Probability question
March 12th, 2014 at 8:51:33 PM
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Hi guys,
What is the probability of rolling the following sequence with two regular 3/4 inch razor edged dice.
2, any 3, any 4, any 5, any 6 in a row.
Many thanks
What is the probability of rolling the following sequence with two regular 3/4 inch razor edged dice.
2, any 3, any 4, any 5, any 6 in a row.
Many thanks
“There is something about the outside of a horse that is good for the inside of a man.” - Winston Churchill
March 12th, 2014 at 8:55:16 PM
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Quote: Tomspurwith two regular 3/4 inch razor edged dice.
Is this to mean "fair dice?" Dice which have a 1/6th probability of each number showing?
March 12th, 2014 at 8:58:32 PM
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Quote: endermikeIs this to mean "fair dice?" Dice which have a 1/6th probability of each number showing?
Yes, also just to mean dice which would normally be found on a craps game and not dice you would find on Sic Bo or any other dice game out there
“There is something about the outside of a horse that is good for the inside of a man.” - Winston Churchill
March 12th, 2014 at 8:59:45 PM
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Given fair dice, the answer depends on if you care about order (would 3-4-2-5-6 count?). From rereading the post I'm thinking it does (so 3-4-2-5-6 would not)
In that case the answer is 5/2519424 (.000001984581).
If order does not matter, the answer is 25/104976 (.000238149672).
In that case the answer is 5/2519424 (.000001984581).
If order does not matter, the answer is 25/104976 (.000238149672).
March 12th, 2014 at 9:09:18 PM
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Quote: endermikeGiven fair dice, the answer depends on if you care about order (would 3-4-2-5-6 count?). From rereading the post I'm thinking it does (so 3-4-2-5-6 would not)
In that case the answer is 5/2519424 (.000001984581).
If order does not matter, the answer is 25/104976 (.000238149672).
So it seems like even the conservative option, the probability would be too small unless you offer a decent jackpot payout?
Ok, one more question Mike. If you have subsets of 3 groups. 2, 3, 4 or 4, 5, 6, what would be the probability of each of the groupings?
Thanks again, you rock!!!
“There is something about the outside of a horse that is good for the inside of a man.” - Winston Churchill
March 12th, 2014 at 9:23:10 PM
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I would think it would be too rare to offer in a casino setting. It would need either some intermediate pays (a la Fire Bet) or a strike system where some rolls could be misses without losing the bet (three strikes and you're out).Quote: TomspurSo it seems like even the conservative option, the probability would be too small unless you offer a decent jackpot payout?
Again assuming that the rolls need to happen consecutively:Quote: TomspurOk, one more question Mike. If you have subsets of 3 groups. 2, 3, 4 or 4, 5, 6, what would be the probability of each of the groupings?
2-3-4, in ascending order: 1/7776 (.0001286)
2-3-4, any order: 1/1296 (.0007716)
4-5-6, in ascending order: 5/3888 (.001286)
4-5-6, any order: 5/648 (.007716)
(Math could be wrong, but I think I have it. Would be great if someone else could confirm)
March 12th, 2014 at 10:59:14 PM
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the probabilities of a 5 roll sequence is going to be very smallQuote: TomspurSo it seems like even the conservative option, the probability would be too small unless you offer a decent jackpot payout?
there are 11^5 (161,051) number of possible sequences where order matters
and not all of the sequences have the same probability
7,7,7,7,7 has the highest when order matters (6^5)/(36^5)=1/7776
There are only 126 unique probabilities for all the possible sequences
numerator freq
1 32
2 160
3 160
4 480
5 160
6 720
8 960
9 320
10 640
12 1920
15 640
16 1440
18 1280
20 1600
24 3360
25 320
27 320
30 2240
32 1632
36 2960
40 2560
45 960
48 4320
50 960
54 1120
60 4800
64 1440
72 4400
75 960
80 3040
81 160
90 2880
96 4080
100 1920
108 2160
120 6400
125 320
128 960
135 640
144 4640
150 2400
160 2560
162 480
180 5040
192 2880
200 2240
216 2600
225 960
240 6080
243 32
250 640
256 480
270 1600
288 3440
300 3840
320 1600
324 720
360 5280
375 640
384 1440
400 1920
405 160
432 2080
450 1920
480 3840
486 80
500 960
512 160
540 2080
576 1760
600 3360
625 160
640 640
648 640
675 320
720 3600
750 960
768 480
800 960
810 320
864 1080
900 2160
960 1600
972 80
1000 640
1024 32
1080 1520
1125 320
1152 560
1200 1920
1250 160
1280 160
1296 330
1350 480
1440 1440
1500 960
1536 80
1600 320
1620 240
1728 320
1800 1200
1875 160
1920 320
1944 40
2000 320
2160 560
2250 320
2304 80
2400 480
2500 160
2592 90
2700 240
2880 240
3000 320
3125 32
3240 80
3456 40
3600 240
3750 80
3888 10
4320 80
4500 80
5184 10
5400 40
6480 10
7776 1maybe better to have one group before or against another
smaller groups looks to be a good idea
and the math looks correct too
Sally
I Heart Vi Hart
March 12th, 2014 at 11:01:53 PM
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Thanks Sally.
So perhaps also it would make more sense to have a subgroup before an "event", such as 3, 4, 5 in a row or perhaps in any order BEFORE a 7 is rolled. Sort of similar to the "small, tall or nothing at all" bet?
So perhaps also it would make more sense to have a subgroup before an "event", such as 3, 4, 5 in a row or perhaps in any order BEFORE a 7 is rolled. Sort of similar to the "small, tall or nothing at all" bet?
“There is something about the outside of a horse that is good for the inside of a man.” - Winston Churchill
March 12th, 2014 at 11:21:33 PM
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I like the "in a row" concept before a 7.Quote: TomspurSo perhaps also it would make more sense to have a subgroup before an "event", such as 3, 4, 5 in a row or perhaps in any order BEFORE a 7 is rolled. Sort of similar to the "small, tall or nothing at all" bet?
Like a "combo craps" bet
I get 3,4,5 b4 7 to be (2*3*4)/15^3 = 0.007111... (wild #!) or 1 in 140.625
or 3,4,5 or 5,4,3 for half the prob
that would make for nice payouts too
many other sequences to play with
the 3 number combos might work well, I mean all good things do come in 3s right?
Sally
I Heart Vi Hart
March 12th, 2014 at 11:27:59 PM
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Thanks Sally,
Trying to see if I can put a side bet into a new game we have going live hopefully soon in Switzerland. I'm toying with the idea of a jackpot bet but the problem with that is that there is only a finite combinations with regards to dice (36 combinations) so in order to make a healthy payout, you need to come up with crazy combinations or "in line" bets.
Both you and Mike have been of a great help!
Trying to see if I can put a side bet into a new game we have going live hopefully soon in Switzerland. I'm toying with the idea of a jackpot bet but the problem with that is that there is only a finite combinations with regards to dice (36 combinations) so in order to make a healthy payout, you need to come up with crazy combinations or "in line" bets.
Both you and Mike have been of a great help!
“There is something about the outside of a horse that is good for the inside of a man.” - Winston Churchill
