Thursday, June 16, 2005

For those who love to Gamble, maybe you shouldn't....

HOUSE EDGE & STD DEV.
The house edge is defined as the ratio of the average loss to the initial bet. The house edge is not the ratio of money lost to total money wagered. In some games the beginning wager is not necessarily the ending wager. For example in blackjack, let it ride, and Caribbean stud poker, the player may increase their bet when the odds favor doing so. In these cases the additional money wagered is not figured into the denominator for the purpose of determining the house edge, thus increasing the measure of risk.

The reason that the house edge is relative to the original wager, not the average wager, is that it makes it easier for the player to estimate how much they will lose. For example if a player knows the house edge in blackjack is 0.6% he can assume that for every $10 wager original wager he makes he will lose 6 cents on the average. Most players are not going to know how much their average wager will be in games like blackjack relative to the original wager, thus any statistic based on the average wager would be difficult to apply to real life questions.

Game Bet/Rules House Edge Standard
Deviation
Baccarat Banker 1.06% 0.93
Baccarat Player 1.24% 0.95
Baccarat Tie 14.36% 2.64
Big Six $1 11.11% 0.99
Big Six $2 16.67% 1.34
Big Six $5 22.22% 2.02
Big Six $10 18.52% 2.88
Big Six $20 22.22% 3.97
Big Six Joker/Logo 24.07% 5.35
Bonus Six No insurance 10.42% 5.79
Bonus Six With insurance 23.83% 6.51
Blackjacka Atlantic City rules 0.43% 1.2
Blackjackb Las Vegas single deck 0.18% 1.2
Caribbean Stud Poker 5.22% 2.24
Casino War Go to war on ties 2.88% 1.05
Casino War Surrender on ties 3.70% 0.94
Casino War Bet on tie 18.65% 8.32
Catch a Wave 0.50% d
Craps Pass/Come 1.41% 1.00
Craps Don't pass/don't come 1.36% 0.99
Craps Field (2:1 on 12) 5.56% 1.08
Craps Field (3:1 on 12) 2.78% 1.14
Craps Any craps 11.11% 2.51
Craps Big 6,8 9.09% 1.00
Craps Hard 4,10 11.11% 2.51
Craps Hard 6,8 9.09% 2.87
Craps Place 6,8 1.52% 1.08
Craps Place 5,9 4.00% 1.18
Craps Place 4,10 6.67% 1.32
Craps Place (to lose) 4,10 3.03% 0.69
Craps Proposition 2,12 13.89% 5.09
Craps Proposition 3,11 11.11% 3.66
Craps Proposition 7 16.67% 1.86
Double Down Stud 2.67% 2.97
Keno 25%-29% 1.30-46.04
Let it Ride 3.51% 5.17
Pai Gowc 1.50% d
Pai Gow Pokerc 1.46% 0.75
Red Dog Six decks 2.80% d
Roulette (single zero) 2.70% e
Roulette (double zero) 5.26% e
Sic-Bo 2.78%-33.33% e
Slot Machines 2%-15%f 8.74g
Spanish 21 Dealer hits soft 17 0.76% d
Spanish 21 Dealer stands on soft 17 0.40% d
Super Fun 21 0.94% d
Three Card Poker Pairplus 2.32% 2.91
Three Card Poker Ante & play 3.37% 1.64
Video Poker Jacks or better (full pay) 0.46% 4.42
Wild Hold 'em Fold 'em 6.86% d

Notes:

a Atlantic City rules are 8 decks, dealer stands on soft 17, player may double on any two cards, player may double after splitting, one card to split aces, no surrender.

b Las Vegas single deck rules are dealer hits on soft 17, player may double on any two cards, player may not double after splitting, one card to split aces, no surrender.

c Assuming player plays the house way, playing one on one against dealer, and half of bets made are as banker.

d Yet to be determined.

e Standard deviation depends on bet made.

f Slot machine range is based on available returns from a major manufacturer

g Slot machine standard deviation based on just one machine. While this can vary, the standard deviation on slot machines are very high.

ELEMENT OF RISK
For purposes of comparing one game to another I would like to propose a different measurement of risk, which I call the "element of risk." This measurement is defined as the average loss divided by total money bet. For bets in which the initial bet is always the final bet there would be no difference between this statistic and the house edge. Bets in which there is a difference are listed below.

Game Bet House Edge Element
of Risk
Blackjack Atlantic City rules 0.43% 0.38%
Bonus 6 No insurance 10.42% 5.41%
Bonus 6 With insurance 23.83% 6.42%
Caribbean Stud Poker 5.22% 2.56%
Casino War Go to war on ties 2.88% 2.68%
Double Down Stud 2.67% 2.13%
Let it Ride 3.51% 2.85%
Spanish 21 Dealer hits soft 17 0.76% 0.65%
Spanish 21 Dealer stands on soft 17 0.40% 0.30%
Three Card Poker Ante & play 3.37% 2.01%
Wild Hold 'em Fold 'em 6.86% 3.23%
HOLD
The hold percentage is the ratio of chips the casino keeps to the total chips sold. This is generally measured over an entire shift. For example if blackjack table x takes in $1000 in the drop box and of the $1000 in chips sold the table keeps $300 of them (players walked away with the other $700) then the game's hold is 30%. If every player loses their entire purchase of chips then the hold will be 100%. It is possible for the hold to exceed 100% if players carry to the table chips purchased at another table. A mathematician alone can not determine the hold because it depends on how long the player will sit at the table and the same money circulates back and forth. There is a lot of confusion between the house edge and hold, especially among casino personnel.

Monday, June 13, 2005

Richard Proenneke

I watched this on WHYY last night, the video is really something.

Richard Proenneke 1917-2003

To live in a pristine land ... to roam the wilderness ... to choose a site, cut trees, and build a home ... Thousands have had such dreams, but Richard Proenneke lived them. Here is a tribute to a man in tune with his surroundings who carved his masterpiece out of the beyond.

In 1968 at the age of 51 Richard (Dick) Proenneke constructed a log cabin at Upper Twin Lakes and lived there alone for almost 30 years. In 1980, Twin Lakes became part of the Lake Clark National Park and Preserve, and Dick became a volunteer backcountry interpreter and naturalist. A diesel mechanic by trade, decades of living in wilderness would transform Dick into what some might call a landscape ecologist.

A keen observer and meticulous recorder, Dick was fascinated by weather phenomena, annual phenological events, cyclic natural fluctuations in animal abundance, and plant-animal interactions. Inquisitive and deliberate, he not only observed and recorded but also asked the question, “Why?”.

A wolverine carcass found in spring at the head of a valley would be systematically probed for weeks. What was its sex and age? Was there evidence of emaciation or broken bones? Was the carcass in an avalanche zone? In A Sand County Almanac Aldo Leopold wrote: “Keeping records enhances the pleasure of the search, and the chance of finding order and meaning in these events.” At Twin Lakes, Dick found order and meaning by recording natural events. He began recording his observations and measurements in 1968 and continued to do so until 1995, the last full year he spent at Twin Lakes.

He wrote most of his notes on wall calendars, the type that rural Iowa hardware stores give to loyal customers at the start of the new year. Entries included dates of lake freeze-up; lake ice break-up; den entry and den emergence by brown bears; first calving by moose; first lambing by Dall sheep; and nest initiation by Gray Jays. Dick also recorded daily high and low air temperatures; monthly winter snow pack and lake ice thickness; and random events such as severe storms, earthquakes, and landslides. Dick had a special interest in wolves and annually recorded winter pack size, number of kills, and composition of kills.

Sustained and simple like the monitoring program we aspire to build, Dick’s calendars and journals are among the longest continuous data sets for any Alaska National Park. Trends in the duration of lake ice cover on Upper Twin Lake plotted from Dick’s records (1969-95) parallel those of other Northern Hemisphere sites and provide evidence that freshwater ecosystems are responding to a warming climate.

Dick’s love for wilderness, passion for observing and understanding the natural world around him, and his dedication to keeping records are an inspiration to all of us as we develop and implement long-term monitoring in the Southwest Alaska Network.