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Michael Hartisch,
a German computer scientist, and scientific staff at department of technology management, faculty of business administration, University of Siegen, headed by Ulf Lorenz [1]. In 2015, Michael Hartisch solved the game Karl’s Race by using retrograde analysis [2]. Karl’s Race is a game of chance invented by Ingo Althöfer in 2006 as "little brother" of EinStein würfelt nicht!, and in honor of Karl Scherer [3] [4]. Further, along with Ingo Althöfer, Michael Hartisch introduced chess endgame tablebases, as usual constructed by retrograde analysis, but not optimized for shortest mate, but shortest time used by robots to execute moves and specially captures in blitz chess matches like KUKA vs. ChessKA [5].

Impact of Rounding

Excerpts of Impact of Rounding during Retrograde Analysis ... [6]:

Abstract

We investigate the game “Karl’s Race” which has elements of chance and is closely related to “Ein-Stein Würfelt Nicht!”. Its state space is significantly smaller, without losing its fascination and complex nature. This game can be analysed completely by using retrograde analysis and thus creates an excellent testing ground for other heuristics dealing with games with chance nodes.

Since analysing games with chance nodes requires saving expected values, and thus rational numbers, an enormous amount of memory is required during the calculation and when saving the exact data. Therefore, we examine the effect of intentional rounding during the retrograde analysis. We find that certain types of rounding only slightly affect the playing strength of players using these data while reducing the required memory space to 25 percent.

Conclusion

We solved the game Karl’s Race by using retrograde analysis. The complex game tree and the large maximum length of the game make Karl’s Race a perfect test bed for heuristics, since their performance can be compared to the actual perfect player. Especially when investigating the functionality of the heuristics such as MCTS and UCT we need interesting games that constitute a challenge, but are sufficiently small to be kept under control. The presented game has these properties and is a two-person zero-sum game with random events.

We further investigated how intentional rounding during the retrograde analysis affects the playing strength of the player using these inaccurate data. Rounding to two or three digits turned out to lessen the strength only slightly: Winning rates were still very close to 50%. Rounding to one digit reduced this quota to 45% or even less when using inadequate rounding techniques. Especially the results for rounding to two digits are appreciable: Using rounded 2-digit values during the retrograde analysis allow us to store only one byte per position during the calculation as well as afterwards when saving the data. This is a reduction of 75% compared to saving four bytes per position when using float variables.


Selected Publications


External Links


References

  1. ^ Lehrstuhlteam | Betriebswirtschaftslehre (Prof. Dr. Ulf Lorenz)
  2. ^ Michael Hartisch (2015). Impact of Rounding during Retrograde Analysis for a Game with Chance Nodes: Karl’s Race as a Test Case. ICGA Journal, Vol. 38, No. 2
  3. ^ Karl's Race A Game on Karl Scherer's Alternating Tiling by Ingo Althöfer, 2006
  4. ^ Square The Square by Karl Scherer
  5. ^ Michael Hartisch, Ingo Althöfer (2015). Optimal Robot Play in Certain Chess Endgame Situations. ICGA Journal, Vol. 38, No. 3
  6. ^ Michael Hartisch (2015). Impact of Rounding during Retrograde Analysis for a Game with Chance Nodes: Karl’s Race as a Test Case. ICGA Journal, Vol. 38, No. 2

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