Tips for winning at 6 Nimmt! (6-player version)

This article was machine-translated from the Japanese version.

This article is for Day 1 of Table Game Tansu Advent Calendar 2022.

Are you familiar with the card game 6 nimmt!?
Since this article won’t make sense without knowing the rules of 6 nimmt!, I’ll proceed on the assumption that you are familiar with them. ¹

1. Introduction

6 nimmt! is a game whose strategy changes dramatically depending on the number of players and whether variant rules are adopted.
Here, I’ll focus on the version I usually play: 6 players with no variant rules (hereafter referred to as “this article’s rules”).

Therefore, most of the tips explained in this article are only effective under this article’s rules. Please be aware of this.

2. Card and Board Notation in This Article

Here, cards are represented as card number (penalty points when that card is taken), and the board is shown in a table as follows.

The #n in the top row is the column number counted from the left, included for clarity.
Also, since penalty points are incurred when a card is placed in the #6 position, 🐮 is placed there to make this evident.

Furthermore, the rightmost card in each row is called the tail here.
The bolded cards in the table above are the tails.

3. Is 6 nimmt! a Game You Can Always Win?

Under this article’s rules, 6 nimmt! is not a game you can always win.
The outcome depends on the board state, which cards have been removed, your hand, your opponents’ hands, your opponents’ strategies, and so on.

Even so, there are tips like “when the board is in this state, playing this card makes it easier to avoid penalty points.”
After playing 1197 games ² on Board Game Arena, I’ve identified several tips that seem effective, and I’ll explain them in this article.

4. The Absolute Fundamental Tip

Please remember this above all else. This is the absolute fundamental tip.

When you think “there’s a chance,” there usually isn’t

A “chance” is no chance.
Let me give one example of such a “chance.” It’s when you play your highest card, 100, when the following row on the board is the one with the largest tail.

Hand: 4(1), 21(1), 60(3), 73(1), 82(1), 97(1), 100(3)

If no one plays a card 56 or higher, 100 will go into #5, and with cards 60–97 in your hand, the possibility of taking this row disappears, allowing you to avoid penalty points.
However, if even one other player plays a card between 56 and 99, 100 will go into #6, resulting in a hefty 16-point penalty.
And it’s precisely in such situations that yet another player will appear and cause you to take penalty points, so it’s better to play it safe with 4 or 21.

This applies to card games in general: if you play a card with a high probability of incurring penalty points, you’ll lose 4 out of 5 times.
Rather than betting on that 1 win out of 5, consistently play safe cards and raise your overall win rate.

5. General Tips

Before getting into early-game tips, I’ll write one general tip that works on any board.

When you should play consecutive cards, play the one with the larger number

Consecutive refers to two or more cards among the playable cards whose numbers differ by exactly 1.

Obviously consecutive cases

First, let me give an example of cards that are obviously consecutive.

Hand: 33(5), 34(1), 46(1), 51(1)

33(5) and 34(1) are obviously consecutive. This is because \(33 + 1 = 34\).
If you play 33 here, you may be at a disadvantage on your next turn if the row with the largest tail ends up in the following state:

Since you blocked #5 with 33, there’s a possibility you’ll end up taking this row on your next turn.
If 33 is placed as a tail somewhere in #1 through #4, you can safely play 34 on your next turn, which is advantageous — but whether such a board state occurs depends on what the other players play.
And precisely in such situations, 33 often ends up in #5.

On the other hand, the worst case when playing 34 under the same conditions is as follows:

In this case, you can avoid penalty points on your next turn by playing 33.
To avoid the case that occurs when playing 33, when cards are consecutive, it’s better to play the larger one.

Substantially consecutive cases

Even if the numbers written on the cards are not consecutive, they may actually be consecutive in practice. Let me give an example.

Hand: 33(5), 36(1), 46(1), 51(1)

At first glance, 33(5) and 36(1) in your hand don’t appear consecutive, but looking at one of the rows on the board, 34 and 35 have already been played.
At this point, 33 and 36 are substantially consecutive. This is because 34 and 35 will never be played again in subsequent turns.

If you play 33 here, you may be at a disadvantage on your next turn if the other row with the largest tail is in the following state:

Since 34 and 35 have already been played on the board, in this case the card most likely to take the row with 33(5) as the tail is 36.
To avoid cases like the above, in this situation as well, it’s better to play 36, which is the larger of the consecutive cards.

The above covers the general tips.
With this in mind, I’ll explain tips divided into the early game, mid game, and late game.

6. Early Game Tips

First of all, you should play the card with the largest number in your hand… or so you might think, but you shouldn’t.

As a premise, in 6 nimmt!, holding many cards with large numbers puts you at a disadvantage later on. ³
This is because as the game progresses, board states where you must play your smallest number or incur penalty points frequently arise, such as the following:

On a board like this, 11 will almost certainly be taken by a card under 10, and cards will be placed in #2 as the second smallest, #3 as the third smallest… and so on, until ultimately the player who played the largest number under 31 will take the cards in the top row.
Why this happens will be explained in detail in the mid-game section.

Given this premise, you’ll want to dispose of your large-number cards quickly in the early game.
However, be aware that the other players around you are likely thinking the same thing.

Here’s an example of the board and hand at the start of the game:

Hand: 2(1), 10(3), 17(1), 39(1), 44(5), 59(1), 71(1), 85(2), 96(1), 101(1)

Suppose you play 101, the maximum value in your hand. The possible cases are mainly three:

1. All players play numbers 66 or above

   In this case, all cards will gather in the third row from the top, and the player who played the second-largest number will incur penalty points.
   If you’re lucky and 101 isn’t the second-largest number, you’re safe — but this falls under the “chance” category, so you’ll incur penalty points 4 out of 5 times.

2. Only one player plays a number 64 or below, and the remaining players play numbers 66 or above

   A common case.
   In this case, the player who played the largest number incurs penalty points, and 101 is a large enough number that the probability of penalty points is high.

3. More than two players play numbers 64 or below, and the remaining players play numbers 66 or above

   Penalty points avoided.
   However, since other players also want to dispose of large-number cards, this case rarely occurs.

The likely cases are 1 or 2, and in both cases 101 is a card with a high probability of incurring penalty points.
Therefore, you should not play large-number cards like 96 or 101 here.

So what should you play? This brings us to Early Game Tip 1.

Early Game Tip 1: If the row with the largest tail on the board is a safe row, play a safe card

What is a safe row and a safe card?

A safe card is, in a word, a card with a low probability of incurring penalty points.
Also, a row where a safe card exists is called a safe row. ⁴

As an example, let’s consider whether the following row is safe.
For simplicity, other rows and the numbers of previously played cards will not be considered within this section.

Hand: 2(1), 10(3), 17(1), 39(1), 44(5), 59(1), 71(1), 85(2), 96(1), 101(1)

This row is not safe.

First, let the number at the tail of this row be \(N (=20)\), and the number of cards already placed in this row be \(M (=3)\).

$$ N = 20 $$ $$ M = 3 $$

At this point, when there exists an \(O\) in your hand satisfying the following condition, that row is called a safe row, and the card \(O\) is called a safe card.

$$ N + 1 \le O \le N + (5 - M) + max(0, 3 - M) \times 2 $$

\(max(0, 3 - M)\) means selecting the larger value between \(0\) and \(3 - M\).
Substituting \(N\) and \(M\) into this example:

$$ 21 \le O \le 22 $$

Since there are no cards in your hand between 21 and 22, this row is not safe.

Let me give another example.
The hand is the same as the previous example.

Hand: 2(1), 10(3), 17(1), 39(1), 44(5), 59(1), 71(1), 85(2), 96(1), 101(1)

This row is safe because the safe card \(O = 71\) satisfying the following condition exists in your hand.

$$ N = 65 $$ $$ M = 1 $$ $$ N + 1 \le O \le N + (5 - M) + max(0, 3 - M) \times 2 $$ $$ 66 \le O \le 73 $$

The above is the basic method for calculating safe rows and safe cards in the early game.
In reality, whether a row is safe fluctuates depending on previously played cards and the board situation, but cases where you need to consider these are not very common when playing your 1st or 2nd card in the very early game.
I wrote a complicated formula, but the important thing is that a card with a low probability of incurring penalty points is a safe card.

With this in mind, let me explain Early Game Tip 1.

If the row with the largest tail on the board is a safe row, play a safe card

I’ll reiterate the example from the start of the game given in 6. Early Game Tips.

Hand: 2(1), 10(3), 17(1), 39(1), 44(5), 59(1), 71(1), 85(2), 96(1), 101(1)

Among these 4 rows, the third row from the top has the largest tail number.
This row is safe, and the safe card is 71. Therefore, following Early Game Tip 1, 71 is the card you should play.

So what should you do when there is no such safe row?
For such cases, I’ll explain Early Game Tips 2 and 3 with additional examples.

Early Game Tip 2: Play the card with the largest value among those smaller than A, the largest tail number on the board (when Early Game Tip 1 cannot be applied, and there’s a high probability that many cards larger than A will be played)

Such cases frequently occur in the very early game when you’re playing your 1st or 2nd card.
As an example, here is the board and hand for such a situation:

Hand: 2(1), 10(3), 17(1), 39(1), 44(5), 59(1), 71(1), 85(2), 96(1), 101(1)

In this case, since the row with 88(5) as the largest tail on the board is not safe, Early Game Tip 1 cannot be used.
And since you have 10 cards in your hand, this means you’re about to play your 1st card, which means there’s a high probability that cards 89 and above exist in your opponents’ hands.

Here, recall the second possible case from 6. Early Game Tips:

2. Only one player plays a number 64 or below, and the remaining players play numbers 66 or above

   A common case.
   In this case, the player who played the largest number incurs penalty points, and 101 is a large enough number that the probability of penalty points is high.

Here, you become that one player.

First, assuming all players try to play the highest possible numbers, most of the cards played will be 89 or above.
And in practice, this is often the case.

Conversely, all numbers 87 and below become cards with a low probability of incurring penalty points.
In other words, among the tails of each row — 18(1), 88(5), 75(2), 47(1) — values from 1 to 87, which are smaller than the maximum value of 88(5), have a low probability of incurring penalty points.
Therefore, in such a case, 85(2), which is the maximum value between 1 and 87 in your hand, is the card you should play.

Early Game Tip 3: Treat the row with the largest tail as if it doesn’t exist, and if the row with the next largest tail is safe, play a safe card (when Early Game Tips 1 and 2 cannot be applied)

Again, as an example, here is the board and hand for such a situation:

Hand: 2(1), 10(3), 17(1), 39(1), 44(5), 59(1), 71(1), 85(2), 96(1)

Applying Early Game Tip 2 to this, the card to play would be 96(1).
This is because the tail number of the row with the largest tail on the board is 102, and the maximum value between 1 and 101 in your hand is 96.

However, in the world of 6 nimmt!, the only numbers larger than 102 are 103 and 104.
And under this article’s rules, there’s a considerable possibility that 103 or 104 have been removed.

On such a board, if other players try to dispose of the highest possible cards, playing 96(1) may result in penalty points.
This is because it’s currently the turn to play your 2nd card, and there’s a high probability that other players holding cards between 83 and 94 exist.

To give a concrete board, you would incur penalty points if the following board state results after playing 96(1):

So which card should you play to avoid penalty points?
Fortunately, you have the card 85(2) in your hand, which is safe against the row with 82(1).
If you play 85 instead of 96, the board would look like this, and you can avoid penalty points:

Therefore, when such a safe card exists, you play it to avoid penalty points.
Expressed in generalized terms, this means treating the row with the largest tail as if it doesn’t exist and playing a safe card for the row with the next largest tail number.

If no such safe card exists, reapply Early Game Tip 2 after treating the row with the largest tail as if it doesn’t exist.
Applied to the above example, 71(1), which is the maximum value between 1 and 81 in your hand, becomes the card to play.

So in the early game, you proceed by using these 3 tips to discard as many large-number cards as possible.
There may be cases where none of these 3 tips can be applied. In such cases, play the safest possible card to avoid penalty points.
To reiterate, playing safe cards prevents penalty points, and preventing penalty points is important in 6 nimmt!

7. Mid-Game Tips

The mid-game refers to the point when board states where there are no safe rows for all players become increasingly common.
Below, I’ll give several examples where there are no safe rows for any player.

Example 1: No safe rows for any player

Hand: 17(1), 39(1), 44(5), 59(1), 71(1), 84(1)

At first glance, the row with 82(1) appears safe.
However, since the other rows are already filled with 5 cards, there’s a very high probability that 82(1) will be taken by a card of 30 or below.
Therefore, there are no safe rows on this board.

Example 2: No safe rows for any player

Hand: 2(1), 10(3), 17(1), 39(1), 44(5), 57(1)

At first glance, the row with 55(3) appears safe.
However, since the tail of the top row is 56(1), it’s almost certain that no cards will follow after 55(3) this turn.
If another player takes the top row, cards will follow after 55(3), but in most cases they’ll take 38(1) ⁵, so this doesn’t need to be considered here.

Therefore, this board is essentially the same as Example 1, and there are no safe rows.

Example 3: No safe rows for any player

Hand: 2(1), 10(3), 17(1), 39(1), 44(5), 85(2)

This board is a reiteration of the example given in 6. Early Game Tips.

You hold 10(3) and 17(1), which are safe cards against the row with 9(1).
And since you have many remaining cards in your hand, there’s a good chance other players also hold cards between 11 and 30.
Because of this, the row with 9(1) may appear safe at first glance, but in this case, 9(1) is frequently taken by a card with a number of 8 or below, and the player who played the card with the largest value ends up incurring penalty points.

Let’s think about why this happens.
Holding a card of 8 or below means that during the game, you’ll almost certainly have to take some card.
Therefore, while lower priority than large-number cards, small-number cards are also something you want to dispose of early if possible.

Now, looking at 9(1) on the board, this becomes a card that players holding small-number cards should take.

Let’s look at the actual board.
First, if no one takes 9(1) and all players play cards between 10 and 30, the board after penalty processing would be as follows:

Since all cards would be played after the originally placed 9(1), the player who played Card A, the 5th largest number, would incur penalty points, then A would be placed in #1, and Card B, the largest value, would follow after it.

This is not a favorable board for players holding cards of 8 or below.
Players holding cards of 8 or below want to take the card with the minimum penalty of (1) if possible, but X+Y will always be at least 2.
When this happens, depending on the subsequent game progression, they may lose the timing to play their cards of 8 or below, and ultimately may end up taking a row with large penalty points.

Next, here is the board after penalty processing when one or more players play cards of 8 or below, and the remaining players play cards between 10 and 30:

This becomes a favorable board for players holding many small-number cards.
If Z becomes 1, a player holding multiple cards of 31 or below can take that Z and continue to create a board favorable to themselves.
And since cards with 1 penalty point are more numerous than cards with 2 or more penalty points, the probability of such a favorable board is high. ⁶

From the above, players holding cards of 8 or below are likely to play those cards on this board.
And if such players exist, cards between 10 and 17 that would normally be safe against 9(1) may no longer be safe.

Expressed on a board, the following state could occur:

In such a case, penalty points are incurred by the cards between 10 and 17 placed in #6, which should normally be safe.
Therefore, there are no safe rows on this board.

I’ve given several examples above where there are no safe rows for any player.
So which card should you play after determining you’re in the mid-game? Here, you’ll use 4 tips depending on the board and hand state.

Mid-Game Tip 1: Play the card with the smallest number (when there is a row with 2 or fewer penalty points on the board, and you can take it)

I’ll reiterate Example 3 where there are no safe rows for any player.

Hand: 2(1), 10(3), 17(1), 39(1), 44(5), 85(2)

As stated earlier, in this example, 9(1) is likely to be taken by a card of 8 or below. Here, ride that trend and play 2(1).
This allows you to avoid penalty points from cards between 10 and 17, and also dispose of the 2 in your hand by taking the minimum penalty of (1).

Mid-Game Tip 2: Play a safe card (when all rows on the board have 3 or more penalty points, and you have a safe card in your hand)

This is a case where, after entering the mid-game, several turns have passed and the state has returned to an early-game-like situation.

Hand: 2(1), 10(3), 17(1), 39(1), 44(5), 85(2)

In this case, following Mid-Game Tip 1, there’s no need to take a card with a number smaller than 11(5).
A 5-point penalty is quite painful, and taking a massive penalty with 2 or 10 should be avoided as much as possible.

On this board, apply Early Game Tip 1.
In this example, the safe card 17(1) ⁷ exists in your hand, so you play it to avoid penalty points.

Mid-Game Tip 3: Play a card with a number larger than A, the tail number of the row with the smallest penalty, and smaller than B, the tail number of the row with the second-smallest penalty (when all rows on the board have 3 or more penalty points, there are no safe cards, and you hold a safe card between A and B that is sufficiently large)

To give an example, I’ll change the hand from Mid-Game Tip 2’s example.

Hand: 2(1), 10(3), 29(1), 39(1), 44(5), 85(2)

Since all rows result in large penalty points, assume all players don’t want to take any row.
If you had a safe card in your hand, you should play it following Mid-Game Tip 2, but in this example, no such card exists.
What you should aim for in this case is to become the player who plays the 6th largest number in the top row. ⁸

If you become the player who plays the 6th largest number, the board after you play would be as follows.
For clarity of the played cards, a #7 that doesn’t normally exist is added.

In reality, since the card in #6 would be placed in #1, your card in #7 would end up in the #2 position.
While not as certain as Mid-Game Tips 1 and 2, this allows you to avoid penalty points.

To create this state, you play the maximum value in your hand that doesn’t exceed 31(1), the tail of the row with the second-smallest penalty.
In this example, 29(1) is large enough to potentially be the 6th card, so you would play it.

However, there is an exception to this tip. It’s when playing a card between A and B could result in taking another row with large penalty points.
Here’s an example of such a case:

Hand: 2(1), 10(3), 29(1), 39(1), 44(5), 85(2)

In Mid-Game Tip 3:

Play a card with a number larger than A, the tail number of the row with the smallest penalty, and smaller than B, the tail number of the row with the second-smallest penalty

in this example, \(A = 11\), \(B = 31\).
If you apply this tip as-is, the card to play would be 29, but playing 29 would almost certainly result in taking the third row from the top and incurring penalty points.

In this case, playing 10(3) from your hand to take 11(5) would be a good choice.
You could also apply the late-game tips described later and play a sufficiently large-number card, but if that fails, you’d take a row other than the top one and incur massive penalty points.
It’s better to take a 5-point penalty and avoid that outcome.

Mid-Game Tip 4: Take a board row with a high-penalty card (when Mid-Game Tips 1 through 3 all cannot be applied)

This is not a tip for reducing penalty points, but rather a tip for preventing the board from becoming favorable for other players.
When this tip is needed, your hand is usually filled with large numbers.
As an example, I’ll change the hand from Mid-Game Tip 1’s example to one with more large numbers.

Hand: 44(5), 57(1), 79(1), 85(2), 95(2), 99(5)

In this case, no matter which card you play, the probability of high penalty points is high.
In this state, if other players play cards between 10 and 30 and you play a high-penalty card from your hand — for example, 44(5) — the next turn would look like this:

If the value of X is small, this becomes a favorable board for players holding cards between 45 and 54.
This is because 44(5) has a high penalty and is less likely to be taken compared to Card A, so they can safely play those cards.
If the value of X is large, for the same reason, it becomes a favorable board for both players holding cards between 45 and 54 and players holding cards between A and 43.

In any case, by using this tip, the cards played on the next turn will be distributed between the top row and the bottom row, returning the board to a state similar to the early game.
It remains a board unfavorable to players holding large-number cards, but the probability of penalty points is lower than if the boards like those in Mid-Game Tips 1 through 3 examples continued.

Also, with this tip, which high-penalty card you play changes depending on your hand state.
As another example, here’s a case where a card of 100 or above exists in your hand:

Hand: 44(5), 79(1), 85(2), 95(2), 99(5), 101(1)

In this case, 99(5) becomes the card you should play.
Since 99(5) has a high penalty and is unlikely to be taken, you can safely play 101(1) from your hand on the next board.
Expressed in generalized terms, when you hold another card that is larger than the high-penalty card you’re playing and sufficiently close to that number, you prioritize playing that high-penalty card.

When all 4 of the above tips cannot be applied, the board is in the late game for you.
Finally, I’ll explain what cards you should play in the late game.

8. Late Game Tips

There is only one late game tip.
This is because there’s little you can do in the late game, and the early and mid-game tips are meant to advance the late game favorably.

Late Game Tip: Play the card whose number is furthest from the tail numbers of each row, excluding rows with obviously large penalty points

Since you’ve exhausted your small-number cards with Mid-Game Tips 1 through 3, in the late game your hand is filled with large numbers.
Also, being unable to apply Mid-Game Tip 4 means you don’t have high-penalty cards in your hand.

However, unless most of your 10 cards are both low-penalty and large-number ⁹, if it’s the late game for you, it’s likely the late game for other players too.

In this case, you’ll play your large-number cards, believing that you hold cards with larger numbers than the other players.

Here’s a late-game example:

Hand: 84(1), 93(1)

In this case, whether you play 84(1) or 93(1) from your hand, there’s a high probability of taking the bottom row and incurring penalty points.
However, other players are also in the late-game hand state, and if their contents are as follows, you may be able to avoid penalty points:

Other player P’s hand: 79(1), 92(1)

The penalty for the third row from the top is 10, and the penalty for the bottom row is 9.
While only a 1-point difference, taking the bottom row results in a smaller penalty score.
Also, 79(1) is too close to 75(2), the tail of the third row from the top, so if P plays 79(1), they’ll almost certainly take that row.
Therefore, P considers 92(1) to have a lower probability of penalty points and will play that card.

Here, if you play 93(1), you avoid penalty points.
This is because P’s card 92(1) takes the bottom row, and 93(1) fits into #2.

When multiple players are in the late game, such exchanges of large-number cards frequently occur.
And whether other players are in the late game can be predicted to some extent.

Let me reiterate the previous late-game example:

At this point, the player who played 69(1) on the previous turn is likely in the late game.

For the player who played 69(1) to place a card in the top row this turn, they would need to have 70(3) or 73(1) in their hand.
However, by Mid-Game Tip 4, 70(3), which carries a somewhat large penalty, is more likely to be played earlier than 69(1), and the fact that this hasn’t happened suggests the probability of holding 70 is low.
Also, since 71 and 72 have already been played on the board, 69 and 73 are consecutive, and by the previously mentioned general tip, the probability of holding 73 is low.
Therefore, there’s a high probability that 69 is the last card of 75 or below for this player.

For this reason, the card the player who played 69(1) on the previous turn will play this turn is almost certainly 76 or above. ¹⁰
If your hand is also in the late game at this timing, play your largest-number card while praying.

Even when there are no other players you think are in the late game, what you can do is the same.
Play your largest-number card while praying.

Example of why you should exclude rows with obviously large penalty points

Even with the same hand, there are cases where you should play 84 instead of 93. Here’s an example:

Hand: 84(1), 93(1)

The card whose number is furthest from the tail numbers of each row is 93(1).
If you apply the late-game tip as-is, 93(1) would be the card to play, but here let’s consider the total penalty points for each row:

The total penalty for the third row from the top is 11, which is clearly larger than the total of 5 for the bottom row.
A penalty of 11 is a significant blow, so you should avoid it even if it means taking 5 penalty points, and therefore on this board, 84(1) is the card you should play.
This is the reason the late-game tip states “excluding rows with obviously large penalty points.”

9. Conclusion

There may be omissions or insufficient explanations, but I currently play 6 nimmt! under this article’s rules generally following these tips.
Most of the tips are written based on my experience, but only Early Game Tip 1: If the row with the largest tail on the board is a safe row, play a safe card was taught to me via chat by a player with an ELO of 500 or above on BGA.
So I can confidently say that Early Game Tip 1 is effective.

This has become a long article, but the most important thing in 6 nimmt! is to not incur penalty points.
The fewer penalty points you incur, the higher you’ll place, and if you can consistently maintain that state, your probability of finishing 1st increases.
The lengthy text I’ve written so far is merely splitting the biggest tip — “don’t incur penalty points” — into smaller tips with concrete examples.

For me currently, these smaller tips are important for avoiding penalty points, but what way of playing cards makes it easier to avoid penalty points varies from player to player.
By all means, play lots of 6 nimmt! and find your own original tips.

This concludes the Day 1 article for Table Game Tansu Advent Calendar 2022.
Tomorrow is Kimunii-san’s About the 2022 German Game of the Year Winner.