Poker is under an indecisive debate and much discussion of the moral Vs. legal privileges that the stalwarts and lovers of the game tend to seek – whether it is a game of skill or a game of luck?…
In Poker, there is serious money exchanging hands and can sure make or break fortunes! Of course, the game lovers and game providers naturally look for scientific ways to prove their point. The statistical model for understanding the nature of this simple yet complex game can perhaps put this issue to rest. It can also then predict the possible outcome of a game underway fairly accurately – a much sought-after and equally elusive aim!
Nail the math
If only it were as easy!… There have been a number of studies that have tried to get into the probabilistic statistics of poker. The mathematics involves application of game theories. One such work that tries to capture the math is Chen and Ankenman’s The Mathematics of Poker.
Any sound and reliable research depends on freely available data. Until the recent popularity of online poker sites, like RollersDen, it was difficult to get hold of accurate poker records as most game hosts were not willing to disclose the details to researchers.
A landmark study
But online poker sites have made collation of data far more easy and convenient. One noteworthy study was the one carried out by Cigital Group, a software consulting firm in Washington D.C. They studied over 100 million hands dealt by poker (Texas Hold’em).
Here is what they reported:
- Only about twelve percent of the dealt hands won due to the best hand.
- Three-quarters of the hands never reach showdown. This meant that the winner never had to show his or her cards, whilst other players folded in by themselves in successive betting rounds.
- In addition to the above, in almost half the cases where there was a showdown, a player who should have won as per the dealt cards, had already folded.
What was their inference?
Cigital concluded that Poker is indeed a game of skill, and that luck played a very small role in the hand. They argued that the lack of showdowns directly implies that poker is skill-based. The winner could have won by his skill, by similar betting, no matter what cards he/she had been dealt, they extrapolated. It was the decisions made by the player that determined whether or not there was a showdown, which is skill-driven.
Yes! Others agree…
A similar independent study of over a billion hands by Robert Hannum, a professor of risk analysis and gaming at the University of Denver, was in line with the findings of Cigital. Hannum found that 85.2% of the hands never had a showdown and 14.8% of the remaining did not have the best cards as the winner.
Economists Thomas Miles and Steven Levitt of the University of Chicago identified 720 players as highly-skilled ones, and noted that their ROI stood at 30.5 %, whereas the average return of all other players was a minus 15.6 %.They calculated the win rate of highly skilled poker players at a whopping 54.9%
Arbitrary numbers are suggested by players as the percentage of skill vs. luck. They could be as varied as 70% skill and 30% luck to a 50-50 weightage of the two. It depends on the mindset and viewpoint of the individual.
Of course no statistical figure of concluding numbers can clinch the actual percentage of skill vs. luck element in poker. But anyone who is familiar with the game will agree that skill is a very important factor in determining the way the winds of winning blow in every poker hand!