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Hitpoint proposal [very long]
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<blockquote data-quote="Ainamacar" data-source="post: 5806918" data-attributes="member: 70709"><p>These are good comments. I've not played Hero before (only browsed the books a bit) but I have played in other systems with dual-counting mechanics. I'm more favorable to your first suggestion, since identifying if at least one die shows its maximum value is extremely rapid. The maximum value of a wound on any individual attack is very predictable, but it is actually harder to calculate the expected wounds for a fight since the probability of the wound depends on the actual number of dice in the attack, and we need to know the distribution of the number of dice in an attack, not just the total number of dice used in the whole combat. To return some of the spikier feel of counting multiple dice we could do that for critical hits or something. These are rare enough that a little extra work might not be an issue.</p><p></p><p>With the second method I'm not sure that it actually saves much time compared to my original idea or your first suggestion, and the amount of variation round to round isn't that large. Even with 4d4 and 5d6 they are within +/- 1 of the average about 75% of the time. In the 10d6 range it is still about 60% of the time. To me, at least, that's a fair amount of work for not that much gain, and I'd probably just stick with 1/die which is essentially instant.</p><p></p><p>Also note that although the average wound damage of the multi-die system works out to be the same using the Hero system and count-the-dice system, these last two require a person to subtract the wound damage from the total of the dice before it can be applied as vitality damage. If we don't, the total damage of the attack is actually increased by 1/die on average. For example, if a 5d6 damage roll is 1,3,5,6,6, then using the Hero system the total of the dice is 21 and the wound damage is 6. However the attack doesn't do 21 vitality damage and 6 wound damage, it actually does 15 vitality damage and 6 wound damage. This adds an extra step to every single dice roll using these methods, and also means simply adding the dice together actually gives the "wrong" number. I think that would cause plenty of confusion.</p><p></p><p>Finally, there is a trick for using the multiple dice quickly, and I think it is faster than the Hero method by a fair margin. There are two key elements. First, this "dual counting" system partitions the dice into disjoint sets. (That is, each die contributes to either normal or wound damage, but not both). Second, identifying whether a die shows the maximum or not is much faster, generally speaking, than doing any arithmetic with it. Combining these properties we are able to do arithmetic with each die just once, and completely defer the wound calculation until the vitality calculation has been completed. Basically we start totaling damage but simply ignore and set aside dice that show the maximum as they come up. As this involves only recognition it is very rapid. In addition, compared to the Hero method one only needs to recognize one type of value (the maximum) instead of the maximum and 1. Furthermore, in most cases the maximum dice that were set aside can be totaled very easily because they are a) starting from 0 again and smaller numbers are easier, b) there won't be very many of them (i.e. for most attacks there will be none at all, or perhaps one), and c) most often they are multiples of the same number so counting and multiplying is a useful shortcut for anyone that remembers their small integer multiplication tables. In this way most of the time one simply adds the dice like normal without any additional math or sets aside a single die (in which case determining the wound damage is trivial, just as in your first suggestion).</p><p></p><p>For example, on a 5d6 fireball 80% of the time there is either zero or exactly one 6, and essentially no extra effort is required. (This also means that the single maximum dice-method is only faster 20% of the time with this fireball, and even less frequently when rolling fewer and/or larger-value dice!) When rolling 5d6 damage using the fast Hero method 85% of the time the dice will have at least one 1 or 6, which (if I've understood the algorithm) means 85% of the time the person must keep some sort of simultaneous count in their head or look over all the dice again after adding. I'd posit that that is, on average, slower than the multiple dice method by a fair margin. Try the multiple dice method on a few 15d6 rolls, I think you'll be surprised!</p><p></p><p>Thanks again for your comments, these are super fun things to ponder. I almost want to find a 4th grade class and watch them roll dice using these methods to see what comes most naturally to them, and to what degree they can pick up on the shortcuts quickly. <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":)" title="Smile :)" data-smilie="1"data-shortname=":)" /></p></blockquote><p></p>
[QUOTE="Ainamacar, post: 5806918, member: 70709"] These are good comments. I've not played Hero before (only browsed the books a bit) but I have played in other systems with dual-counting mechanics. I'm more favorable to your first suggestion, since identifying if at least one die shows its maximum value is extremely rapid. The maximum value of a wound on any individual attack is very predictable, but it is actually harder to calculate the expected wounds for a fight since the probability of the wound depends on the actual number of dice in the attack, and we need to know the distribution of the number of dice in an attack, not just the total number of dice used in the whole combat. To return some of the spikier feel of counting multiple dice we could do that for critical hits or something. These are rare enough that a little extra work might not be an issue. With the second method I'm not sure that it actually saves much time compared to my original idea or your first suggestion, and the amount of variation round to round isn't that large. Even with 4d4 and 5d6 they are within +/- 1 of the average about 75% of the time. In the 10d6 range it is still about 60% of the time. To me, at least, that's a fair amount of work for not that much gain, and I'd probably just stick with 1/die which is essentially instant. Also note that although the average wound damage of the multi-die system works out to be the same using the Hero system and count-the-dice system, these last two require a person to subtract the wound damage from the total of the dice before it can be applied as vitality damage. If we don't, the total damage of the attack is actually increased by 1/die on average. For example, if a 5d6 damage roll is 1,3,5,6,6, then using the Hero system the total of the dice is 21 and the wound damage is 6. However the attack doesn't do 21 vitality damage and 6 wound damage, it actually does 15 vitality damage and 6 wound damage. This adds an extra step to every single dice roll using these methods, and also means simply adding the dice together actually gives the "wrong" number. I think that would cause plenty of confusion. Finally, there is a trick for using the multiple dice quickly, and I think it is faster than the Hero method by a fair margin. There are two key elements. First, this "dual counting" system partitions the dice into disjoint sets. (That is, each die contributes to either normal or wound damage, but not both). Second, identifying whether a die shows the maximum or not is much faster, generally speaking, than doing any arithmetic with it. Combining these properties we are able to do arithmetic with each die just once, and completely defer the wound calculation until the vitality calculation has been completed. Basically we start totaling damage but simply ignore and set aside dice that show the maximum as they come up. As this involves only recognition it is very rapid. In addition, compared to the Hero method one only needs to recognize one type of value (the maximum) instead of the maximum and 1. Furthermore, in most cases the maximum dice that were set aside can be totaled very easily because they are a) starting from 0 again and smaller numbers are easier, b) there won't be very many of them (i.e. for most attacks there will be none at all, or perhaps one), and c) most often they are multiples of the same number so counting and multiplying is a useful shortcut for anyone that remembers their small integer multiplication tables. In this way most of the time one simply adds the dice like normal without any additional math or sets aside a single die (in which case determining the wound damage is trivial, just as in your first suggestion). For example, on a 5d6 fireball 80% of the time there is either zero or exactly one 6, and essentially no extra effort is required. (This also means that the single maximum dice-method is only faster 20% of the time with this fireball, and even less frequently when rolling fewer and/or larger-value dice!) When rolling 5d6 damage using the fast Hero method 85% of the time the dice will have at least one 1 or 6, which (if I've understood the algorithm) means 85% of the time the person must keep some sort of simultaneous count in their head or look over all the dice again after adding. I'd posit that that is, on average, slower than the multiple dice method by a fair margin. Try the multiple dice method on a few 15d6 rolls, I think you'll be surprised! Thanks again for your comments, these are super fun things to ponder. I almost want to find a 4th grade class and watch them roll dice using these methods to see what comes most naturally to them, and to what degree they can pick up on the shortcuts quickly. :) [/QUOTE]
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