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<blockquote data-quote="Esker" data-source="post: 7894081" data-attributes="member: 6966824">I mean, sure you can, you just lose some distinctions between DCs. But that's what the confirmation mechanic corrects for. Here's another simplified hypothetical to zoom in on a particular aspect of the situation.Suppose I don't have any d20s on hand, and so for the night I decide I'm going to roll a d10 and double the result. First: do you agree that if the target number I need is odd, then this produces the same results as rolling a d20? If I would have needed a 19 or 20, now I need a 10 (which becomes 20). If I would have needed a 17,18,19 or 20, now I need a 9 or 10 (which become 18 or 20).So far so good?Now, on even DCs my success chances are too high. If I would have needed a 20, which should have a 5% chance, now I will get a 20 with a 10% chance. So, to correct for that, I roll a d6 whenever I tie the DC, and subtract 1 on a 3 or lower. Now what are my chances of getting that 20 I need? Well, the only way to do it is to roll a 10 on the d10, and a 4 or higher on the d6. That's a 10% * 50% = 5% chance. What are the chances of hitting a target of 18 or better? I can either: roll a 10 on the d10 (ignoring the d6), which happens 10% of the time, or I can roll a 9 on the d10 and a 4 or higher on the d6, which happens 10% * 50% = 5% of the time. In total, 15%. Just as on a d20.So, if I lost all of my d20s and used this system instead, would it affect the game at all?I agree. And?I explained in my last post what I was plotting. It actually does give you the same values as the PMF, just shifted by 1. Did you add up the values? They actually do sum to 1.</blockquote>

[QUOTE="Esker, post: 7894081, member: 6966824"] I mean, sure you can, you just lose some distinctions between DCs. But that's what the confirmation mechanic corrects for. Here's another simplified hypothetical to zoom in on a particular aspect of the situation. Suppose I don't have any d20s on hand, and so for the night I decide I'm going to roll a d10 and double the result. First: do you agree that [I]if the target number I need is odd[/I], then this produces the same results as rolling a d20? If I would have needed a 19 or 20, now I need a 10 (which becomes 20). If I would have needed a 17,18,19 or 20, now I need a 9 or 10 (which become 18 or 20). So far so good? Now, on even DCs my success chances are too high. If I would have needed a 20, which should have a 5% chance, now I will get a 20 with a 10% chance. So, to correct for that, I roll a d6 whenever I tie the DC, and subtract 1 on a 3 or lower. Now what are my chances of getting that 20 I need? Well, the only way to do it is to roll a 10 on the d10, and a 4 or higher on the d6. That's a 10% * 50% = 5% chance. What are the chances of hitting a target of 18 or better? I can either: roll a 10 on the d10 (ignoring the d6), which happens 10% of the time, or I can roll a 9 on the d10 and a 4 or higher on the d6, which happens 10% * 50% = 5% of the time. In total, 15%. Just as on a d20. So, if I lost all of my d20s and used this system instead, would it affect the game at all? I agree. And? I explained in my last post what I was plotting. It actually does give you the same values as the PMF, just shifted by 1. Did you add up the values? They actually do sum to 1. [/QUOTE]

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