Is there any automated way to calculate the slot machine reels icons based on the LIMITS:

  • of reels

  • of lines

  • % that is returned to player
  • Include free spin icon or not
  • Include bonus game or not

I am only looking for an automated way, as there is already a post about manual calculation per case Here

Also note, that I don't explicitly set how many different icons there can be (banana/cherry, bar, 7, etc), this is free for the algorithm to decide.

Edit: seems like my question was not understood.

A simple example, in a 3x1 slots machine (only one line of icons on the end result) would be this:


  • 3 reels
  • 1 line
  • 50%
  • no
  • no


  • Randomly start with the minimum type of different icons, ie 5
  • randomly construct a reel of size 10(all reels have to be the same for the game to be fair)
  • Calculate chance of each icon type appearing (easy, just examine all 10*10*10 routes for this example)
  • Ad hoc start with a base 1.000 points payout
  • Each icon will have a payout value of it's probability * 1.000 * 0,50

PROBLEM SOLVED (in this simpler case). I'm looking for a more general solution, thats all


2 Answers 2


There are a lot more variables in play then you have listed as both the free spins and bonus games will also have their own set of probabilities and payouts pending of the scope of the games.

Most (if not not all) casino slot machines will have weightings associated with how often symbols 'land' on the win lines so it is possible to calculate the icon order on the reels and the symbol probabilities based on the first four limits you have listed although more information is needed about the payouts and winning combinations. I just don't think there is an off the shelf solution so you have to model it yourself.

The last two limits will need more information as the percentage payout will change based on the game mechanics and weightings of the free spin and bonus games.

The gambling industry hires mathematicians to model games on slot machines as bonus games and even free spin games can be wildly different from one game to another.

  • \$\begingroup\$ Free spins just add recursion to the probability, so thats a solvable problem. For the bonus game, if it pays out points, you can factor in the average base points, and if it pays out multipliers you can factor in the average multiplier (same goes with all icons that produce points and multipliers, jackpots, etc, I just added this exception to further illustrate the difference) \$\endgroup\$ Dec 10, 2011 at 16:29

I think you may have misunderstood something in the related question.

This is a problem of probability and everything that was previously stated directly applies. It's only "manual" in as much as he's using constants. You would merely replace those constants with whatever variables you're using.

Part of that is knowing how many possible icons there are. For example, you wouldn't expect a machine with reels of two icons to have the same probability of success as a reel with seven icons. You would have to calculate how many possible icons they have first then calculate the spin as was explained in the previous question.

  • \$\begingroup\$ The logic in your post is flawed in the sense that it doesnt really matter what the probability is, as long as you can tweak the payout per icon type. IE: if we have 100 icons that worth 1 point each, and 1 icon that worths 1 point, probability may be different but the payout is exactly the same. My question isn't about finding the probability X for each Y icons, but rather "how many Y icons we need with a mixed payout of % and how are we going to arrange them" \$\endgroup\$ Dec 10, 2011 at 16:13
  • \$\begingroup\$ Forgive me, I guess I didn't fully understand that. After reading your edit it seems that you have the understanding of the issue but you're trying to find a generalized formula of sorts. I would suggest this post for adjusting the odds/payout rate stackoverflow.com/questions/3986249/… \$\endgroup\$
    – Mike Cluck
    Dec 10, 2011 at 17:04
  • \$\begingroup\$ thanks for the find! I am going to read up on it and also maybe post on the math exchange \$\endgroup\$ Dec 10, 2011 at 18:02

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