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Farkle on face book12/20/2023 ![]() If I decide to write (number of dice) as d, that makes the chance of losing (4^ d)/(6^ d). That is, for 1 die, there are 4 losers for 2 dice, 16 losers for 3 dice, 64 losers. If you are also of a mathematical bent, you might notice that there are 4 ^ (number of dice) losers for each combination. 216 * 6 total combinations 125 winners * 6 don't-care on the extra die, plus (216 - 152) losers times 2 new winners. We can apply this same logic to four dice. That's better than a half-and-half chance! So, all told: that's 20 red+green winners times 6 blue possibilities PLUS 16 red+green losers times 2 blue winners. The blue die changes those 16 losers to winners in two cases, giving you 32 new winning combinations. ![]() Of the 36 for each red+green, you already get to pick up either the red or green for 20 combinations, leaving 16 losers. There are 36 combinations of red+green where the blue is a 1 or 5, so that's 72 combinations where you get to pick up the blue die. (Good so far the math is still holding up.)īut the blue die does matter! When it's a 1 or 5, we still get to continue. We already know 20 of the red+green combinations allow you to continue if the blue didn't matter at all, that would be 20 * 6 = 120 chances to continue out of 216, which is 5/9 (the common factor is 24). But what's your actual chance of not Farkling? Well, if we imagine adding a blue die to the previously-considered red and green, you get 36 red+green combinations * 6 blue combinations, or 216 total combinations. Of course, with three dice to roll you can hit the big time! Roll triples, and you get a high score. That's still a little better than 1/3, of course. Four of those combinations (1+1, 1+5, 5+1, and 5+5) are already covered by picking up the red die! So that's a total of 20 combinations out of 36, or 5/9. You might jump to the conclusion that your chances are 24/36, or 2/3 - but you'd be wrong. 12 of the combinations have a red die you can pick up, and 12 have a green die you can pick up. There are 36 possible combination when you roll two dice. That's seat-of-the-pants, though let's think about the actual probability. ![]() I figured that rolling two dice gives me that same 1/3 chance, PLUS the possibility that I could pick up both dice so I only picked up one and rolled two. There are six possible values, and only two winners, so your chance of surviving to roll again is 1/3. When rolling a single die, the only way to score is to roll a 1 or a 5. Should I pick up both 1s and roll the single die, or pick up only one die and roll the remaining two? My first problem came up when rolling three dice and getting two 1s and a trash value. Triples score 100 times their face value (so triple 2s are 200, triple 5s are 500), with triple 1s getting a bonus: 1000! Finally, there are two six-dice scores: a straight (1500 points) and three pairs (750 points). This led me to wonder, "What are the odds?" Well, the scoring system isn't too tough. I started calculating how much I "needed this turn", and refusing to bank my points unless I got it. You only get 10 turns to score naturally, this means you should roll more than 1,000 points before banking and moving on to your next turn. It all started when I decided to shoot for the high score. Farkle three times in a row, and you lose 500 points, to boot.īeing the mathematically inclined person I am, I've been trying to find the most advantageous method of picking up the dice. You lose all the points you made this turn. The trick is that if, at any time, you roll no scoring combination, you "Farkle". If you reach at least 300 points, you can "bank" the points you've made this turn and start with 6 fresh dice. If you run out of dice, you get to continue with 6 more. If any of those dice make one of the scoring combinations, you can pick them up and roll the remaining dice again, hoping to score some more. It's a mindless but somehow interesting game.
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