| --- Log opened Sun Jun 07 00:00:56 2020 |
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| 06:27 | <&McMartin> | Oh hey, Rust made the top 20 in the TIOBE index, displacing Objective-C |
| 06:27 | <&McMartin> | It's a silly metric but still the one I think of as the best one people commonly use. |
| 06:28 | <&McMartin> | (It's basically doing google searches for programming sites/posts/etc about the languages, but this measures active churn in/discussion about the language and its use, which is usually the metric I want.) |
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| 12:14 | | * Reiver ponders a theoretically simple, but perhaps not, math problem |
| 12:15 | <&Reiver> | There is an ancient dice game called OWZAT, a skill-free dice-rolling 'simulation' of cricket. |
| 12:15 | | * Vorntastic perks up |
| 12:15 | <&Reiver> | Two dice are used: One has values 1, 2, 3, 4, 6, and OWZAT (How's that, the appeal one makes to the Umpire when convinced the batter is out) |
| 12:16 | <&Reiver> | The second dice is the Umpire dice - I won't bore you with the specifics, but boils down to 4/6 chances of OUT, 1/6 0, 1/6 +1 run & roll again. |
| 12:17 | <&Reiver> | (Representing the 4 kinds of OUT you can get, a NOT OUT, and a NO BALL, in which you get a free run added to your score and another go as penalty for the bowler screwing up) |
| 12:18 | <&Reiver> | Simply put, you roll the first dice, adding the score as you go, until you get an OWZAT, at which point you roll the Umpire dice to determine the 'batsman's fate. Ten batsmen out means it's all over. |
| 12:18 | <~Vorntastic> | Okay. |
| 12:19 | <&Reiver> | ... Given this is entirely probabilistic, what's the average score you'd expect? |
| 12:20 | <~Vorntastic> | Okay, so, when you say Roll Again on the umpire die do you roll the *umpire die* again or... |
| 12:20 | <&Reiver> | Ah, no, the batting die |
| 12:20 | <~Vorntastic> | And if it's the regular die what's the difference between not out and no ball |
| 12:20 | <&Reiver> | The 'roll again' aspect is because, /technically/, there is a limit to the maximum number of rolls allowed |
| 12:21 | <&Reiver> | NOT OUT: Carry on |
| 12:21 | <&Reiver> | NO BALL: Add one run to your total, carry on |
| 12:21 | <~Vorntastic> | Technically? |
| 12:21 | <&Reiver> | Well |
| 12:22 | <&Reiver> | Depending on how you want to run it, and the original ruleset (which was a slip of paper), it's either 50 rolls or /300/ |
| 12:22 | <~Vorntastic> | Hahaha, okay |
| 12:22 | <&Reiver> | I ... do not especially believe either limitation comes up very often |
| 12:22 | <~Vorntastic> | Okay let's see |
| 12:22 | <&Reiver> | Though it might matter on 50! |
| 12:23 | <~Vorntastic> | Yes, the expected length of a game is 90 rolls |
| 12:23 | <&Reiver> | (One-day innings have 50 overs. In proper field cricket, each Over is 6 bowls... plus extras for any No Balls, because you can't waste a batsmans time that way, even if you wanted to) |
| 12:23 | <&Reiver> | aha, interesting already |
| 12:26 | <~Vorntastic> | Let's see |
| 12:26 | | * Reiver eyes that. If the average is 90 rolls, and the average roll is (1+2+3+4+6+1/6)/6*90, is that it? |
| 12:26 | <~Vorntastic> | For expectation, yeah |
| 12:29 | <~Vorntastic> | The actual distribution is a different matter but that's the average, 242.5 or so |
| 12:29 | <&Reiver> | huh. |
| 12:30 | <&Reiver> | 1) What's the distribution like? |
| 12:30 | <~Vorntastic> | That's a deeper question indeed, probably best answered with Monte Carlo methods for a first pass. |
| 12:30 | <&Reiver> | Yikes. Alrighty then! |
| 12:30 | <&Reiver> | 2) What happens with the 50-roll limit, bearing in mind the 1-in-36 chance of getting an extra roll... okay that last wrinkle looks way less interesting when phrased like that, huh |
| 12:31 | <&Reiver> | That would work out to be... muliply by 51.5 instead of 90, roughly speaking, right? |
| 12:31 | <~Vorntastic> | You on average get 1.35ish bonus rolls per game yes |
| 12:32 | <&Reiver> | Averaging to 138, ish. |
| 12:32 | <&Reiver> | What's interesting is that is not a completely unreasonable score for a one-day innings. |
| 12:33 | <&Reiver> | Of course, the real deal actually involved 300 throws, but also you have /dramatically/ different odds of getting a 6 vs a 0 there~ |
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| 12:37 | <~Vorntastic> | It is possible to run this exhaustively of course; the big trick is to make sure that each state is only processed for die rolls after every path to it has been taken |
| 12:38 | <~Vorntastic> | Which is thankfully possible because every roll is guaranteed to increase something. |
| 12:39 | <~Vorntastic> | (regular is bats and runs; out is bats and outs, not out is bats only, and no ball is runs only) |
| 12:40 | <&Reiver> | ah-hah |
| 12:41 | <~Vorntastic> | (though 1-cycles, where a move does nothing, is also relatively easy to deal with) |
| 12:46 | <&Reiver> | interesting |
| 12:49 | <~Vorntastic> | Bad news is this is actually also technically infinite, because it is technically possible to get owzat-no ball over and over and over, but you can just... Stop trying after a while because it's a rare enough occurrence that after like 200 of those you've reached "too small to fit in a double" territory anyway |
| 13:06 | <&Reiver> | Yeah, was going to say, it's /technically/ infinite, by that one tiny roll |
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| --- Log closed Mon Jun 08 00:00:58 2020 |