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sumbloke

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About sumbloke

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  1. Randomness XIII: Cognitive Dissonance While You Wait

    I hope noone expects you to not eat jelly beans during Lent...
  2. I rewatched The Sound of Music last night. I haven't seen it for ages. I think the last time might have been when I was sixteen, going on seventeen...
  3. Randomness XIII: Cognitive Dissonance While You Wait

    SWMBO is of Chinese descent, so the lunar new year celebration is more in the forefront of my mind...
  4. Randomness XIII: Cognitive Dissonance While You Wait

    I went to the Blood Bowl World Cup a couple of years ago. There were 912 competitors and I ended up ranked #153. I was not disappointed - I only had one loss out of nine rounds (in round 8) and spent 2/3 of the tournament leading my team. I also ended up the highest ranked Aus/NZ coach (equal points for win/draw/loss with two of them, but I had a better tiebreak score).
  5. Randomness XIII: Cognitive Dissonance While You Wait

    No, no, no. Tesseract perles are the bombs
  6. Randomness XIII: Cognitive Dissonance While You Wait

    Did you learn the whole history of the name?
  7. Randomness XIII: Cognitive Dissonance While You Wait

    https://goo.gl/images/DajQkT
  8. Randomness XIII: Cognitive Dissonance While You Wait

    Well, while you lazy cats get out of bed, I'm heading home for dinner. And I will have Spaghetti with my home made tomato/herbs sauce, including ground beef, mushrooms, zucchini, Garlic and Red Bell Peppers. Top it off with grated cheese and olives on the side, maybe some sweet cheese filled peppers too.. When these were posted, I'd only just got home from doing some overtime... Best sandwich: Vegemite, tomato sauce and cheese. Works even better if toasted, but very nice untoasted.
  9. Randomness XIII: Cognitive Dissonance While You Wait

    I heard a different joke with a similar punchline. A couple of Canadians were trying to get away from it all and decided to go to the furthest place they could. They figured out that this was in the Australian outback. So they fly to Australia and head to the outback and drop into the local pub. There's a bunch of Aussies in there who are surprised to see strangers and one of them goes over to the Canadians and asks "So where are you blokes from?" "Saskatoon, Saskatchewan." The Aussie goes back to his mates and one asks him "So where are they from?" "Dunno, they don't speak English"
  10. Randomness XIII: Cognitive Dissonance While You Wait

    The artist that makes the pigment is named Stuart Semple, and he runs a website called Culture Hustle. The glow pigment is called LIT. And that's about as good of directions that I can give to find it without breaking forum rules and linking directly to it. Really happy the forecast for today changed over the last couple days. When I first looked at it, it was for 4-8 inches of snow starting at about 10pm, which would have meant I was going to be stuck at work until like 5am clearing parking lots and sidewalks. But now it's freezing rain starting at 3am, which means I'll be home and quite possibly in bed before it hits. Thanks for the info. I find his range quite intriguing...
  11. Randomness XIII: Cognitive Dissonance While You Wait

    Any chance for some more details that I can use to find this? Or at least, to find the post on the book of faces?
  12. Randomness XIII: Cognitive Dissonance While You Wait

    Do you want to build a snowman...?
  13. Randomness XIII: Cognitive Dissonance While You Wait

    We've been having a bit of winter here the last half a week. It's supposed to be summer...
  14. Math and Excel Formula Help?

    I've added some comments to the code so it's a bit easier to follow.
  15. Math and Excel Formula Help?

    I can't think of a consistent way to calculate it in Excel, but I threw together some javascript to calculate it. You can run it on a page which has jQuery installed (such as this page). var maxNumberOfDice = 12; // Add a table to the page for the combinations $("body").append("<table id='combinations'><thead><tr><th>Combinations</th></tr></thead><tbody></tbody></table>"); for (var i=1;i<=(maxNumberOfDice+5);++i) { $("table#combinations thead tr").append("<th>"+i+"</th>"); } // Add a table to the page for the probabilities $("body").append("<table id='prob'><thead><tr><th>Probability</th></tr></thead><tbody></tbody></table>"); for (var i=1;i<=(maxNumberOfDice+5);++i) { $("table#prob thead tr").append("<th>"+i+"</th>"); } // Recursive function to calculate the combinations function calculateCombinations(numberOfDice) { var dice = new Array(7); // We want to use the value on the dice and can use element 0 as a total // If we've recursed down to only one die, the table is simple if (numberOfDice == 1) { for ( var i=1; i<=6; ++i ) { dice[i] = [1,1]; } return dice; } // Recurse down to one less die lessDice = calculateCombinations(numberOfDice - 1); // Array for how many possibilities have each total value var totals = new Array(numberOfDice+6); for (var i=1; i<numberOfDice+6; ++i) { totals[i]=0; } var total=0; // Add rows to each table for this number of dice $("table#combinations tbody").append("<tr><td>"+numberOfDice+" dice</td></tr>"); $("table#prob tbody").append("<tr><td>"+numberOfDice+" dice</td></tr>"); // Add combinations to the new array // i is the new die that's just been rolled. All other dice come from the lessDice array for ( var i=1; i<=6; ++i ) { // Initialise the array to zeroes dice[i] = new Array(numberOfDice+1); for (var j=0;j<=numberOfDice;++j) { dice[i][j] = 0; } // runningTotal is used for how many combinations in the lessDice array have a lower high value than the value we're looking at var runningTotal = 0; // Look through the lessDice array (j is the index in that array) for ( var j=1; j<=6; ++j ) { if ( i < j ) { // If the new die is less than the value we're looking at in the lessDice array, we just copy those values over and add them to the tallies we have going for (var k=1; k< lessDice[j].length; ++k) { dice[j][k] += lessDice[j][k]; dice[j][0] += lessDice[j][k]; totals[j+k-1] += lessDice[j][k]; total += lessDice[j][k]; } } else if (j == i) { // If the new die is equal in value to what we're looking at, // the "single maximum die value" ([i][1]) is set to the runningTotal i.e., the number of combinations with a lower maximum die // the rest of the values are copied over but shifted one space over because there is one more die of this maximum value dice[i][0] += runningTotal; dice[i][1] += runningTotal; totals[i] += runningTotal; total += runningTotal; for (var k=1; k< lessDice[i].length; ++k) { dice[i][k+1] += lessDice[i][k]; dice[i][0] += lessDice[i][k]; totals[i+k] += lessDice[i][k]; total += lessDice[i][k]; } } runningTotal += lessDice[j][0]; } } // Populate the table. cumulativeTotal starts at the total value and gets decreased, to calculate probabilities of rolling i or higher var cumulativeTotal = total; for (var i=1; i<numberOfDice+6; ++i) { $("table#combinations tbody tr").last().append("<td>"+totals[i]+"</td>"); $("table#prob tbody tr").last().append("<td>"+((0.0+cumulativeTotal) / total)+"</td>"); cumulativeTotal -= totals[i]; } return dice; } calculateCombinations(maxNumberOfDice); The results for up to 12 dice are: Combinations 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 2 dice 0 3 5 7 9 11 1 3 dice 0 3 16 34 58 88 16 1 4 dice 0 4 38 137 319 609 167 21 1 5 dice 0 5 90 495 1596 3866 1426 271 26 1 6 dice 0 6 207 1718 7534 23197 10803 2759 400 31 1 7 dice 0 7 469 5810 34370 134015 75622 24319 4733 554 36 1 8 dice 0 8 1052 19344 153346 754472 500990 194553 47603 7473 733 41 1 9 dice 0 9 2340 63741 674058 4170843 3189282 1452438 428428 84469 11104 937 46 1 10 dice 0 10 5165 208470 2932255 22756502 19705569 10299876 3557313 844691 139356 15751 1166 51 1 11 dice 0 11 11319 677864 12659471 122965062 118987055 70211757 27791313 7719943 1532917 217328 21539 1420 56 1 12 dice 0 12 24642 2193568 54342017 659601288 705552925 463919852 207034938 65860300 15290429 2607937 324074 28593 1699 61 1 Probability 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 2 dice 1 1 0.9166666666666666 0.7777777777777778 0.5833333333333334 0.3333333333333333 0.027777777777777776 3 dice 1 1 0.9861111111111112 0.9120370370370371 0.7546296296296297 0.4861111111111111 0.0787037037037037 0.004629629629629629 4 dice 1 1 0.9969135802469136 0.9675925925925926 0.8618827160493827 0.6157407407407407 0.14583333333333334 0.016975308641975308 0.0007716049382716049 5 dice 1 1 0.9993569958847737 0.9877829218106996 0.9241255144032922 0.7188786008230452 0.22170781893004116 0.03832304526748971 0.003472222222222222 0.0001286008230452675 6 dice 1 1 0.9998713991769548 0.995434670781893 0.9586119684499315 0.7971322016460906 0.2999399862825789 0.06839420438957476 0.009259259259259259 0.0006858710562414266 0.00002143347050754458 7 dice 1 1 0.9999749942844078 0.9982996113397348 0.9775448673982624 0.8547668038408779 0.37603237882944673 0.10589206104252401 0.019018632830361225 0.002111196844993141 0.00013217306812985825 0.0000035722450845907635 8 dice 1 1 0.9999952370065539 0.999368903368389 0.9878519852156683 0.8965537360920591 0.447360587181832 0.14908407636031093 0.03325224336991312 0.00491064624295077 0.00046141499009297364 0.000025005715592135344 5.953741807651273e-7 9 dice 1 1 0.9999991069387288 0.9997669110082305 0.9934419533988721 0.9265558318091754 0.5126871261050144 0.19621776644185338 0.05209375238149672 0.009581257462023065 0.0011994805161814764 0.00009764136564548088 0.000004663764415993497 9.92290301275212e-8 10 dice 1 1 0.9999998346182831 0.999914414961515 0.9964667023097343 0.9479725656869719 0.5716216285944724 0.2457275452643144 0.0753864276120256 0.01655497447035513 0.0025853296891141255 0.0002806362353723179 0.000020143493115886805 8.599849277718505e-7 1.65381716879202e-8 11 dice 1 1 0.9999999696800186 0.9999687704191293 0.9981003318836192 0.9632062477375781 0.6242700299089528 0.2962986392039521 0.10276962390786325 0.026166706270075134 0.004887749144248844 0.0006624750560269155 0.0000634404265948619 0.000004071146597176357 1.5711263103524191e-7 2.7563619479867003e-9 12 dice 1 1 0.9999999944872761 0.9999886741087557 0.9989809628811689 0.9740165849085611 0.6709999363941916 0.34687339726740596 0.1337515594393357 0.038641021938171406 0.008385217804339993 0.0013608916936746036 0.00016282197541683837 0.000013944435094864718 8.089922317340965e-7 2.848240679586257e-8 4.593936579977834e-10
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