Article - Ponder vs. Preordain

[Maqi]

Hello fellows!

In my last article I said I would write about the manabases of Esper Artifact Control and the Scapeshift deck respectively. Since then some time has passed and my interests moved on to other fields.
If somebody is really interested in this topic, please tell me. I will then keep my promise and elaborate my thoughts on these decks.

Today however, I have a different thing in mind that I want to share.

A friend of mine (hitman) and me had a discussion about Ponder and Preordain lately. The discussion was mainly about the question of how much better Ponder was than Preordain. I felt that it is better, but not by a wide margin (I therefore almost always play both, if I want an effect like this).

His opinion was that Ponder is way better than Preordain and that he actively dislikes Preordain (and therefore most of the time doesn't run it even though he may run Ponder).

We pondered for while (pun intended) and came to the conclusion that Ponder is in most cases clearly better. After our discussion I continued thinking about this for a while and found the results quite interesting. Therefore I decided I'll share my thoughts with you here.

To gauge the relative quality of Ponder vs. Preordain we have to take a look at the different scenarios that determine the outcome of the respective cantrips. I'm working with a simplified model here because it is impossible to take a gazillion of possible game states into the equation. I therefore set, that the outcome of Ponder / Preordain is mainly determined by the top 3 cards of your deck.

(I will however take into account some typical possibilities that a player might usually have at his disposal when it comes to decide which cantrip wins a specific scenario that is not so clear cut.)

Those "top of the library cards" can be ones that you (1.) actively want to draw, (2.) that you actively don't want to draw and/or (3.) cards that you are indifferent to draw. During my further explanations I will call these "good", "bad" and "indifferent" cards. (I won't go deeper than this and will ignore finer nuances in card value for the sake of simplicity).

In addition I will use a point system to measure the net gain of each cantrip in any given scenario, so that the outcomes are more easily compared to each other. A good card nets you 1 point, a bad card equals -1 point while an indifferent card has a point value of 0.

There are essentially seven different scenarios of how your top 3 cards can be arranged:

I
good / good / good
Ponder: There's no incentive to shuffle. You will get 1 point now and 2 points more with your next two card draws. Total: 3 points.
Preordain: Exactly the same result as Ponder.
Conclusion: Draw.

Ponder 0:0 Preordain

II
good / good / bad
Ponder: You will most likely draw one of the cards you want (1 point). The next draw step will net you another 1 point. The next one will net you -1 point. Result = 1 point.
Preordain: You will opt to not scry. After all three draws you will also have 1 point.
Conclusion: Ponder is slightly better here, since it provides you with more knowledge because you know which card rests in third place and you might be able to shuffle it away with a fetchland or something along those lines. With Preordain you just don't know what the third card is and have no clue if shuffling will do you any good.

Ponder 1:0 Preordain

III
good / bad / good and bad / good / good
Ponder: You will most likely rearrange both good cards on the top. After 3 draws you will have a net gain of 1 point.
Preordain: You will put the bad card on the bottom of your library. After 3 draws you will have a net gain of 2 points plus the expected value of the unknown third card.
Conclusion: Preordain wins because the expected value* of the unknown card is greater than -1.

* A statistical indicator that measures the average value of a given unknown event based on the probability distribution of the population (of events).

Ponder 1:1 Preordain

IV
good / bad / bad and bad / good / bad
Ponder: You will most likely shuffle. Your expected gain is determined by the unknown card plus two additional drawn unknown cards the turns after that.
Preordain: You will put the bad card on bottom, then draw a 1 point card, then a –1 point card. Net value = 0. Your third draw is unknown.
Conclusion: Both cantrips give you the option of taking the good card on the spot. Should you have a shuffle effect for the bad cards, you will most likely use it in the case of Ponder. Ponder has the advantage of giving you more insight (as usual). However, if you have no shuffle effect at your disposal, you will almost always be forced to shuffle the 3 cards in the first place and move into top deck mode. If this is better than Preordain's option of "1 good / 1 bad card" may vary from situation to situation. I consider this case a draw.

Ponder 1:1 Preordain

V
bad / bad / good
Ponder: You will most surely shuffle. Expected gain from your next three draws is unknown for each (and solely determined by the distribution of the cards in your library). This equals approximately 0 points.
Preordain: You will put two on bottom. And draw the good card. This equals 1 point.
Conclusion: Preordain wins because of its ability to keep a card and shuffle nevertheless.

Ponder 1:2 Preordain

VI
bad / bad / bad
Ponder: Since you don't want any of these cards, you will shuffle. Your next draw has an expected value depending on the total amount of cards of each category left in your library.
Preordain: You'll put away the first two, then draw -1 points.
Conclusion: Ponder wins.

Ponder 2:2 Preordain

VII
indifferent / indifferent / indifferent
Ponder: You will get 0 points. Expected value for the blindly drawn card (if you so choose) depends on the total amount of cards of each category left in your library.
Preordain: You will get 0 points.
Conclusion: Ponder gets the nod here because it allows for the option of aiming for more than 0 points card quality value. Even though the option is a risky one since you are not guaranteed to draw better than "indifferent".

Ponder 3:2 Preordain

You have to take into account that scenario III (which Preordain wins) weighs double, because it covers two possible distribution patterns. (As does scenario IV, but that's a draw). Therefore we should update our results:

Ponder 3:3 Preordain

Wow! I had not thought that Preordain is so close to Ponder!

One might argue that Scenario V (which again Preordain wins) is not as likely as, say, Scenario II because your deck likely consists of more cards that you want to draw than cards which you don't want to draw (although that may differ quite a bit form deck archetype to deck archetype. Just compare RDW to Ramp or Oath decks, which rely more heavily on (not) drawing specific cards at certain times in the game).

If you look at the cases where Preordain wins (III and V) you'll see that it does so because of its ability to keep a good card and shuffle the other's away.

Ponder on the other hand only gives you the option of drawing or shuffling.

That being said, one must keep in mind that other factors also matter, which are not represented in the above simplified model. Every fetchland or other shuffle effect you might have, clearly let's Ponder be the much better "digging" cantrip because you can circumvent its liability of having to keep bad cards on the top of your deck sometimes.

Then again, with Preordain you might not have needed this shuffle effect in the first place and could have saved it for another time...

A bold statement (after taking all the above into consideration) might be that Preordain is actually better than Ponder in decks that consist of many "bad" cards, which you only want to draw at specific times and/or is light on shuffle effects.

What do you think? Is there any flaw in my reasoning?

I hope I did not bore you with things you already knew all along. Please discuss! I'm very interested in your thoughts.

[ChristophO]

While I apreciate the effort your argumentation is flawed because you neglect common szenarios. To compare the cards you would have to take the following situations regarding shuffle effects into account (Most common being fetchlands ofc), before talking about "good-bad-indfifferent". The evaluation of Situation IV, for example, is pointless without talking about avaiable shuffles.

First, you would really have to talk about the following szenarios:

• Shuffle avaiable on the same turn
• Suffle on the next turn
• no Shuffle avaiable

And in addition to that there is a second important axis:

• Are indifferent cards left in deck?

If you redo your 7 situations, you will come to the following conclusions:
1: Without a shuffle effect Ponder is inferior to Preordain.
2: With a shuffle effect Ponder is more powerful
3: Preordain is better at digging out of a screw (since being screwed means no fetchland most likely)
4: Both cards are great at fixing your draws

[Maqi]

Thanks for your reply, Christoph.

I acknowledge that a model like the above might be too simple to really reflect the respective values of Ponder vs. Preordain.

The "indifferent" category is a tricky one. It might be, that there actually isn't such a thing as "indifferent". You either want a card, or don't.
Maybe that's the reason I somehow (subconsciously) omitted scenarios like "indifferent / good / indifferent".

Nevertheless I think the conclusions I draw in my article are quite similar to yours.

However your point #1 is invalid as is clearly shown in scenario VI. In the case of 3 bad topdecks Ponder is better than Preordain even without a shuffle effect.

I totally agree on your points #2 and #4.

Regarding #3: I'm not sure if this is correct. Someone can do the math?

[MMD]

Much ado about nothing.  I would keep things simple according to my experiences and current deck designs:  Preordain and Ponder are must plays in every blue based deck. Period.

Both have their strengths & weaknesses but they have a very similar power level and when both are must plays it is IMO not necessary to find out which one is stronger.

I would even run Ponder in a Mono Blue deck without fetchlands as you sometimes need to fix your very next draw and you already miss some first turn spells. I play a lot of Midrange/Control and personally prefer Preordain as it is stronger on the opener. But there are a lot of (mentioned) scenario's where Ponder is better.

Simply run both, especially if you do not have enough spells in your deck to enable you a reliable first turn play which is the case for every blue based deck I have built so far.

[Maqi]

Much ado about nothing. I would keep things simple according to my experiences and current deck designs:  Preordain and Ponder are must plays in every blue based deck. Period.

You might very well be right, MMD.

[Madsam]

Hmm sorry but your "experiment" doesn't work

I have redone this and added Serum Visions, although I split all combined experiments (III and IV) to evaluate the must draw in serum visions correctly, aaaand guess what? It's 3/3/3 Pon/Pre/SV.

Now one can argue that no one plays SV although it achieves the same value as the other cards did.

You could also consider Portent, which does the same as Ponder, draws the card later, but has the possibility to manipulate the opponents draws, what I think is really strong lategame if you are in a better position than you opponent or will be if he doesnt draw the answer for something.

[Maqi]

Serum Visions clearly loses scenario V (bad/bad/good) though, doesn't it?

[Ball.Lightning]

I think, that only way how to compare these three cards is to test them in various situations, as you did. But you should not score the results with method "Winner takes it all", but you should use some sort of scale. One contender can give just slight advantage and this fact of small advantage should be seen in the results. The same holds for Serum Visions - it is possible, that it can win threetimes and provide minor advantage, but in other six examples it looses badly.

[Madsam]

                 I  II IIIa IIIb IVa  IVb  V  VI
Ponder           1  2   2    2   2     3   3  4
Preordain        1  1   2    3   3     3   4  4
Serum Visions    1  2   3    3   4     4   4  4

Same Experiments as OP, VII is irrelevant, considered I a win win situation, so everyone gets a point

@Ball.Lightning I totally agree

[Nastaboi]

Good/Good/Good: Ponder wins as it gives more information, and you get to draw 3rd card immediately if you want to.
Good/Good/Bad: Ponder wins
Good/Bad/Good: Preordain wins (tie /w fetchland)
Bad/Good/Good: same
Good/Bad/Bad: Ponder wins /w fetchland, Preordain without
Bad/Good/Bad: same
Bad/Bad/Good: same
Bad/Bad/Bad: Ponder wins
Indifferent: If it does not matter, then it does not matter. Exclude from calculations.

Preordain is slightly better (5/8) when you don't have a shuffle effect. When you do have one, Ponder is clearly better (6/8) or at least equally good.

Another problem with these calculations is that we can't tell what are the frequencies for "good" and "bad". One more thing for Ponder is that seeing three cards at time gives you better evaluation on "good" and "bad".

[ChristophO]

Szenarios:
I
good / good / good
II
good / good / bad
III
good / bad / good and bad / good / good
IV
good / bad / bad and bad / good / bad
V
bad / bad / good
VI
bad / bad / bad
VII
indifferent / indifferent / indifferent

Suffle effect avaiable on the same turn:
I No clear winner (albeit Ponder gives better information)
Ponder: Best case szenario. You have great information. If board changes and good cards turn bad, you can still shuffle.
Prordain: Best case szenario, both cards on top are good

II Ponder wins because you can avoid drawing the bad card
Ponder: You place bad card third and shuffle next turn
Prordain: Still best case szenario, but this time you brick on the unknown third draw

III No clear winner (albeit Ponder gives more Information)
Ponder: You place bad card in third spot and shuffle next turn
Preordain: You put the bad card on bottom and draw the good one avoiding a bad draw. You luck out on the unknown third card.

IV Ponder wins because you avoid drawing the bad third card
Ponder: You can avoid both bad cards
Preordain: See III, but you are unlucky with the third unknown card

V No clear winner
Ponder: You avoid 2 bad cards!
Preordain: You avoid 2 bad cards and luck out on unknown draw!

VI Ponder wins because Preordain has to draw one bad card while Ponder shuffles
Ponder: You gamble for random card
Preordain: You gamble for random unknown card and lose

VII
Try to read the game state better! There are no truly indifferent cards!
If this can not be done, play your cantrip at a later time!

Shuffle effect on next main phase
I No clear winner (albeit Ponder gives better information)
Ponder: Best case szenario. You have great information. If board changes and good cards turn bad, you can still shuffle with shuffle effect.
Prordain: Best case szenario, both cards on top are good

II Ponder wins because you can avoid drawing the bad card
Ponder: You place bad card third and shuffle next turn
Prordain: Still best case szenario, but this time you brick on the unknown third draw

III No clear winner (albeit Ponder gives more Information)
Ponder: You place bad card in third spot and shuffle next turn
Preordain: You put the bad card on bottom and draw the good one avoiding a bad draw. You luck out on the unknown third card.

IV No clear winner (Ponder player can gamble though)
Ponder: You can not avoid drawing one bad card and needs to decide wether good + bad > 2 * random card
Preordain: You avoid one bad draw but the third unknown card is bad

V Preordain wins
Ponder: You can not avoid one bad card or you need to gamble
Preordain: You avoid 2 bad draws and luck out on the unknown card

VI Ponder wins because Preordain has to draw one bad card while Ponder shuffles
Ponder: You gamble for random card
Preordain: You gamble for random unknown card and lose

VII
Try to read the game state better! There are no truly indifferent cards!
If this can not be done, play your cantrip at a later time!

No Shuffle effect
I No winner (ponder more informatrion)
Ponder: you draw 3 good cards
Preordain: you draw 3 good card too

II No winner (ponder more informatrion)
Ponder: you draw 2 good + one bad
Preordain: you draw 2 good + one bad (unknown)

III + IV + V Preordain wins
Ponder: You can not avoid the bad card(s) or you gamble for new unknown cards
Preordain: You avoid one or two bad draws and draw a good card and a random third

VI Ponder wins because Preordain has to draw one bad card while Ponder shuffles
Ponder: You gamble for random card
Preordain: You gamble for random unknown card and lose

VII
Try to read the game state better! There are no truly indifferent cards!
If this can not be done, play your cantrip at a later time!


Conclusion
Ponder wins when you can shuffle and loses when you can not. If you can only shuffle next turn, it is closer but determining a "winner" is tough without talking about the odds of the different szenarios occuring (depends on likelyhood of "good" and "bad = 1-good"). Either way in almost all szenarios for all three cases both Spells greatly improve the quality of your drawn cards (sole exception is Ponder without shuffle effect for 3 cards of mixed quality 2 baad one good or 2 good one bad). Regarding Serum Visions: Serum Visions is clearly inferior because you will always draw an unknown card first. Srcy 2 still is powerful though and I believe the card is underplayed in blue decks. It is also pretty tough to decide for 3 different cards and for turns in advance with quite a bit of unknown information which cards will be good and which will be bad...

Either way: the important question is still how often you will have acess to a shuffle effect after pondering to make Ponder better than Preordain in those cases. Preordain ALWAYS fixes your draws (exception good good on top where no fixing is needed).   

[Tiggupiru]

Ponder also "sees" four cards when you need to find a combopiece or specific answer. Preordain only sees the maximum of three. That alone puts Ponder better in my book. Not to mention all the shuffling and stuff.

MMD is right, though. The comparison here is nothing more than theoretical (albeit very interesting and thought provoking), since I see no reason not to just run both if you want the other.

All in all, very well written article and scenario-based approach worked really well to keep things easy to read and still provided all the information you wanted to say. I don't mind reading more from you.