Mesmer’s Envoy vs. Mesmer’s Errand

Summary: In the Set.2 several new methods of drawing cards has been introduded. Some uses the draw cards as means to restore your hand so that you have more selections to choose from. However, with Set.2 I can see that some want to use the draw cards to draw specific target card(s). In this entry, I used statistical analysis to compare Mesmer’s Envoy from Set.2 to the Mesmer’s Errand from Set.1 to decide which spell is the better draw card, mainly for the purpose of drawing specific target card.

Mesmer’s Envoy vs.Summoner Mesmer’s Errand

spell-198.gif

Hand Restore

Envoy draws three cards, and returns two cards to the library and discard the spell itself result in net gain of 0 cards in the hand.

In contrast, Errand draws two cards and discard the spell itself result in net gain of 1 card in the hand.

Therefore, Envoy does not provide the means to restore your hand; whereas Errand does.

Mana Cost

Both spells cost 1 mana. No difference in this aspect.

Net Library Reduction

This is opposite of hand restoration. More cards you draw the less cards remain in the library. This means you are increasing your chance to be out decked, as well as increasing the probability to draw the target card in subsequent turn because there are less cards in the library.

Envoy has net draw of 1 cards i.e. net library reduction of 1; whereas, errand has net library reduction of 2.

The following table summarizes these findings:

Envoy Errands
Hand Restore No Yes
Mana Cost 1 1
Card Draws 3 2
Net Library Reduction 1 2

.

Probability of Drawing the Target Card

Although many of us use draw card spells or creatures to restore the number of cards in our hand, another important reason that majority of us use draw card spells or creatures are to increase our chance to draw a specific card(s) [target card] from our deck.

This would become much more important in the Set.2 since many of UltraRares in the Set.2 are so powerful that almost the one card can drive the entire deck e.g. Zolda for Lizard Deck, Warlords for unielemental decks, or Vamus for Undead deck etc. So being able to draw such key card during a game is crucial part of the tactics/strategy.

In this section, I compare the chance(probability) of drawing the target card (1 specific Ultrarare in this example) between Mesmer’s Envoy or Mesmer’s Errand. Although the specific number would change, the relation will not change even when the target card becomes 2 or 3 in the deck rather than one Ultrarare.

Below is a table summarizing the probability of drawing 1 in deck target card given X cards remaining in the deck.

# Cards Remaining Envoy Errands
25 12.00% 8.00%
24 12.50% 8.33%
23 13.04% 8.70%
22 13.64% 9.09%
21 14.29% 9.52%
20 15.00% 10.00%
19 15.79% 10.53%
18 16.67% 11.11%
17 17.65% 11.76%
16 18.75% 12.50%
15 20.00% 13.33%
14 21.43% 14.29%
13 23.08% 15.38%
12 25.00% 16.67%
11 27.27% 18.18%
10 30.00% 20.00%
9 33.33% 22.22%
8 37.50% 25.00%
7 42.86% 28.57%
6 50.00% 33.33%
5 60.00% 40.00%
4 75.00% 50.00%
3 100.00% 66.67%
2 100.00% 100.00%
1 100.00% 100.00%

Table 1: Probability of drawing 1 in deck target card given X cards remaining in the deck

What does this table tell?

This table tells the chance/probability of you drawing the target card (1 in the deck) using Envoy or Errand when X number of cards are remaining in the deck. It is important to note that this is NOT cumulative probability. This means if you play a game and have 20 cards remaining in your deck and use Envoy, this table will give you the exact probability under the circumstance, but will not give probability of what is my chance BY 20th turn before playing the game.

For example, the first row second column value 12% means you have 12% chance to draw a Scion Biolith Lord (assuming this is your target) using Mesmer’s Envoy during your first turn, 25 cards remaining in your library. Similarily, third column is the corresponding value using Mesmer’s Errand instead of Envoy.

So is Envoy better than Errands?

If you were to use Envoy or Errand when the number of card remaining in the library is the same, Envoy would give 50% better chance to draw the target card than Errand; however, to compare the two, we need to also take the net library reduction into the consideration as well because this will affect the subsequent draws i.e. affect cumulative probability.

For example, using Envoy at first turn makes the subsequent draw as 2nd draw (24 cards remaining) when using the Errand at the same turn makes the subsequent draw as 3rd draw (23 cards remaining).

Therefore, looking at the subsequent draw alone Envoy gives 1/24; whereas, Errand gives 1/23. Thus, in all subsequent draw Errand gives the better probability than Envoy. Question here would be these increase in probability significant enough to compensate the initial 50% difference? Here is the table to compare the probability of subsequent draws.

Draw Envoy Errands
1 15.67% 12.00%
2 19.33% 16.00%
3 23.00% 20.00%
4 26.67% 24.00%
5 30.33% 28.00%
6 34.00% 32.00%
7 37.67% 36.00%
8 41.33% 40.00%
9 45.00% 44.00%
10 48.67% 48.00%
11 52.33% 52.00%
12 56.00% 56.00%
13 59.67% 60.00%
14 63.33% 64.00%
15 67.00% 68.00%
16 70.67% 72.00%
17 74.33% 76.00%
18 78.00% 80.00%
19 81.67% 84.00%
20 85.33% 88.00%
21 89.00% 92.00%
22 92.67% 96.00%
23 96.33% 100.00%
24 100.00%

Table 2: Cumulative Probability of drawing the target card (1 in deck) after using Envoy or Errands in the first turn.

This table demonstrates 12th draw after the first turn, the overall cumulative probability of drawing the target card after using the Errand in the first turn becomes higher than that of using the Envoy.

At this point, one may ask “How will this change if I use my first Envoy or Errand later in the game?”

Using the same math, if you use the first Envoy or Errand when 15 cards are remaining in the library, it takes 8 additional draws before Errands cumulative probability of drawing the target card becomes higher than that of the Envoy.

Taking to some extreme, using Envoy or Errands when 5 cards are remaining in the library, it takes 3 additional draws (just a card before deck out).

These result can be summarized as following:

The earliest cumulative probability using errand becomes higher than that of Envoy is at 14th draw after the game start. This happens when you use Errand during your first turn.

The last analysis we need to do is the case when you use multiple Envoy or Errand. How will this change the chance you can draw your target Ultrarare.

This question can be rephrased as “Can the effect of increasing the difference in the # of cards remaining in the library compensate the original chance difference?”

First I have done the analysis of using three Envoy back to back in comparison to three Errand back to back at turn 1. This turned out 33% and 24 % for Envoy and Errand, respectively.

Next, do the same analysis but at turn 12 resulted in 58% and 46% for Envoy and Errand, respectively.

*Note these probability are not cumulative from beginning, but rather cumulative from the first use of Envoy/Errand. This is valid analysis because up until that point two have exactly the same probablity.

Conclusion

From the statistical analysis, it was proven that the use of Envoy generally gives better overall chance to draw a specific target card from your library; however, the player need to remember that it will not provide the method to restore your hand, which Errand can be used for.

Although this conclusion stating the conceputually obvious, I hope this was helpful for a few of us who wanted to have some mathematical proof. 😉

Details of Mathematical Analysis
This section provides the math I used to construct the table given in this section. If you are not interested in the math, please skip this section.
Table 1
——- Mesmer’s Envoy Probability Analysis ——–
# of Card Remaining 25
1/25 + (24/25) x 1/24 + (24/25) x (23/24) x 1/23
Probability is 0.12
# of Card Remaining 24
1/24 + (23/24) x 1/23 + (23/24) x (22/23) x 1/22
Probability is 0.125
# of Card Remaining 23
1/23 + (22/23) x 1/22 + (22/23) x (21/22) x 1/21
Probability is 0.130434782608696
and so on…
——- Mesmer’s Errand Probability Analysis ——–
# of Card Remaining 25
1/25 + (24/25) x 1/24
Probability is 0.08
# of Card Remaining 24
1/24 + (23/24) x 1/23
Probability is 0.0833333333333333
# of Card Remaining 23
1/23 + (22/23) x 1/22
Probability is 0.0869565217391304
and so on…
Table 2: Probability of drawing the target card (1 in deck) after using Envoy or Errands in the first turn.
——- Draw At Least One Card By Nth Draw Probability ——–
(After Mesmer’s Envoy during the first turn) = 12%
1st Draw
0.12 + 1/24 x 0.88
Probability is 0.156666666666667
2nd Draw
0.12 + 1/24 x 0.88 + (23/24) x 1/23 x 0.88
Probability is 0.193333333333333
3rd Draw
0.12 + 1/24 x 0.88 + (23/24) x 1/23 x 0.88 + (23/24) x (22/23) x 1/22 x 0.88
Probability is 0.23
and so on…
——- Draw At Least One Card By Nth Draw Probability ——–
(After Mesmer’s Errands during the first turn) = 8%

1st Draw
0.08 + 1/23 x 0.92
Probability is 0.12
2nd Draw
0.08 + 1/23 x 0.92 + (22/23) x 1/22 x 0.92
Probability is 0.16
3rd Draw
0.08 + 1/23 x 0.92 + (22/23) x 1/22 x 0.92 + (22/23) x (21/22) x 1/21 x 0.92
Probability is 0.2
and so on…
——– Three Envoy in Turn 1 ——–
Pr(Two envoy) = Pr(Envoy 25 cards remaining) + (1- Pr(Envoy 25 cards remaing)) x Pr(Envoy 24 cards remaining)
Pr(Three envoy) = Pr(Two envoy) + (1 – Pr(Two Envoy)) x Pr (Envoy 23 cards remaining)
——– Three Errand in Turn 1 ——–
Pr(Two Errand) = Pr(Errand 25 cards remaining) + (1- Pr(Errand 25 cards remaing)) x Pr(Errand 23 cards remaining)
Pr(Three Errand) = Pr(Two Errand) + (1 – Pr(Two Errand)) x Pr (Envoy 21 cards remaining)
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4 responses to this post.

  1. Posted by ImDoneItsOver on April 30, 2008 at 9:40 pm

    ERRRR More Math. I like ENVOY reminds me of Graceful Charity (yugioh)

    Reply

  2. Posted by Rufus Omega on May 1, 2008 at 7:28 am

    Personally I find Envoy to be the more useful card, and I have noticed that more players use it than Errand now. Really though, it depends on the type of deck it’s in. In a spell heavy deck, especially one with spells that require the discard of additional creatures, I would say the Errand is better. In a specific card based deck the Envoy is definately the way to go.
    The only problem with Mesmer’s Envoy and other draw and return cards is that they shuffle the deck afterward so multiple uses can have you draw the same card over and over. This has happened to me a few times with Siam’s Lookout, trying to draw one specific card but getting the same unwanted card two or three times in a row. It’s annoying, but in the long run still gives a better chance of getting the desired cards. It’s just a case of being patient and forcing myself to not eat the cards in frustration.

    Reply

  3. Posted by ImDoneItsOver on May 1, 2008 at 4:26 pm

    Yah ENVOY is a more general Strat card (wish I had one:( ) I think the comp has trouble with the shuffle thing . The same thing happens to me with Siam’s Lookout 😦 but man I love that frog 🙂

    Reply

  4. Posted by Motions on May 5, 2008 at 8:56 am

    1 thing many people forget is by playing mesmer’s envoy you get 3 cards, but you also dismiss 2 cards and mesmer’s envoy itself so you won’t get extra cards. with errand you get 2 cards and you only dismiss errand so it provides you an extra card. when playing a dismiss deck errand is better.

    Reply

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