Saturday, July 15, 2006

Fun with Statistics - Doing it the hardway


This somewhat got away from me, so I thought it best to turn this on its head. The following is a bit of an estimation to find out the viability of the Kangwon Casino, the only Casino in Korea open to residents. Kangwon's numbers make sense, or a least what was published in a recent article. I am surprised, given the nature of casino operations's history of creative accounting, to find things line up (at least on the surface). I was also pleasantly surprised to find that the average player of Kangwon could easily be spending average amounts on their vacation, that is to say the average gambler there is not necessarily a problem gambler. 

Read on if you want


Its been a while since I have done a "Fun with statistics" post as I like to call them. This article on the casino in Kangwon-do, the only Korean casino open to Koreans, seems ripe.

According to this article, the casino will miss its 820 billion won revenue target this year, missing its forecast by 10% (conservatively). The article also mentions that the casino hosted 1.9 million last year, with an estimated drop this year of about 10%.

Now lets crunch the numbers. The easy one is this years revenue is about 740 billion, and visitors of 1.7 million.

Now let us say that each guest gets a hotel room, and some meals for about 75,000 won on average (two people 100,000 won hotel bill split, 25,000 each food and beverage). This leaves us with a casino "take" of 613 billion won (740 billion minus 1.7 million times 75,000).

Now I do not know what the most popular bets are at the casino, but lets do some guessing. I have not been there but in the Korean foreign casinos the two most popular games I see are Blackjack, Roulette, and Baccarat (I am leaving out Sic Bo and Fan Tan since my knowledge of these are weak). The average house advantage of these for the basic bets are respectively .5% (basic strategy blackjack), 5.3% (double zero roulette), and 1.2% (player bet). This averages to a house advantage of 2.23%.

So then with a 613 billion won take and a 2.33% advantage means 26.3 trillion won in action was taken by the casino. Or per person, 15.5 million won per person. Now that is action. Let us use more guesses to say that each player plays for two days, four hours at a time, with a 10 minute break per hour. Let us also say ballpark that each bet takes 1.5 minutes to take and conclude (hand of blackjack, spin roulette, etc.). This equals 267 bets each visitor. Meaning the average bet is a bit less then 60,000 won each.

This seems a little high. Lets look at the assumptions that may bring it down. The obvious is the first assumption on the proportion of Kangwon Casino's revenue from gambling was off, they get more in hotel and F&B revenue. It could also be the visitors make risker bets (non-basic strategy blackjack, the "tie" in baccarat, etc.), or for that matter games other than they three used are played more.  Finally it could be they just play longer.

So then lets work on each one, using algebra and the hard numbers we do have.

Assume the average bet was 10,000, finding the other and leaving others the same:

1. Time played - means 1602 bets were taken. Given the same time per bet (not unreasonable IMHO), the average guest would need to spend 48 hours in the casino. So I think we can scratch this one off the list.

2. House advantage - The amount of action would be about 4.5 trillion, meaning an average house advantage of 13.6% which would be equal to some of the worst bets the casino. I doubt that the patrons are constantly betting such poor bets.

3. Other revenue - Such would equal about 100 billion in take, and an average F&B per person of 375,000 per visit. Too many bottles of soju for me to believe this bill.

While all the calculations proved to give fantastic results, it does give you some sense of scale. Just doubling the basic 20,000 won bet yields more understandable figure of about a 6.75% house advantage.

Likewise, if we increase the bet to 30,000 with same house advantage, we get a hotel and F&B per person of 250,000 won.

So lets work backwards, lets double the Hotel Bill and work it out. A 150,000 won per head bill works down to a 46,000 won average bet with first house advantage of 2.33%. Now to get this down to a more understandable bet level, lets halve this and work out the house advantage.

Doing so leaves the following won averages at Kangwon Casino:

1. Room F&B 150,000
2. Casino take (revenue) 485 billion
3. Average Bet 23,000
4. Average Action per Head 6.14 million
5. Casino Action 10.4 trillion
6. House Advantage 4.66%

Now these are all understandable figures (to me anyway). So lets dig deeper...

According to the National Statistics Office, the average household in Korea spends 100,000 won a month in "culture and leisure". Let us assume the average visitors to Kangwon Casino are a husband and wife, and take the entire "culture and leisure" budget for the year with them (note: This is some what unreasonable since it precludes other consumption and the consumption by other members in the household, mainly children). This means two people split 1,200,000, or 600,000 each. From that take out our 150,000 hotel and F&B bill and you get a gambling budget of 450,000 per visitor.

In taking that last figure and performing some spreadsheet magic you can find out that one can gamble for the time and house advantage specified for 450,000. The gambler will on average have about 100,000 won left. This nicely dovetails with our earlier assumption, this could conceivably be the amount spent on leisure in that year not at the casino.


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