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Is Point Buy Balanced?
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<blockquote data-quote="ECMO3" data-source="post: 9836237" data-attributes="member: 7030563"><p>Right and giving them</p><p></p><p></p><p></p><p>Giving them equal ability scores will not give them equal initiative rolls, an equal number of hits, equal damage done by them and it will not result in them taking the same damage.</p><p></p><p>They will still be unbalanced at the table.</p><p></p><p>You mention initiative - For example, if you and I both have a 14 Dexterity and I roll a 15 on initiative and you roll a 6. I have a higher initiative than you, we are not balanced even though our dexterity is the same. If another player with an 8 Dexterity rolls a 9 initiative, he has a higher initiative than you too. This sort of disparity will exist on every d20 roll you make. You can not eliminate it or reduce it significantly by giving them all equal ability scores. As a matter of fact in this example the ONLY way the imbalance would be eliminated is if you had a 20 Dex, I had a 3 Dex and the other PC had a 16-17. Any other combination of Dexterity scores and it will remain unbalanced. This is an arbitrary and trivial case which is only true for when one PC rolls a 15, one rolls a 6 and one rolls a 9, but this sort of variation will exist on every roll.</p><p></p><p></p><p></p><p>Flipping a coin is a far smaller distribution than the dice we deal with in 5E. If we flipped a coin (1d2) and added that to our stats, you would have a point, but most rolls are a d20 and rolls of other dice where ability bonuses are applied are usually behind or after a d20, giving them an even larger distribution. </p><p></p><p>A better analogy would be if you roll a 20 on a d20 you get $100,000, if I roll a 20 I get $10. The average amount you gain by rolling is $5k, the average I get is 50 cents.</p><p></p><p>However, the chance of a balanced outcome is 90.25%</p><p></p><p>If you change it so we both get $100,000 on a 20 the chance of a balanced outcome is 90.5% or very close to what it was beforehand.</p></blockquote><p></p>
[QUOTE="ECMO3, post: 9836237, member: 7030563"] Right and giving them Giving them equal ability scores will not give them equal initiative rolls, an equal number of hits, equal damage done by them and it will not result in them taking the same damage. They will still be unbalanced at the table. You mention initiative - For example, if you and I both have a 14 Dexterity and I roll a 15 on initiative and you roll a 6. I have a higher initiative than you, we are not balanced even though our dexterity is the same. If another player with an 8 Dexterity rolls a 9 initiative, he has a higher initiative than you too. This sort of disparity will exist on every d20 roll you make. You can not eliminate it or reduce it significantly by giving them all equal ability scores. As a matter of fact in this example the ONLY way the imbalance would be eliminated is if you had a 20 Dex, I had a 3 Dex and the other PC had a 16-17. Any other combination of Dexterity scores and it will remain unbalanced. This is an arbitrary and trivial case which is only true for when one PC rolls a 15, one rolls a 6 and one rolls a 9, but this sort of variation will exist on every roll. Flipping a coin is a far smaller distribution than the dice we deal with in 5E. If we flipped a coin (1d2) and added that to our stats, you would have a point, but most rolls are a d20 and rolls of other dice where ability bonuses are applied are usually behind or after a d20, giving them an even larger distribution. A better analogy would be if you roll a 20 on a d20 you get $100,000, if I roll a 20 I get $10. The average amount you gain by rolling is $5k, the average I get is 50 cents. However, the chance of a balanced outcome is 90.25% If you change it so we both get $100,000 on a 20 the chance of a balanced outcome is 90.5% or very close to what it was beforehand. [/QUOTE]
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