BrainKing - 掲示板 (Backgammon)

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6. ７月 2007, 09:59:43

Hrqls

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件名: chances of rolling a 1 in 2 moves

what is the chance of rolling a 1 ?
i think its 11/36 ?

what is the chance of rolling a 1 in 2 moves after another ? (rolling 2 1s in total)
is that 11/36 * 11/36 ?

or can i determine it this way :
(lets assume the chance of rolling a 1 in 1 move is 1/3 to make the calculation a bit easier, and ignore the rule of big numbers)
so i roll a 1 in 3 rolls, for the next move i roll a 1 in 3 rolls as well giving me 2 1's in 6 rolls .. which would lead to a chance of 1/6 to roll a 1 in 2 moves directly after another ? .. hmm .. this doesnt feel right in a lot of aspects .. but i can put my finger on it exactly :)

i am asking this because i am playing tric trac on another site and want to know what my chance is to bear off 2 pieces on the 1 position .. i think its 10/36 * 10/36 + 1/36 = 17/162 ?

6. ７月 2007, 10:07:54

Thad

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件名: Re: chances of rolling a 1 in 2 moves

Hrqls: You want to roll a 1 on two consecutive rolls? Assuming it's ok to roll a pair of 1s, then your calculation of 11/36 * 11/36 (about 0.0933) is correct. So you have about a nine and one third percent chance of rolling at least one 1 on two consecutive turns.

Remember, probability (or chance) is winners divided by total. In this case, a winner is a roll containing a 1, and you were correct that there are eleven of them. There are thirty six total ways of rolling a pair of dice.

Also, when dealing with two disjoint probabilities, simply multiply them together (as you did).

Hope that hleps.

6. ７月 2007, 10:56:38

playBunny

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件名: Re: chances of rolling a 1 in 2 moves

Hrqls:


A single 1 followed by single or double 1      10/36 * 11/36 = 110/1296
Or a double 1                                   1/36         =  36/1296
Or no ones followed by a double 1              25/36 *  1/36 =  25/1296
                                                               ========
                                                               171/1296 = 13%

6. ７月 2007, 12:43:12

Hrqls

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件名: Re: chances of rolling a 1 in 2 moves

playBunny: ah thanks!!!!
thats true .. i forgot about 0 and double or 1 and double which is also sufficient :)

thad and abigailll thanks as well! when i tought it over last night (in my head wihle lying in bed) the chance of 1/3 + 1/3 sounded very nice .. but i knew i was wrong .. in my head i also came to 17/162 by pure match .. but it had big numbers in it so i could easily have mistaken myself :)

btw i forgot about a double 6 being ok as well as tric trac will also make you move double 1 on that roll .. or 1+2 on a roll which also gives double 1 .. hmm the double 6 doesnt work as i would have to move the 6 first .. but 1+2 does work .. ok i am a bit confusing today .. i am suffering from it myself as well :)

thanks!!

6. ７月 2007, 12:09:16

AbigailII

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件名: Re: chances of rolling a 1 in 2 moves

Hrqls: It would be 10/36 * 10/36 if all you want is exactly one 1 on each of the two rolls. But if you want at least two ones in two rolls, the chance is 1/36 + 10/36 * 11/36 + 25/36 * 1/36 == 171/1296 == 0.132. After all, you should consider rolling two 1s on either the first or the second roll.