Let me know how it goes!

]]>I have a quick question. Dont I have to multiply the probability of Wild for each reel with 3? since there are 3 rows on each reel?

Thanks

]]>Note that the entries in each column in the matrix need to add up to 1.

Leftmost column is the probabilities to transfer from initial state to each of the possible states.

I use an additional state “no more spins” as the end state, so that a chain is a complete cycle of original spin possibly followed by a number of re-spins. The top left entry in the transition matrix should thus be zero, since no wilds on initial spin means that we transfer to the end state.

Second column contains the probabilities to transfer from state “wild on Reel 2”. There are four possible states to transfer to, namely “wild

on Reels 2+3”, “wild on Reels 2+4”, “wild on Reels 2+3+4” and “no more spins”. The probabilities are the products of the probabilities of wild/no wild on Reels 3 and 4. The remaining rows in this column are 0.

And so on…

I hope this helps!

]]>Thanks you for reply, I multiply from the left with the transition matrix, which I calculate for all the possible start/end start that WILD can appear on reel 2, 3, 4. But I cant seem to get the result in your article.

Here is my calculation sheet: https://docs.google.com/spreadsheets/d/1XfpluQxZ8PgPdRd-8Arn1ge2p9Xvd7nC4JnT5o78Olk/edit#gid=0

It would be great if you can help point me to the right direction.

]]>What seems to be the problem with your transition matrix?

I use a column vector which I multiply from the left with the transition matrix, thus the entries of each column in the matrix need to sum up to 1. It is common to use row vectors which are multiplied from the right with the transition matrix, the latter of which thus needs to have rows adding up to 1. Could this be causing confusion?

]]>Thanks you for the awesome article. Im trying to recreate the results you show in the article, but I cant seem to be able to get the transition matrix right.

Can you help?

Thanks ðŸ™‚

]]>Itâ€™s quite straightforward to do tumbling reels. However, it is not practically possible to do them in your everyday Excel sheet. I write a piece of code to step through all combinations of initial stop positions. Note that given the reels, the sequence of tumbles is completely determined by the initial stop positions.

Good luck!

]]>Great blog, really informative.

I know this question has nothing to do with sticky wilds but wasn’t sure where else to ask.

If you have a set of reel bands, is it possible to calculate the payout percentage of these bands if they were used as “tumbling reels”, just like da Vinci’s diamonds.

Thanks

]]>State 0 means the initial state, where the reels did not spin yet.

State 8 means the reels have spun at least once, but there are no more respins.

States 1-7 mean one or more reel has a (sticky) wild on it and the other reels will spin again. 1, 2, 4 represent the reels 2, 3, 4 (these are the only reels that have wild symbols on them). If more than one of these reels are wild, the corresponding numbers are added to get the state.

Hope this helps!

]]>Can you kind enough let me know how to apply markov chain for sticky wild. Maybe you can get me some basic example. Thanks

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