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MTG Arena’s Opening Hand Algorithm and Smoothing: Finding the Ideal Land Count for BO1

Circuitous Route Art by Milivoj Ćeran
Circuitous Route Art by Milivoj Ćeran

Welcome back! I wrote previously about the impact of hand smoothing on Arena’s Best of One format; I won’t rehash that piece here but it showed that the effect of hand smoothing is both clear and significant. Initially this hand smoothing analysis was applied only to 60 card decks with 24 lands. While 24/60 cards is perhaps the most common ratio, it’s by no means the only one, and having access to additional numbers should be highly beneficial for people’s deckbuilding.

After some more data collection, I can now present rates for land ratios from 20 to 26 over a minimum of 100 hands. For comparison purposes, I’ve presented these numbers side-by-side with what you’d mathematically expect for those land ratios, labelled Normal, in decks without Smoothing. The tables are expanded further to include the odds of hitting your third, fourth, and fifth land drops on their respective turns, whether you are on the play or on the draw.

In general, you’ll see that the numbers for Smoothing are anything but smooth; the graphs tend to spike intensely compared to the Normal numbers, with very limited outliers. The general effect of this is that, based on your initial land selection, you can have a very high degree of confidence in how many lands you’re likely to have in your opening hand, which means you can Mulligan with greater confidence for higher quality hands. In Bo3, keeping a one lander may be a reasonable gamble based on what else is in your hand and knowing that your opponent has a decent chance at a subpar hand (20+% chance of a 0, 1, 5, 6, or 7 land hand in a 26 land deck). In Best of One, this is much less likely to work out, as the chance of your opponent having such a hand is somewhere in the range of 1%.

A couple of final notes: First, as has been pointed out by a reader, anecdotal experience indicates that hand smoothing does not appear to distinguish between basic lands and non-basics. Second, no amount of data collection is going to be perfect. We’re dealing with an unknown algorithm that ‘leans’ away from true random, with little insight provided by its creators. While larger sample sizes might provide more accuracy, the odds of that are actually quite low, in a system such as this. For instance, the odds of flipping a coin 10,000 times and getting heads 5,000 of those times is only 0.8%. So, treat these numbers as a guide that provides insight, not absolute rules. Finally, remember that no matter how improbable, the possible is never impossible.

27 Lands

27 Lands3rd Land4th Land5th Land
LandsBo1NormalPlayDrawPlayDrawPlayDraw
70.0%0.2%100%100%100%100%100%100%
60.0%2.5%100%100%100%100%100%100%
50.0%11.0%100%100%100%100%100%100%
430.8%24.8%100%100%100%100%91.25%96.82%
359.6%31.0%100%100%84.40%92.58%61.94%77.97%
29.6%21.6%72.57%86.02%45.68%65.04%25.62%46.65%
10.0%7.7%23.58%48.56%11.10%28.29%3.63%18.71%
00.0%1.1%0%12.49%0%4.32%0%2.81%
27 LANDS IN DECK

27 Lands is the most common land count in Jeskai or Control; from looking at the numbers, you can probably guess why. Fires and Control decks are both looking to hit high land counts with land drops on every turn in order to drop their most common win conditions, Cavalier or Trawler respectively. 27 lands give significantly improved odds of opening with 4 lands, with minimal odds of being saddled with 2 or fewer. If you feel really strongly about starting out with 4 lands in your hand, then this is where you’ll want to be.

26 Lands

26 Lands3rd Land4th Land5th Land
LandsBo1NormalPlayDrawPlayDrawPlayDraw
70.0%0.2%100%100%100%100%100%100%
60.0%2.0%100%100%100%100%100%100%
50.5%9.6%100%100%100%100%100%100%
416.5%23.2%100%100%100%100%89.78%95.69%
365.0%31.2%100%100%82.67%91.25%58.75%74.86%
218.0%23.4%70.54%84.40%42.81%61.94%23.07%42.83%
10.0%9.1%21.77%45.68%9.82%25.62%3.02%16.36%
00.0%1.4%0%11.10%0%3.63%0%2.29%
26 LANDS IN DECK

If having that fourth land in hand isn’t essential, then 26 lands is a better spot for control decks or Fires. Your odds of having a 3-land hand are better here than anywhere else on the curve, while maintaining fantastic chances to hit your ensuing land drops. 26 lands give an 80+% chance of having a playable hand, at least in terms of lands, and a high degree of confidence in mulliganning if you don’t love your opening draw.

25 Lands

25 Lands3rd Land4th Land5th Land
LandsBo1NormalPlayDrawPlayDrawPlayDraw
70.0%0.1%100%100%100%100%100%100%
60.0%1.6%100%100%100%100%100%100%
50.0%8.2%100%100%100%100%100%100%
415.4%21.4%100%100%100%100%88.17%94.42%
363.5%31.2%100%100%80.81%89.78%55.48%71.57%
221.2%25.2%68.43%82.67%39.96%58.75%20.64%39.07%
10.0%10.5%20.03%42.81%8.64%23.07%2.50%14.19%
00.0%1.7%0%9.82%0%3.02%0%1.85%
25 LANDS IN DECK

Each step up or down of one land represents a fairly small statistical step. Interestingly, in Bo3, the odds of a 3-land hand is the same with 25 or 26 lands; the odds change instead on either side (2 or 4). With Smoothing, that synchronicity seems to continue, within a reasonable margin of error for the data. As an aggressive mulliganner, the benefit of a potential mulligan is still strong enough that given the option, I’d probably play 25 lands over 26 in most situations if I really wanted to hit 3 land in my opening hand, unless I really felt the need to squeeze in another land to hit a color ratio, or maybe add something along the lines of Blast Zone for potential non-mana value.

24 Lands

24 Lands3rd Land4th Land5th Land
LandsBo1NormalPlayDrawPlayDrawPlayDraw
70.0%0.1%100%100%100%100%100%100%
60.0%1.3%100%100%100%100%100%100%
50.0%6.9%100%100%100%100%100%100%
49.6%19.6%100%100%100%100%86.42%93.00%
356.7%30.9%100%100%78.83%88.17%52.15%68.10%
232.7%26.9%66.26%80.81%37.14%55.48%18.35%35.38%
11.0%12.1%18.36%39.96%7.56%20.64%2.04%12.22%
00.0%2.2%0%8.64%0%2.50%0%1.48%
24 LANDS IN DECK

24 lands represent a much more noticeable shift in likelihood of hitting 3 lands in the opening draw as compared to 25. 24 is where you’ll see the odd few Fires decks, along with some of the Aggro decks other than RDW in Bo3, though I’ve seen a few ‘big’ Mono-red builds that went this high as well; in Bo1 though, you can pretty safely slice one land off those. If you’re playing a variant of Fires without much land fetch, ramp, or draw ability, then this is probably a bit too dangerous.

23 Lands

23 Lands3rd Land4th Land5th Land
LandsBo1NormalPlayDrawPlayDrawPlayDraw
70.0%0.1%100%100%100%100%100%100%
60.0%1.0%100%100%100%100%100%100%
50.0%5.8%100%100%100%100%100%100%
43.8%17.8%100%100%100%100%84.49%91.42%
357.7%30.3%100%100%76.71%86.42%48.76%64.48%
237.5%28.6%64.01%78.83%34.36%52.15%16.19%31.81%
11.0%13.8%16.76%37.14%6.57%18.35%1.65%10.43%
00.0%2.7%0%7.56%0%2.04%0%1.17%
23 LANDS IN DECK

Once again the step down from 24 to 23 is more incremental. If you’re looking at 24 land in Bo3, then 23 is probably where you want to be in Bo1, or even down to 22. The odds of a playable hand and post-draw playability are all but negligible between 24 and 23.

22 Lands

22 Lands3rd Land4th Land5th Land
LandsBo1NormalPlayDrawPlayDrawPlayDraw
70.0%0.0%100%100%100%100%100%100%
60.0%0.7%100%100%100%100%100%100%
50.0%4.8%100%100%100%100%100%100%
40.0%16.0%100%100%100%100%82.40%89.65%
347.1%29.4%100%100%74.46%84.49%45.34%60.71%
250.0%30.0%61.68%76.71%31.63%48.76%14.17%28.36%
12.9%15.7%15.24%34.36%5.68%16.19%1.32%8.82%
00.0%3.3%0%6.57%0%1.65%0%0.92%
22 LANDS IN DECK

By now, you’re probably noticing that we’re getting more significant shifts on the even land counts as we descend. 22 lands is where we shift to greater odds of a 2 land opening hand than 3 and the odds of a 4 land hand drops off the chart. This is the space a lot of aggro decks will want to hit, knowing that they’re locked in at 2-3 lands, and if they need 3 they have a 70% chance of hitting three with one mulligan. Hitting the 4th land drop still has really strong odds on a 3-land hand, but the chances of hitting that fifth land drop on turn five take a real hit at this level, especially on the play.

21 Lands

21 Lands3rd Land4th Land5th Land
LandsBo1NormalPlayDrawPlayDrawPlayDraw
70.0%0.0%100%100%100%100%100%100%
60.0%0.5%100%100%100%100%100%100%
50.0%3.9%100%100%100%100%100%100%
41.0%14.2%100%100%100%100%80.12%87.69%
342.3%28.3%100%100%72.06%82.40%41.89%56.81%
254.8%31.3%59.29%74.46%28.96%45.34%12.30%25.05%
11.9%17.7%13.79%31.63%4.87%14.17%1.04%7.38%
00.0%4.0%0%5.68%0%1.32%0%0.71%
21 LANDS IN DECK

21 lands is where we start cutting into hardcore weenie/aggro territory. 21 is a safe spot for just about any current build of RDW, and is pretty much doom for any other deck to play at. Your chances of hitting a T4 land drop for Torbran are not favorable here if you settle for less than 3 lands in hand.

20 Lands

20 Lands3rd Land4th Land5th Land
LandsBo1NormalPlayDrawPlayDrawPlayDraw
70.0%0.0%100%100%100%100%100%100%
60.0%0.4%100%100%100%100%100%100%
50.0%3.1%100%100%100%100%100%100%
42.9%12.4%100%100%100%100%77.64%85.51%
334.0%27.0%100%100%69.52%80.12%38.43%52.80%
259.2%32.4%56.82%72.06%26.34%41.89%10.57%21.92%
13.9%19.9%12.41%28.96%4.14%12.30%0.81%6.11%
00.0%4.8%0%4.87%0%1.04%0%0.54%
20 LANDS IN DECK

20 lands is still a pretty good spot even for ‘big’ builds of RDW if they feature Light Up the Stage. For smaller builds of RDW that lean more into weenies and Anax and eschew Torbran, this is a sweet spot.

Below 20 lands, ‘Here be dragons’. It’s very feasible to be effective at 19 or 18 lands with small RDW up until you hit Mythic, and then the margins become much tighter and you have to play cleaner. I’ve gotten through Platinum and Diamond with 60+% win rates in the 18/19 land range, and even hit 1400 mythic with 19 land RDW, but you need to have a great feel for the deck, especially when to play Steamkin. At this point in time though, RDW is so common in Bo1 that playing so aggressive on land in Mythic is not something I’d do as everyone is built to beat RDW in Bo1 Mythic.

Bo1 Land/Hand COMBINED
Red5ive

Red5ive

Brendan Dillon is an old school mono-artifact dude with a penchant for overthinking the little things.

7 Responses

  1. 20pesos says:

    Great follow up article!
    It was nice to know why 27 lands is the sweet spot for mid-range and control decks in Bo3. Ofcourse, the main insight of “smoothing” in Bo1 is that aggro can afford to be extra aggro. I think midrange and control decks can also expect to have some mana consistency and can tweak their decks to pull of combos and response to early threats.

    • Red5ive Red5ive says:

      While it definitely favors aggro a bit, I think that Bo1 would even without Smoothing. Aggro benefits most by doing what it does regardless of what the opponent does, so g1 pre-sideboard is a strength for aggro. Post sideboard is always going to lean a bit more towards control. I’ll be looking at some options for optimizing control for Bo1 in the near future.

  2. beren says:

    Friend, my fear is that you are contributing to Arena not incorporating improvements in its algorithms.
    You are looking at just 1 or 2 faces of a 6-sided cube, that is, forgetting to look at the other 4 faces.
    To understand the serious problem of Arena randomness just do what I will say next:
    “Play some ranked drafts. Create a common deck with 23 spells and 17 lands, in any 2-color archetype.”
    Because only in a more simple and limited model you will be able to see certain things, for example:
    1- It is very normal to happen land of a single color. The amount is how you speak and your text, however it happens very often in games to come only 1 color of terrain. (against all odds)
    2- you will see that some cards always appear during the games, while others almost never come (and sometimes even never, even if you reach a 6-3 having played 9 games in the draft)
    3 – you will notice that the weight of the cards varies a lot. Instead of the Arena assigning an equal weight to the 40 cards it is clearly noticeable that he unfortunately assigns different weights.

    Fortunately in the standard game there are many ways to get around these problems, as there are cards that help you get around these errors in randomness. In the limited no and all these problems become wide open to the player.

  3. daid13 says:

    This looks interesting, I will have a think about how to tweak my bo1 version of monowhite devotion using this knowledge.

    Is the higher chance of 4 lands as you get less than 22 correct or a typo? I

    • Red5ive Red5ive says:

      If you mean the 0% for 22 lands and the 1% at 21 lands, it’s not a typo. Those numbers represent actual data collected and sometimes even though the statistical odds of something happening may be lower, the data collected may come out slightly different during data collection.
      In this case, over 100+ hands, I drew one 4 land hand with the 21 land deck and and none with the 22 land hand. Pretty small variance there.

  4. Clervis says:

    Hi Red5ive,
    I did some modeling based off of one of your articles. Check it out.

    https://www.reddit.com/r/MagicArena/comments/fjdnab/smoothing_breakpoints_for_your_land_draw/

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