Reply to thread

Message

<blockquote data-quote="TwoSix" data-source="post: 9551197" data-attributes="member: 205">I was a little confused at first, because the results didn't match my gut intuition.&nbsp; But if you plug it into a spreadsheet, and draw a little picture, it makes more sense.Assuming A is success on a 15- (75% chance), and B is success on a 5- (25% chance).A and B both fail 75 out of 400 combinations, or 3/16.&nbsp; Importantly, I'm assuming that &quot;high wins&quot; and &quot;low wins&quot; DOESN'T MATTER in this case, since both sides failed.&nbsp; Since &quot;both fail&quot; is the converse of &quot;both succeed&quot;, but high/low doesn't matter, this means the portion of the odds where both succeed has a larger influence on the overall ratio of win vs losses than might initially be intuited.A passes, B doesn't:&nbsp; 225/400, or 9/16B passes, A doesn't: 25/400, or 1/16This leaves the block from [1,1] to [15,5], 75 combinations, where both succeed. 5 are ties (the diagonal from [1,1] to [5,5]).The remaining 20 combinations in the square from [1,1] to [5,5] are going to be divided evenly, 10 and 10, between A and B no matter which way the high/low rule is applied.Where the high/low rule matters are the last 50 combination, the block from [6,1] to [15,5].&nbsp; Since that block ONLY has values where A&gt;B, then the high/low rule completely determines whether or not A or B wins the block.&nbsp; And those 50/400 combinations are what tilt the odds so much depending on whether or not you use &quot;low roll wins&quot; or &quot;blackjack style&quot;.[ATTACH=full]391859[/ATTACH]</blockquote>

[QUOTE="TwoSix, post: 9551197, member: 205"] I was a little confused at first, because the results didn't match my gut intuition. But if you plug it into a spreadsheet, and draw a little picture, it makes more sense. Assuming A is success on a 15- (75% chance), and B is success on a 5- (25% chance). A and B both fail 75 out of 400 combinations, or 3/16. Importantly, I'm assuming that "high wins" and "low wins" DOESN'T MATTER in this case, since both sides failed. Since "both fail" is the converse of "both succeed", but high/low doesn't matter, this means the portion of the odds where both succeed has a larger influence on the overall ratio of win vs losses than might initially be intuited. A passes, B doesn't: 225/400, or 9/16 B passes, A doesn't: 25/400, or 1/16 This leaves the block from [1,1] to [15,5], 75 combinations, where both succeed. 5 are ties (the diagonal from [1,1] to [5,5]). The remaining 20 combinations in the square from [1,1] to [5,5] are going to be divided evenly, 10 and 10, between A and B no matter which way the high/low rule is applied. Where the high/low rule matters are the last 50 combination, the block from [6,1] to [15,5]. Since that block ONLY has values where A>B, then the high/low rule completely determines whether or not A or B wins the block. And those 50/400 combinations are what tilt the odds so much depending on whether or not you use "low roll wins" or "blackjack style".[ATTACH=full]391859[/ATTACH] [/QUOTE]

Verification