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Safe Harbor Games Dice

Posted By: W Womack
Date: Sunday, 27 September 2009, at 8:18 p.m.

In Response To: Safe Harbor Games Dice (Jason Lee)

If I were making the usual it cheats, modifies rolls based on positions, etc. I would gladly relegate it to the limbo of dice complaints. But note that I have not claimed favoritism for either player, rolls dependent upon position, or any of the other common complaints associated with dice complaints. Neil Robins made the original observation that based on his analysis of about 100 matches from SHG that the frequency of doubles was significantly less than one would expect from random dice. I did a similar analysis using my last 118 matches played on SHG and simply determined the ACTUAL frequency of doubles based on these records. Over approximately 25,000 observations the actual (i.e. based on actual records of matches, without regards to other factors such as who won, did I think the program cheated, did I think my opponent was lucky) frequency of doubles is such lower than the expected value!

I did not do it in the original post, but a chi square test of the observed and expected numbers of doubles gives a probability of less than 0.0001 that the SHG results are from a population with the expected frequency of doubles.

So back to you form you have the line:

I haven't formalised my suspicions, presented a falsifiable hypothesis, designed an experiment, gathered data and made reasonable conculsions because I (check all that apply):

however none of the options apply because I have:

Formalised my suspicions -- i.e. SHG dice do not give the expected frequency of doubles.

Presented a falsifiable hypothesis: Doubles occur at the expected frequency with SHG dice.

Gathered Data -- 118 matches representing over 25,000 dice rolls.

Designed an experiment --not really an experiment maybe, but an analysis of the data, adjusted based on input regarding first roll doubles.

Made a reasonable conclusion: 1) the actual frequency of doubles is less than expected by what seems to be a large amount ~9.4% vs 16.66667%

2) a statistical test indicates that this frequency of doubles will occur with a probability of less than 0.0001 if the sample is drawn from a population with the expected distribution.

Therefore, something is amiss with the SHG dice! Barring some error in my analysis-- which is possible -- seems like a reasonable conclusion to me.

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