tag:blogger.com,1999:blog-4167684119478977136.post705329185867279469..comments2024-03-22T08:23:38.715+00:00Comments on Trouble At T’Mill - a wargaming blog: Probability for Wargamers 2 - The Gambler's FallacyMike Whitakerhttp://www.blogger.com/profile/02165272678144625943noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-4167684119478977136.post-83113443915701117202017-10-11T22:46:29.412+01:002017-10-11T22:46:29.412+01:00As a corollary, a gaming buddy of mene hates oppos...As a corollary, a gaming buddy of mene hates opposed die rollsfor combats. "Even with great odds, it's no good if you roll a 1 and your opponent rolls a 6" he says. I say it's the same as if you roll 2xD6 and get a total of 2. I even re-wrote a CRT to show it. He still wouldn't have itnitpickergeneralhttps://www.blogger.com/profile/04155941088394913107noreply@blogger.comtag:blogger.com,1999:blog-4167684119478977136.post-26292778489781846252012-09-29T15:29:09.491+01:002012-09-29T15:29:09.491+01:00I've enjoyed these posts and comments. I hav...I've enjoyed these posts and comments. I have a least one friend who moans about dice luck and the dice gods being against him who should visit here and read these posts.<br />Cheers,<br />MikeMad Padrehttps://www.blogger.com/profile/00410143683610813671noreply@blogger.comtag:blogger.com,1999:blog-4167684119478977136.post-86707657306645866032012-09-28T10:44:26.008+01:002012-09-28T10:44:26.008+01:00I thought I'd leave off replying to this one f...I thought I'd leave off replying to this one for a while.<br /><br />After all...<br /><br />...there is an art to the building up of suspense.Mike Whitakerhttps://www.blogger.com/profile/02165272678144625943noreply@blogger.comtag:blogger.com,1999:blog-4167684119478977136.post-74060027934778688632012-09-27T18:49:15.657+01:002012-09-27T18:49:15.657+01:00Heads
Heads
Heads
Heads
Heads
Heads
Qu...Heads<br /><br /><br />Heads<br /><br /><br />Heads<br /><br /><br />Heads<br /><br /><br />Heads<br /><br /><br />Heads<br /><br /><br />Quote - Tom Stoppard - Rosencrantz and Gildernstren are Dead (scene 1)Piscatoreshttps://www.blogger.com/profile/09993952341776678764noreply@blogger.comtag:blogger.com,1999:blog-4167684119478977136.post-20714527344797468722012-09-26T12:44:58.172+01:002012-09-26T12:44:58.172+01:00The odds are the same as getting it wrong 17 times...The odds are the same as getting it wrong 17 times but I'm pretty sure the tosser (oh, come on, I couldn't leave that pun just lying there) wouldn't have raised an eyebrow over that :-)Erwin Randomhttps://www.blogger.com/profile/13017053959009769346noreply@blogger.comtag:blogger.com,1999:blog-4167684119478977136.post-32110139634982242102012-09-23T23:29:07.014+01:002012-09-23T23:29:07.014+01:00AJ The probability that the coin toss can be pred...AJ The probability that the coin toss can be predicted 17 times in succession might be regarded as 100% - certain - as it's bound to happen sooner or later. <br /><br />But seriously, on that occasion, the probability would by 1 chance in 2 raised to the power of 17. That is 1 in 131,072 or 131071:1 against.<br /><br />But remember Granny Weatherwax's Law of Probability: Million-to-one shots crop up nine times out of ten. :-)Archduke Piccolohttps://www.blogger.com/profile/15533325665451889661noreply@blogger.comtag:blogger.com,1999:blog-4167684119478977136.post-54021210601693422532012-09-23T23:24:50.738+01:002012-09-23T23:24:50.738+01:00That was one of the things I was trying to demonst...That was one of the things I was trying to demonstrate.Archduke Piccolohttps://www.blogger.com/profile/15533325665451889661noreply@blogger.comtag:blogger.com,1999:blog-4167684119478977136.post-67846260892545761292012-09-23T20:48:24.211+01:002012-09-23T20:48:24.211+01:00It is, as I think I noted earlier, easier to note ...It is, as I think I noted earlier, easier to note that P(succeeding) == 1 - P(failing all three).<br /><br />There's a reason they work out to the same :DMike Whitakerhttps://www.blogger.com/profile/02165272678144625943noreply@blogger.comtag:blogger.com,1999:blog-4167684119478977136.post-81785481896997191022012-09-23T16:23:07.268+01:002012-09-23T16:23:07.268+01:00I once correctly called the coin toss seventeen ti...I once correctly called the coin toss seventeen times in succession. What are the odds of that? (It totally freaked-out the guy tossing the coin! =)A Jhttps://www.blogger.com/profile/07834159033854153921noreply@blogger.comtag:blogger.com,1999:blog-4167684119478977136.post-26581817152325666742012-09-23T14:40:40.522+01:002012-09-23T14:40:40.522+01:00The probability of getting 3+ in three rolls is pr...The probability of getting 3+ in three rolls is precisely the same whether they are rolled simultaneously or one after the other, stopping when you achieve the result. <br />P(success) = 1 - P(failure) = 26/27<br /><br />But the rolls in sequence can be expressed as a SUM of probabilities, taking each in turn:<br />P(success) = P(hit on the first roll) + P(hit on the second roll GIVEN THAT YOU MISSED ON THE FIRST) + P(hit on the third roll GIVEN THE PREVIOUS TWO ROLLS WERE MISSES). Now the second and third terms of the right side of this equation are in fact products of probabilities, as appears in the following equation. <br />P(success) <br />= P(hit on the 1st) + P(hit on the 2nd) x P(miss on the first) + P(hit on the 3rd) x P(miss on the 2nd) x P(miss on the 1st)<br /><br />=2/3 + 2/3.1/3 + 2/3.1/3.1/3<br />=18/27 + 6/27 + 2/27<br />=26/27 ... as above.<br /><br />If you miss on the first roll, that probability collapses: you now in effect have zero chance of rolling 3+ on the first roll, since we have established that you didn't (does that make sense?). But you still have 2/3 chance of success on the 2nd roll, and if that carks out, 1/3.2/3 chance of success on the third.<br /><br />Adding gives you <br />P(success after missing on 1st roll) = 2/3 + 1/3.2/3 = 2/3[1+1/3] = 2/3.4/3 = 8/9 ~ 89%<br /><br />And of course, if you miss on the first two, the probability of hitting on either of those rolls collapses to zero, and you are left with 2/3 of a chance on you final roll - 67%.<br />Cheers,<br />Ion<br /><br /><br /> <br /><br />Archduke Piccolohttps://www.blogger.com/profile/15533325665451889661noreply@blogger.com