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profi boulder caves 26 (4n)
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by
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dustin
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DUSTIN                            2025-06-17 21:26
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WHILE THIS ONE IS PROBABLY NOT ;)

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HEYWOOD                           2025-06-18 00:24
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GIVEN THE RELATIVELY LOW DIAMOND VALUE I WONDER WHAT THE OPTIMUM POINT IS TO TRAP THE AMOEBA AND COLLECT THE TIME BONUS POINTS.

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DUSTIN                            2025-06-18 09:38
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heywood, HERE SOME CALCULATIONS ABOUT THAT:  
  
| AFTER THE ΘΘΘ SLOW GROWTH TIME EXPIRES, THE ΘΘΘ HAS BY DEFAULT A 1/4 CHANCE TO (TRY TO) GROW EACH FRAME.   
  
| HOWEVER, IF THE ΘΘΘ HAS ONLY ONE POSSIBLE DIRECTION TO GROW INTO, IT WILL TRY TO GROW INTO AN IMPOSSIBLE DIRECTION 3 OUT OF 4 TIMES. THIS MAKES THE TOTAL CHANCE FOR IT TO ACTUALLY GROW 1/4 * 1/4 = 1/16 PER FRAME.  
  
| SO, ON AVERAGE, THE ΘΘΘ GROWS ONE STEP EACH 16 FRAMES (IF IT CAN GROW ONLY INTO ONE DIRECTION).  
  
| WITH A SPEED OF 7 FPS, THIS MEANS THE ΘΘΘ TAKES 16/7 = 2.3 SECONDS TO GROW ONE STEP.  
  
| SO WITH 3 POINTS PER BONUS Α, THIS IS STILL A PAYOFF COMPARED TO GETTING JUST ONE POINT PER EXTRA SECOND IN THE END.  
  
| CONCLUSION: IT SHOULD BE MOST PROFITABLE TO JUST LET THE ΘΘΘ GROW AS BIG AS POSSIBLE, AS SHOWN IN darkwood'S RUN.   
  
| HOWEVER, IN THE ORIGINAL, THE SPEED ISN'T EXACTLY 7 FPS; IN FACT, IT VARIES BECAUSE THE SPEED IS QUITE FAST AT THE BEGINNING BUT SLOWS DOWN THE BIGGER THE ΘΘΘ GROWS. SO TO DETERMINE WHAT IS THE BEST HISCORE STRATEGY IN THE ORIGINAL, IT'S PROBABLY BEST TO JUST TRIAL-AND-ERROR IT OUT ;)

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DUSTIN                            2025-06-18 09:48
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EDIT: AS LONG AS THE ΘΘΘ CAN GROW BOTH LEFT AND RIGHT, MAKING IT EFFECTIVELY DOUBLE AS QUICK, IT SHOULD ALWAYS BE MOST PROFITABLE TO LET IT GROW. SO, ALSO IN ORIGINAL, Κ SHOULD AT LEAST LET THE ΘΘΘ GROW UNTIL IT'S GROWN OUT AT THE LEFT SIDE.

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DUSTIN                            2025-06-18 10:00
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...AT LEAST ON LEVEL 1. ON LEVEL 5, WITH 5 POINTS PER REMAINING SECOND, THINGS CAN CHANGE :D