Luck & Morale

Author: tentorium

Since "Heroes 3 SoD" has been released or, perhaps, even earlier fans of "Heroes of Might and Magic" were arguing about the battles: what they are and what they are supposed to be. Should the game be more like a chess match or a poker match?

Players who support the "Chess" point of view choose "WT"- a game version without morale and luck, while players with a "Poker" point of view choose ordinary SoD.

In LWM morale and luck have become an essential part of the game. They are supposed to bring an element of surprise into battles. But, apparently, luck chances aren't random.

Recently the Administration shared this formula with us:

There was an analysis of this formula in some articles. There were tables with probabilities of luck to appear, but all conclusions were rather general.

Let's assume that we would like to use the formula in a specific battle. In addition to those articles, there were tables with chances for each "luck point" at some moments of a battle. But would we check the tables after every turn? Or, what if we need 28th turn? There is a simpler and better method to deduce the probabilities without any "counting" or "cheking". Using this method, we can easily determine the probability of Luck/Morale to appear for each stack at any point of a battle.

The disadvantage of the method is that it perfectly works only when Luck/Morale Points are equal to 2 or 5. But while most players already know chances for 5, just a few know about 2.

Why is it working only for 2 and 5?

Let's rewrite the "Luck Formula", and substitute Luck with Luck=0,2. After simplifying the formula we will get:

Here, a is an amount of moments where luck appeared, b is an amount of moments without luck. This formula is relatively simple, because the probability equation becomes a discrete set of values with a general formula 0.2^(N/4), where N is a natural number or 0.

Let's analyse the method with Luck=0,2.

Let's take a chessboard. There are 8 rows with 8 squares in each. Let's write down probabilities in the bottom row:

Let’s take chess pieces according to stacks, for example:

pawn-sprites, knight- unicorns, 2 bishops with a different colour (so we won't mix it up)- 2 stacks of druids, rook- elite forest keepers, queen- treefolks, king- dragons.

In the beginning of the battle place one chess piece on each row above 20%, it represents the chance of Luck/Morale to appear, so at that point of battle (the first turn) the chance is 0,2 or 20%. Then after one of our stacks has made a move we are looking at whether luck appeared or not. If luck/morale doesn't appear, move the appropriate piece one square forward (to the right). If luck/morale appeared move 4 squares backwards. That's it!

Using this system we can check the chance of Luck/Morale to appear for a current stack at a current turn. The only thing that can happen is if we have to move a piece to the left several squares more than there are on the board. It is a very rare case, but it happens after Luck/Morale appears several times in the row (for one stack). Basically, you can draw several more squares to the left and write:

You can assume that Luck/Morale won't appear for that stack in the battle anymore.

When Luck=0,5, you can also use the ”Chess Method”. Formula:

It is even easier: if luck appears, move an appropriate piece one square to the left. If luck doesn't work, move the piece one square to the right. You are starting from a position 0,5 and usually you will stay around it during the whole battle.

Let's have a look at another ”Luck Values”.

Luck=1

Formula:

The method works here as well, the values of probabilities are:

In the beginning of the battle all stacks have 10% chance of Luck/Morale to appear. If luck doesn't appear, move one square to the right, if it worked, move 9 to the left. If a piece moved out the left side, luck won't appear on that stack anymore. For Luck =1 the method is used until the first time luck appears.

Luck=3

Formula:

When luck=3, the method can't be used. You can only forecast the chances of luck for the first turns:

During the first turn, the probability of luck to appear is 30%. If it doesn't work during the fist turn, the chance is 50% during the second turn. If it doesn't work again, the chance is 84% during the third turn. And if it doesn't work during the first 3 turns, it certainly works on the 4th one.

Luck=4

Formula:

The method doesn't work except for the first time luck appears. The first turn:

During the first turn the chance is 40%. If it doesn't work, the chance is 73% during the second turn. If it doesn't work first 2 times, Luck has to appear during the third turn.

The game becomes more interesting when we suddenly realize that we were playing with our eyes closed before, not knowing the whole situation on the battlefield. We were always focusing only on visual aspects without paying attention to non-visual ones, they include a lot of probabilities, which we have beautifully described using pieces on a chessboard.

Good luck with battles and tournaments!

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