On my return from a tournament at the Sands Regency, Rollie Heath approached me at the airport and asked "What percentage of Cribbage is luck?" Tough question.
"On average" the player winning the most cuts should win more games according to research and compiled statistics (by DeLynn Colvert, Dwight Christiansen and others) that show first dealer will win about 56% of the time, all other "things" being equal, ie luck AND skill.
To simplify the analysis let's suppose that player A wins all 22 cuts, which is about a 1 in four million (but NOT zero) chance of happening. How many games should player A win "on average"? To eliminate the luck factor in a single game, these players agree to play 22 games 100 times, where player A is first dealer EVERY time. Using my CRIBAVGS program, player A should win 12 games about 17 times, 13 games 16 times, and so on. In summary, player A should win 12 or more games 64 times. Player B should win 12 or more games 22 times despite not ever being first dealer. (Both players should win 11 games 14 times). We will use these results as a benchmark.
Larry Hasset reported to the Board of Directors that the best tournament players (experts) qualify about 60% of the time. Using my CRIBAVGS program this translates into a 10% "ability advantage" over the average player.
Experts' results are included in Colvert's et al above-mentioned results. This means that the ability disparity is about 20% between an expert and a totally unskilled player according to the Bell curve (ie "Normal" or Gaussian Probability distribution). Player A as expert against an unskilled player should win 12 or more games 99 times in a 100. Player B as expert should win 12 or more games 85 times. So an ability disparity of 20% shows skill accounts for 35% more wins (99-64) as first dealer), 63% more wins (85-22) as not first dealer, and luck the difference.
Now we have the answer to Rollie's question. "Luck" depends on the ability disparity between the players. Cribbage is at most 100% luck (two players of same ability) and at least 37% luck (two players of different ability) "on average".
So next time you win a grand slam, congratulate yourself on your luck because it is NOT impossible to get one, and also pat yourself on the back for your skill in making it happen.
If you have any comments or questions about this article email me.