt with:
R Instant Flip a coin. If you win the flip, [Card Name] deals 3 damages to target creature or player and another 3 damges to target creature or player.

2. To what extent does lightning bolt inferior/superior to:
R Instant Roll a six-faced dice. If you win the roll, you win the game.
Again, ignore the effects that modify the flipping/rolling.

Move on, for the sake of amusement.

[Skeggi]

The first card isn't as good because it gives a narrow effect for alot of uncertainty. The latter card, assuming you win on a 6, is so broken, people would build decks around it, copying the card, putting it on a stick, whatever.

It's hard to see what you're trying to say. A card like Mana Crypt is very good, because there is a chance of you getting damage, but it will always do what it's supposed to do: deliver mana. And that may be the future of coin flipping and dice rolling cards; they always should do what they're supposed to do, but they may have a drawback. That should be the minimum consistency of a card I think.

[Maveric78f]

1. Assuming the card can do the same thing as 2 lightning bolts with 50% probability and nothing with the remaining 50% probability. Both cards have the same expected value. That's the reason why you may think that they have theoretically the same power level. However, they don't have the same standard deviation. The unpredictability of the effect you play (i.e. the standard deviation) is a huge weakness, since you cannot build your strategy reliably.
2. This card would possibly be good as a wish target when you are in a desperate situation. Apart from that, it looks quite poor, since after playing 4 of them (so the playset you are allowed to play), you have only 52% chance to win the game. Imprinting it on a scepter looks weaker than imprinting chant or even counterspell imo.

Would the following card be good?
Random Vindicate %0
instant
Target a permanent or a spell.
Roll a six-faced dice.
1: if this is a land, destroy it and draw a card.
2: if this is a creature, destroy it and draw a card.
3: if this is an enchantment, destroy it and draw a card.
4: if this is an artifact, destroy it and draw a card.
5: if this is a planeswalker, destroy it and draw a card.
6: if this is a spell, destroy it and draw a card.

I think it would not be good elsewhere than in an Ad Nauseam combo deck.

[ykpon]

btw such cards already exist: Mana Clash, Fiery Gambit, Stitch in Time. they all have a very powerful effect but don't see play at all (ok, i've tested Mana Clash in legacy burn, but who cares ).

[DrJones]

Mana Clash is red's answer to Storm Combo because it doubles the chances of a red deck being able to kill the opponent before he goes off.

[Nihil Credo]

Benefits are not always obvious to evaluate. Let's say you can play a lottery game where you bet 1000€ for a 1% chance of winning 200000€. Damn good deal, right? Not quite.

What do those 1000€ you often lose mean to you? If they were going to just stay in your bank account otherwise, then you would probably do well to take the bet. If you needed them to buy a new car three months sooner than otherwise, then losing them is already pretty rougher than it looks. And if they're all that stands between you and death by starvation (because you live in Ronpaulitania or something), then you aren't going to take the bet no matter how high the prize gets, because while you may end up owning on average some fantastic sum, you'll also on average become a Schrödinger's cat with terminal cancer.

In other words, you have to look at the outcomes. In this case, the difference in quality of life between YourBankAccountBalance and YBAB+199000€ may be bigger, comparable, or smaller than the one between YBAB and YBAB-1000€ depending on the value of YBAB.

In Magic, what matters is winning. Where is the line between a victory and a loss more likely to lie: between drawing a blank and drawing a Bolt, or between drawing a Bolt and drawing a Doublebolt? At the moment, I think the answer is still the former. But if, for example, Tarmogoyf keeps becoming more and more common, along with other creatures able to take him on, then we might very well end up with 3 damage not being that much better than zero. Of course, long before we get there any burn spell will have become unplayable anyway.

[Kuma]

From the Wizards is ruining Magic thread:

Everything I've read in this thread confirms my belief that virtually all Magic players, even a lot of good ones, don't know how to take mulligans. Whether or not your opponent mulligans should have zero bearing on whether or not you do. The purpose of a mulligan is to give yourself the strongest hand possible. If an average six card hand is stronger than your seven, you take the mulligan; it doesn't matter if your opponent is holding seven cards or zero. For all this fear of mulling into oblivion, it doesn't happen enough to worry about.

Benefits are not always obvious to evaluate. Let's say you can play a lottery game where you bet 1000€ for a 1% chance of winning 200000€. Damn good deal, right? Not quite. What do those 1000€ you often lose mean to you? If they were going to just stay in your bank account otherwise, then you would probably do well to take the bet. If you needed them to buy a new car three months sooner than otherwise, then losing them is already pretty rougher than it looks.

If that deal was presented to me, I'd borrow as much money as I could and would play it indefinitely, assuming I had enough resources to play it until my winnings approached my expected winnings. I'd double my money in no time. The above situation assumes you only get to buy a limited number of lottery tickets. While that may be a fair comparison in the context of a single Magic game, it doesn't paint an accurate picture of a Magic tournament or even one's Magic career. The problem is if you always play for a single Magic game, you'll lose more games overall than if you play to maximize your wins over a longer period of time, say forever as in the Law of Large Numbers.

What do your opponent's mulligans tell you? Nothing other than they didn't like their previous hands and that they found some combination of cards they could live with. Just because someone mulled to four doesn't mean they're playing Ichorid. And even if it did, that doesn't mean their hand is bad. Their hand could be Lion's Eye Diamond, Deep Analysis, and two Golgari Grave Trolls. You can't assume your opponent has a bad hand just because they're holding less cards than you. All you can know for sure is what your hand contains and if you can, on average or in the context of the matchup, make it better by taking a mulligan.

I think the better comparison is Deal or No Deal. If everyone played the game to maximize the expected value of their winnings (play until the banker offered them money equal or greater than the average value of the remaining cases), the studio would pay out a lot more money. The reason people take unfavorable deals is because they only get one shot at the game. And I don't blame them --- I'd do the same thing. No one wants to walk away with $.50 after being offered $100,000. However, If say I got to play the game two or more times, I'd take a lot more risks the first time(s) out. Because if I screw up, I'll have other opportunities to make good money.

I'm not saying it's always possible to know if an average six card hand is better than any given seven, but that needs to be the thought process when taking mulligans.

In other words, you have to look at the outcomes. In this case, the difference in quality of life between YourBankAccountBalance and YBAB+199000€ may be bigger, comparable, or smaller than the one between YBAB and YBAB-1000€ depending on the value of YBAB.

I haven't said anything to the contrary. I just said it differently.

[Nihil Credo]

You wrote nothing that I disagree with except for the following:

You can't assume your opponent has a bad hand just because they're holding less cards than you. All you can know for sure is what your hand contains and if you can, on average or in the context of the matchup, make it better by taking a mulligan.

"Small hand" does not strictly imply "bad hand", sure. But a small hand is MUCH less likely to have the nuts than a full hand, which can definitely impact your choices.

Here's a practical example: you are playing Merfolk against Goblins in game three, on the draw, and your opener is Island, BEB, Mind Harness, 3x Lord of Atlantis, Force of Will. If you get an Island or a Vial in your next 2-3 draw steps this hand is bonkers and quite likely to win the game; if not, your opponent is going to punch through your defences while your board remains empty. Given that Goblins is a very bad matchup for you, you'd rather take those odds than bet on winning from a six-carder.
But, wait! Your opponent has mulliganed to four! What does it mean? Well, your hand is still as good (and as swingy) as before, but now an unknown six-carder has a much higher chance of pulling it off. It's not guaranteed (this is Legacy, so any viable deck can still topdeck the nuts), but a mulligan now is probably a safer bet than putting your odds on having mana on the top of your deck.

For a reverse example, let's say the matchup is Eva Green vs. Ichorid. Your first seven are: fetchland, Bayou, Ritual, Ritual, Tombstalker, Sinkhole, Tarmogoyf. That hand's got a crazy amount of pressure, but zero hate: all Ichorid needs to beat it is a turn 1 discard outlet and some OK dredges, particularly since it's on the play. Mulligan time? Well, Ichorid has just mulliganed to four. It could still have land, LED, Breakthrough discarding Troll into a turn 1 win, but it's much less likely to happen with four cards than with seven. The chance of beating them with a turn 4 clock plus a Sinkhole just went way up, and the odds of keeping have significantly improved.

(Note: obviously, some decks mulligan better than others. Ichorid and Ad Nauseam can still do nutty thing at 4 cards, while a 4-carder from Tempo Thresh is rarely a huge threat unless you open yourself up to two pieces of early LD.)

[MattH]

A lot of what Nihil is saying can be found in this (now free) Chapin article:

http://www.starcitygames.com/magic/f...verything.html

[Kuma]

Here's a practical example: you are playing Merfolk against Goblins in game three, on the draw, and your opener is Island, BEB, Mind Harness, 3x Lord of Atlantis, Force of Will. If you get an Island or a Vial in your next 2-3 draw steps this hand is bonkers and quite likely to win the game; if not, your opponent is going to punch through your defences while your board remains empty. Given that Goblins is a very bad matchup for you, you'd rather take those odds than bet on winning from a six-carder.

I'm not an expert with Merfolk, but I'd probably keep that hand against Goblins regardless of how many cards they kept. You can BEB Lackey and FoW Aether Vial. Merfolk runs around 13-14 Islands, so you've got about a 1 in 4.5 chance of hitting an Island every draw step. You have at least two draw steps before not having a second Island becomes an issue, and since you also have Mind Harness, which is at worst a Fog, probably even more time to hit that Island. That hand is almost certainly better against any Goblin hand than an average six.

But, wait! Your opponent has mulliganed to four! What does it mean? Well, your hand is still as good (and as swingy) as before, but now an unknown six-carder has a much higher chance of pulling it off. It's not guaranteed (this is Legacy, so any viable deck can still topdeck the nuts), but a mulligan now is probably a safer bet than putting your odds on having mana on the top of your deck.

I get what you're trying to say: "You don't have to take as many risks when your opponent mulls into oblivion," right? This is true, but I think it's the wrong thought process. The question is still whether or not the risk/reward of you keeping your "needs X card" hand are lesser than the risk/reward associated with a random six from your deck.

Also, you have a lot more chances to hit mana, since they're not likely to bring the pain, especially considering the amount of disruption you have. I think mulling in those situations is a bad idea.

For a reverse example, let's say the matchup is Eva Green vs. Ichorid. Your first seven are: fetchland, Bayou, Ritual, Ritual, Tombstalker, Sinkhole, Tarmogoyf. That hand's got a crazy amount of pressure, but zero hate: all Ichorid needs to beat it is a turn 1 discard outlet and some OK dredges, particularly since it's on the play. Mulligan time? Well, Ichorid has just mulliganed to four. It could still have land, LED, Breakthrough discarding Troll into a turn 1 win, but it's much less likely to happen with four cards than with seven. The chance of beating them with a turn 4 clock plus a Sinkhole just went way up, and the odds of keeping have significantly improved.

This is a better example, but I'm still probably keeping that hand on the play against Ichorid if they don't mulligan. There's a good chance they kept a slower but more stable hand because they figured I'm gripping hate. Besides, in my experience, it almost always takes more than one piece of hate to stop Ichorid. And Ichorid rarely combos out turns 1-2, there's just too many things that can go wrong. The decision certainly becomes easier if they mull to four, but mulling into hate with no clock likely won't beat smart Ichorid players.

"Small hand" does not strictly imply "bad hand", sure. But a small hand is MUCH less likely to have the nuts than a full hand, which can definitely impact your choices.

I'm not so sure it impacts my choices as much as it makes them less relevant.

[Nihil Credo]

I'll skip the discussions about the two examples I made; I was only interested in coming up with hands with respectively high and low performance variance. Tweak them as you feel necessary to that end.

I get what you're trying to say: "You don't have to take as many risks when your opponent mulls into oblivion," right? This is true, but I think it's the wrong thought process. The question is still whether or not the risk/reward of you keeping your "needs X card" hand are lesser than the risk/reward associated with a random six from your deck.

What you seem to miss is that your deck is not a binary machine, that either works or not. It can have a god-hand, a decent performance, or it can crap out. And the payoff of your hand quality does depend on your opponent's performance (of which his hand size is a pretty good indicator).

What your opponent's performance does is set what level of performance is required from you to win the game.

If you're staring down a full hand and/or a bad matchup, you need a god hand to win. The difference between an average hand and a shit hand is minimal, as you'll probably lose with both.

If you're staring down a mull to 3 and/or a good matchup, the opposite happens. Here, a decent hand and a god hand will translate into a win with very similar percentages.

(The next example is massively over-simplified, but that simplification in no way hurts my general point - that the opponent's mulligans can affect your mulligan choices)

Let's say you have a hand with a 50% chance of being great and 50% of being shitty, depending on your next couple of draws. You need to pick between that and a mulligan, which can provide a full range of outcomes - let's categorize them as 20% great, 50% average, 30% bad.

Against a full hand and/or a bad matchup, your first hand is a 50% win and a mulligan is just 20%, so you keep. Against a small hand and/or a good matchup, your first hand is still a 50% win, but a mulligan is now 70% likely to win you the game, so you mulligan. QED.