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Craps Bets ~ Win and Hit Frequencies
Frequency is the number of times an event occurs in any experiment.
What is a win or hit frequency? Frequency means "how often" and when applied to gambling at craps how often something happens or does not happen, or how often a bet wins or losses. When something 'hits' it is said to have happened or a bet has won.
There are 3 different, but important, frequency statistics that we deal with, one of them being the most important.
- Absolute Frequency. Is the actual number of times the event actually occurs during an experiment.
The exact number of successes in a distribution or sample. - Relative Frequency. Is the ratio of the absolute frequency of a particular successful event, with the total number of events. It is the absolute frequency normalized to the total number of events that occur in the experiment
The percentage of an absolute frequency related to the total successes. (absolute/total successes = relative frequency) - Cumulative Frequency. This is the running total of all the frequencies. It shows the number, percentage, or proportion of outcomes that are less than or equal to particular values or a group of values.
It is the most important frequency out of the 3 since in the short run it can be the most accurate in terms of what HAS happened to what is EXPECTED to happen.
| rolls | group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | count | run | ev | diff | % off | avg |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 18 | 1 | 8 | 6 | 9 | 9 | 5 | 7 | 11 | 10 | 8 | 9 | 8 | 3 | 9 | 33 | 10 | 4 | 2 | 3 | 1 | 1 | 3 | -2 | -67% | 18.0 |
| 36 | 2 | 4 | 8 | 9 | 5 | 6 | 10 | 8 | 11 | 10 | 8 | 10 | 9 | 5 | 7 | 6 | 5 | 3 | 5 | 1 | 2 | 6 | -4 | -67% | 18.0 |
| 54 | 3 | 7 | 8 | 3 | 7 | 5 | 7 | 6 | 7 | 6 | 44 | 7 | 6 | 8 | 12 | 8 | 10 | 9 | 7 | 6 | 8 | 9 | -1 | -11% | 6.8 |
| 72 | 4 | 6 | 12 | 9 | 6 | 10 | 3 | 44 | 22 | 7 | 6 | 9 | 33 | 5 | 6 | 3 | 9 | 44 | 7 | 2 | 10 | 12 | -2 | -17% | 7.2 |
| 90 | 5 | 8 | 44 | 7 | 10 | 8 | 4 | 44 | 10 | 55 | 8 | 9 | 7 | 8 | 8 | 8 | 7 | 6 | 5 | 3 | 13 | 15 | -2 | -13% | 6.9 |
| 108 | 6 | 2 | 8 | 9 | 22 | 3 | 6 | 8 | 7 | 7 | 6 | 10 | 11 | 12 | 33 | 3 | 7 | 6 | 11 | 3 | 16 | 18 | -2 | -11% | 6.8 |
| 126 | 7 | 5 | 12 | 55 | 4 | 5 | 8 | 7 | 11 | 9 | 7 | 3 | 7 | 9 | 33 | 4 | 9 | 7 | 10 | 4 | 20 | 21 | -1 | -5% | 6.3 |
| 144 | 8 | 10 | 6 | 6 | 2 | 6 | 6 | 7 | 6 | 7 | 9 | 5 | 9 | 2 | 9 | 7 | 2 | 6 | 7 | 4 | 24 | 24 | 0 | 0% | 6.0 |
| 162 | 9 | 11 | 6 | 8 | 7 | 5 | 5 | 10 | 5 | 11 | 6 | 6 | 9 | 8 | 4 | 7 | 5 | 7 | 55 | 3 | 27 | 27 | 0 | 0% | 6.0 |
| 180 | 10 | 22 | 5 | 9 | 9 | 11 | 12 | 55 | 7 | 9 | 6 | 5 | 11 | 6 | 11 | 8 | 8 | 44 | 9 | 1 | 28 | 30 | -2 | -7% | 6.4 |
| 198 | 11 | 4 | 9 | 9 | 6 | 9 | 11 | 9 | 7 | 11 | 9 | 6 | 4 | 7 | 9 | 10 | 2 | 3 | 5 | 2 | 30 | 33 | -3 | -9% | 6.6 |
| 216 | 12 | 6 | 8 | 8 | 7 | 7 | 6 | 5 | 5 | 7 | 55 | 8 | 7 | 2 | 12 | 7 | 7 | 5 | 7 | 7 | 37 | 36 | 1 | 3% | 5.8 |
| 234 | 13 | 11 | 22 | 11 | 7 | 9 | 10 | 7 | 5 | 10 | 6 | 2 | 4 | 3 | 5 | 6 | 9 | 4 | 7 | 3 | 40 | 39 | 1 | 3% | 5.9 |
| 252 | 14 | 7 | 9 | 7 | 22 | 8 | 6 | 7 | 11 | 9 | 10 | 8 | 9 | 5 | 4 | 7 | 7 | 7 | 55 | 6 | 46 | 42 | 4 | 10% | 5.5 |
| 270 | 15 | 7 | 5 | 8 | 6 | 5 | 9 | 22 | 6 | 12 | 22 | 11 | 7 | 44 | 44 | 9 | 6 | 9 | 7 | 3 | 49 | 45 | 4 | 9% | 5.5 |
| 288 | 16 | 3 | 55 | 12 | 3 | 22 | 11 | 33 | 11 | 44 | 9 | 33 | 9 | 7 | 4 | 6 | 11 | 5 | 6 | 1 | 50 | 48 | 2 | 4% | 5.8 |
| 306 | 17 | 6 | 2 | 4 | 12 | 5 | 12 | 6 | 9 | 8 | 7 | 7 | 7 | 11 | 5 | 3 | 8 | 5 | 9 | 3 | 53 | 51 | 2 | 4% | 5.8 |
| 324 | 18 | 7 | 3 | 7 | 6 | 6 | 9 | 12 | 5 | 11 | 9 | 10 | 5 | 5 | 7 | 7 | 9 | 7 | 5 | 58 | 54 | 4 | 8% | 5.6 |
Relative Frequency Graph for the Seven or 1/6 probability.
| actual | expected | ||||
|---|---|---|---|---|---|
| roll | absolute | relative | roll | absolute | relative |
| 1 | 9 | 15.52% | 1 | 10 | 16.67% |
| 2 | 10 | 17.24% | 2 | 8 | 13.89% |
| 3 | 8 | 13.79% | 3 | 7 | 11.57% |
| 4 | 5 | 8.62% | 4 | 6 | 9.65% |
| 5 | 3 | 5.17% | 5 | 5 | 8.04% |
| 6 | 3 | 5.17% | 6 | 4 | 6.70% |
| 7 | 3 | 5.17% | 7 | 3 | 5.58% |
| 8 | 2 | 3.45% | 8 | 3 | 4.65% |
| 9 | 6 | 10.34% | 9 | 2 | 3.88% |
| 10 | 1 | 1.72% | 10 | 2 | 3.23% |
| 11 | 4 | 6.90% | 11 | 2 | 2.69% |
| 12 | 0 | 0.00% | 12 | 1 | 2.24% |
| 13 | 1 | 1.72% | 13 | 1 | 1.87% |
| 14 | 0 | 0.00% | 14 | 1 | 1.56% |
| 15 | 1 | 1.72% | 15 | 1 | 1.30% |
| 16 | 0 | 0.00% | 16 | 1 | 1.08% |
| 17 | 0 | 0.00% | 17 | 1 | 0.90% |
| 18 | 1 | 1.72% | 18 | 0 | 0.75% |
| 19 | 0 | 0.00% | 19 | 0 | 0.63% |
| 20 | 0 | 0.00% | 20 | 0 | 0.52% |
| 21 | 0 | 0.00% | 21 | 0 | 0.43% |
| 22 | 0 | 0.00% | 22 | 0 | 0.36% |
| 23 | 0 | 0.00% | 23 | 0 | 0.30% |
| 24 | 0 | 0.00% | 24 | 0 | 0.25% |
| 25 | 0 | 0.00% | 25 | 0 | 0.21% |
| 26 | 1 | 1.72% | 26 | 0 | 0.17% |
| 27 | 0 | 0.00% | 27 | 0 | 0.15% |
| 28 | 0 | 0.00% | 28 | 0 | 0.12% |
| 29 | 0 | 0.00% | 29 | 0 | 0.10% |
| 30 | 0 | 0.00% | 30 | 0 | 0.08% |
| 31 | 0 | 0.00% | 31 | 0 | 0.07% |
| 32 | 0 | 0.00% | 32 | 0 | 0.06% |
| 33 | 0 | 0.00% | 33 | 0 | 0.05% |
Relative Frequency Graph for the Seven.
Actual distribution from 323 actual dice rolls Nugget 2007.
Actual distribution from 323 actual dice rolls Nugget 2007.
Superimposed Relative Frequency Graph for the Seven.
Actual and expected outcomes. In the short run the curve has disappeared.
Actual and expected outcomes. In the short run the curve has disappeared.
| actual | expected | ||||||
|---|---|---|---|---|---|---|---|
| roll | relative | cumulative | % | roll | relative | cumulative | % |
| 1 | 9 | 9 | 15.52% | 1 | 10 | 10 | 16.67% |
| 2 | 10 | 19 | 32.76% | 2 | 8 | 18 | 30.56% |
| 3 | 8 | 27 | 46.55% | 3 | 7 | 25 | 42.13% |
| 4 | 5 | 32 | 55.17% | 4 | 6 | 31 | 51.78% |
| 5 | 3 | 35 | 60.34% | 5 | 5 | 36 | 59.82% |
| 6 | 3 | 38 | 65.52% | 6 | 4 | 40 | 66.52% |
| 7 | 3 | 41 | 70.69% | 7 | 3 | 43 | 72.10% |
| 8 | 2 | 43 | 74.14% | 8 | 3 | 46 | 76.75% |
| 9 | 6 | 49 | 84.48% | 9 | 2 | 48 | 80.63% |
| 10 | 1 | 50 | 86.21% | 10 | 2 | 50 | 83.86% |
| 11 | 4 | 54 | 93.10% | 11 | 2 | 52 | 86.55% |
| 12 | 0 | 54 | 93.10% | 12 | 1 | 53 | 88.79% |
| 13 | 1 | 55 | 94.83% | 13 | 1 | 54 | 90.66% |
| 14 | 0 | 55 | 94.83% | 14 | 1 | 55 | 92.22% |
| 15 | 1 | 56 | 96.55% | 15 | 1 | 56 | 93.52% |
| 16 | 0 | 56 | 96.55% | 16 | 1 | 57 | 94.60% |
| 17 | 0 | 56 | 96.55% | 17 | 1 | 58 | 95.50% |
| 18 | 1 | 57 | 98.28% | 18 | 0 | 58 | 96.25% |
| 19 | 0 | 57 | 98.28% | 19 | 0 | 58 | 96.88% |
| 20 | 0 | 57 | 98.28% | 20 | 0 | 58 | 97.40% |
| 21 | 0 | 57 | 98.28% | 21 | 0 | 58 | 97.83% |
| 22 | 0 | 57 | 98.28% | 22 | 0 | 58 | 98.19% |
| 23 | 0 | 57 | 98.28% | 23 | 0 | 58 | 98.49% |
| 24 | 0 | 57 | 98.28% | 24 | 0 | 58 | 98.74% |
| 25 | 0 | 57 | 98.28% | 25 | 0 | 58 | 98.95% |
| 26 | 1 | 58 | 100.00% | 26 | 0 | 58 | 99.12% |
| 27 | 0 | 58 | 100.00% | 27 | 0 | 58 | 99.27% |
| 28 | 0 | 58 | 100.00% | 28 | 0 | 58 | 99.39% |
| 29 | 0 | 58 | 100.00% | 29 | 0 | 58 | 99.49% |
| 30 | 0 | 58 | 100.00% | 30 | 0 | 58 | 99.57% |
| 31 | 0 | 58 | 100.00% | 31 | 0 | 58 | 99.64% |
| 32 | 0 | 58 | 100.00% | 32 | 0 | 58 | 99.70% |
| 33 | 0 | 58 | 100.00% | 33 | 0 | 58 | 99.75% |
Cumulative Frequency Graph for the Seven or 1/6 probability.
Cumulative Frequency Graph for the Seven or 1/6 probability.
Actual distribution from 323 rolls Nugget 2007.
Actual distribution from 323 rolls Nugget 2007.
Superimposed Cumulative Frequency Graph for the Seven from 323 rolls Nugget 2007
Actual and expected outcomes. In the short run the curves are very similar.
Actual and expected outcomes. In the short run the curves are very similar.
Observations and conclusions that we can make from relative frequency tables and graphs. coming soon.
Cumulative Frequencies, being a running total of successes in an experiment, in this example 323 dice rolls, charting the absolute frequencies of the #7, show how often a bet wins or hits within any percentage range.