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| This gets very nerdy by you're my only hope 10/16/2017, 12:16pm PDT | ||||
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to hit get any higher? wrote: There are better units that have a higher chance to hit. We're assuming with the example that both sides have exactly the same forces. But yes the +1 is definitely more valuable when units have a higher chance to hit. That's another point I was saying that the +1 isn't better in the late game. And any combat bonus is more important the more fighting you're doing relative to... can you do anything else in this game? Yes? But we're talking strictly about the combat. Does losing one unit early on hurt as much as losing however many towards the end? What is Other Guy's idea of a bonus that's useful on the first turn? Losing units early hurts more. You can throw your early expansion unit at your opponent's and losing that unit is going to cripple your early expansion and possibly the game. Think of losing your starting colony ship in Master of Orion. The argument you describe is either two people talking at cross purposes or your friend is retarded. It's strictly about the probability of the +1 in combat. I'm saying the bonus is exactly the same and more dice just cements the law of averages. He's saying the probability actually gets higher. I woke up this morning to find that he actually wrote a simulation to run 10,000 simulated fights in a 2vs2 battle, a 5vs5, and a 8vs8 of the same unit. It says the final win chance in each instance for the side with the +1 is 58.4%, 68.5%, 73.8%, and then points to that saying it proves the +1 is more valuable in higher count battles. I told him it's just the law of averages ensuring a "win", but that it's treating all victories as exactly the same which throws the whole point out the window. A battle with fewer rolls is going to have a higher chance of crushing defeats or victories (skewed towards extreme victories) while lots of rolls is just going to average out to the +1 side being ensured a minor victory. That sim treats Pyrrhic victories the same as total victories with no losses. I came up with the example of betting a set amount of money, say $100. You set the odds of winning a single bet at 60%. Then, it doesn't matter if you bet it all on one roll or spread it out to one hundred $1 bets. In the end, the mean for both will be exactly the same ($20 ahead). The only difference is the mode for the first group will be +$100 ahead while the mode for the 2nd group will be +$20. The only possible results for the first group is -$100 or +$100, with 60% having +$100 so it's a bigger risk that you'll lose money but it's balanced out by the possibility of higher winnings. Then he actually made these graphs out of the sim o_O https://imgur.com/a/Eh8LF Showing the results of when both sides hit on an 8 or more (10 sided die) vs one side hitting on 7 or more. He's saying it clearly proves the red side does better at higher unit counts. All I'm seeing is it proves the extreme results on the left and right ends become more unlikely as the chances for a middle of the road result increases. |
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Hey math nerds! by 10/15/2017, 10:02pm PDT  Does combat itself become more common later on? Do the numbers you need to roll by 10/16/2017, 1:48am PDT This gets very nerdy by 10/16/2017, 12:16pm PDT Is the fighting iterative? by 10/16/2017, 1:11pm PDT It is by 10/17/2017, 1:00pm PDT Is there an answer to this? by 10/22/2017, 2:43pm PDT |
