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enter image description here

I have this problem above and I'm trying to think of how to apply alpha-beta pruning to the above. The algorithm states that on you're opponents turn the (expecti turn) you just return the lowest value, but does that mean you apply the probabilities to those values? So for the far left you'd get 2 as the largest value then multiply that by 0.5, but then that set's $\\beta$ in the expecti node to $0.5*2=1$ and when it goes into the branch to the right it's comparing values without the probabilities applied to it when updating $\beta$.

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  • $\begingroup$ Could you please put your specific question in the title? $\endgroup$
    – nbro
    Apr 29 at 10:24
  • $\begingroup$ I don't understand the current title "How to alpha-beta pruning to expectiminimax" because a "verb" is missing. Please, edit your post to fix this. $\endgroup$
    – nbro
    May 4 at 10:18
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alpha-beta-prunning algorithm is using for improve performance and reject the options, which not consist the condition - or it's possible to set some factors of probability to take into consideration or not.

This algorithm work on tree structure - and if there are a lot of levels (10-20) - It allows you to eliminate paths - which will logically not be used - saving memory and computing resources.

In this particular case - for finding the minimum value it works like this:

First branch:

  • Go to B
  • Go to D - and there is 2 and 3 - so return the min 2
  • Go From B to E - and choose 5 - the minimal value in B points is actually 3 - so there isn't need for checking the next - cause everything below E, will be higher than D (3)

Second branch:

  • Go to
  • Go to F - and check 0 and 1
  • If C have 1 - than not necessary to go to G - cause 1 is the smaller.

The given sequence is a simplification - and in the case of this algorithm there are also layers - min & max

enter image description here

Source: https://www.javatpoint.com/ai-alpha-beta-pruning#:~:text=Key%20points%20about%20alpha%2Dbeta,values%20to%20the%20child%20nodes.


Implementation, however, is a more complex matter - unless we do copy and paste :-)

https://gist.github.com/exallium/1446104/5109388cfc21578f555dcac0ba54da680326af7b

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  • $\begingroup$ This answer describes the application of alpha-beta pruning to minimax, not to expectiminimax. $\endgroup$
    – beroal
    Jul 29 at 14:20
  • $\begingroup$ Hi, Whats the difference? $\endgroup$
    – Piotr Żak
    Jul 29 at 14:25
  • $\begingroup$ Alpha-beta pruning for minimax doesn't specify what to do with chance nodes. $\endgroup$
    – beroal
    Jul 31 at 12:10

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