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Posted 02 September 2012 - 07:59 PM
Posted 02 September 2012 - 08:15 PM
Posted 02 September 2012 - 09:07 PM
Posted 03 September 2012 - 01:44 AM
Here are the exact odds using Matlab:The easiest way to compute those probabilities is by taking the polynomial P = 0.1*x + 0.1*x^2 + ... + 0.1*x^10, and computing the coefficients of P^10.
I'll try to figure out the odds if I get some time tomorrow. I have some tennis to watch now.
>> d = 0.1*ones(10, 1); >> p = 1; >> for n=1:10, p=conv(p, d); end >> p p = 0.000000000100000 0.000000001000000 0.000000005500000 0.000000022000000 0.000000071500000 0.000000200200000 0.000000500500000 0.000001144000000 0.000002431000000 0.000004862000000 0.000009236800000 0.000016786000000 0.000029338000000 0.000049522000000 0.000081004000000 0.000128748400000 0.000199292500000 0.000301015000000 0.000444372500000 0.000642070000000 0.000909127000000 0.001262800000000 0.001722325000000 0.002308450000000 0.003042737500000 0.003946630600000 0.005040293500000 0.006341258000000 0.007862932000000 0.009613054000000 0.011592197200000 0.013792438000000 0.016196306500000 0.018776131000000 0.021493874500000 0.024301538800000 0.027142181000000 0.029951548000000 0.032660287000000 0.035196634000000 0.037489438900000 0.039471355000000 0.041082002500000 0.042270910000000 0.043000045000000 0.043245764000000 0.043000045000000 0.042270910000000 0.041082002500000 0.039471355000000 0.037489438900000 0.035196634000000 0.032660287000000 0.029951548000000 0.027142181000000 0.024301538800000 0.021493874500000 0.018776131000000 0.016196306500000 0.013792438000000 0.011592197200000 0.009613054000000 0.007862932000000 0.006341258000000 0.005040293500000 0.003946630600000 0.003042737500000 0.002308450000000 0.001722325000000 0.001262800000000 0.000909127000000 0.000642070000000 0.000444372500000 0.000301015000000 0.000199292500000 0.000128748400000 0.000081004000000 0.000049522000000 0.000029338000000 0.000016786000000 0.000009236800000 0.000004862000000 0.000002431000000 0.000001144000000 0.000000500500000 0.000000200200000 0.000000071500000 0.000000022000000 0.000000005500000 0.000000001000000 0.000000000100000
Posted 04 September 2012 - 09:46 AM
All these are terribly rare (1 in 10 billions apart from the "pyramid"); I wouldn't bother.Special Rolls:
LUCKY 7's (roll all 7's): win 30x
THE COUNTER (Roll 1 2 3 4 5 6 7 8 9 10 or 10 9 8 7 6 5 4 3 2 1): win 30x
Staggered (roll any 2 numbers in a staggered fashion aka 2 3 2 3 2 3 2 3 2 3): Win 20x
The Buildup (every number must be equal or larger than the last. Example - 1 1 2 3 4 4 5 6 7 10): Win 12x
The number problem ( 3 8 1 6 5 4 7 2 9 10): win 31x (Starting from left to right each number is divisible by it's sum of digits exception*- the 10 counts as a 0 digit. So 3 is divisible by 1, 38 is divisible by 2, 381 is divisble by 3, 3816 is divisble by 4 and so on)
Fibonnacci (1 1 2 3 5 8 1 3 2 1): Win 31x
Pyramid scheme (each of the first four numbers builds up to the 5th number and then gets smaller again example 1 1 3 4 10 9 9 8 6 5 ): Win 4x
Omae Wa Mou Shindeiru
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