Odds Guide
ODDS Medicaid Guide for Families of Children who Experience Intellectual or Developmental Disabilities (I/DD). In this guide, we will provide you with tips on how to improve your blackjack odds and illustrate what factors influence the house edge. Every little bit counts; removing just a fraction of the house edge percentage will make you a more profitable blackjack player. Blackjack House Edge Explained Player’s Advantages in Blackjack.
Jun 01, 2020 Purpose/Rationale: ODDS responded rapidly to the COVID-19 pandemic and state of emergency by rapidly releasing a series of transmittals. This guide replaces many of those transmittals and consolidates the information. This guide will be updated as Oregon begins to reopen through a phased process established by the Governor. Knowing how to read odds makes it so you can place the most informed bets. Likewise, you will have a better chance of having your bet pay off. Remember, however, that no bet is a sure thing. And, now that you can calculate your own odds, compare multiple sportsbooks’ odds. Some may have different odds for the same event.
Written by Clay Smith
Idiot’s Guide
That’s right - I will be your guide. The good thing about having an idiot for a guide is that I have to make it simple to understand it myself, which means, hopefully, you will understand it as well.
Probability or Odds
Probability
Probability means the risk of an event happening divided by the total number of people at risk of having that event. I will use the example in a recent JAMA article. In a deck of 52 cards, there are 13 spades. So, the risk (or probability) of drawing a card randomly from the deck and getting spades is 13/52 = 0.25 = 25%. The numerator is the number of spades, and the denominator is the total number of cards.
Odds
Odds seems less intuitive. It is the ratio of the probability a thing will happen over the probability it won’t. In the spades example, the probability of drawing a spade is 0.25. The probability of not drawing a spade is 1 - 0.25. So the odds is 0.25/0.75 or 1:3 (or 0.33 or 1/3 pronounced 1 to 3 odds).
Moving back and forth
To go from odds to probability, simply take the numerator/(denominator + numerator). In the spades example, the odds of 1/3 is converted by taking 1/1+3 = 0.25 - and now we are back to probability. To go from probability to odds, simply take the numerator/(denominator-numerator). In the spades example, given that the probability of drawing a spade is 1/4, take 1/(4-1) = 1:3 odds or odds = 0.33.
Statistical Significance
If an odds ratio (OR) is 1, it means there is no association between the exposure and outcome. So, if the 95% confidence interval for an OR includes 1, it means the results are not statistically significant. Example, exposure to colored vs white Christmas lights was associated with an increase in jocularity score, OR = 1.2 (95%CI 0.98-1.45). Sorry, this is not statistically significant. Let’s just go with white lights…
Use
Either the OR or risk ratio (RR) could be used in many study types. However, only the OR can be used in case-control studies. Because in order to calculate the RR, one must know the risk. Risk is a probability, a proportion of those exposed with an outcome compared to the total population exposed. This is impossible in a case-control study, in which those who already have the outcome are included without knowing the total population exposed.
Risk Ratio
RR is a very intuitive concept. It is the probability (or risk) of one outcome over the probability (risk) of another. Let’s use a study we covered on JF to discuss this concept. Survival was lower in pediatric patients intubated during arrest compared with those not intubated: 411/1135 (36%) vs 460/1135 (41%). So, the RR is 36.2%/40.5% = 0.89. This means survival was reduced by a factor of 0.89 for pediatric arrest patients who were intubated during arrest vs. those who were not. As an example, if survival was expected to be 40%, then intubating during arrest would reduce it to: 40% x 0.89 = 35.6%.
Let’s do one more example. Supination-flexion (SF) vs hyperpronation (HP) to reduce nursemaid’s elbow was more likely to fail. The risk of failure with SF was 96/351 (27%) vs. 32/350 (9%) with HP. The RR was 3. This has a very intuitive meaning: risk of failure with SF was three times more likely than HP.
Odds Ratio
The OR is a way to present the strength of association between risk factors/exposures and outcomes. If the OR is <1, odds are decreased for an outcome; OR >1 means the odds are increased for a given outcome. Let’s look at the examples again and consider odds.
For pediatric arrest, the risk of survival if intubated during arrest was 411/1135 (36%) vs 460/1135 (41%) if not intubated. Let’s convert to odds and calculate an OR.
Intubated: 411/1135-411 = 411/724 = 0.57 odds.
Non-intubated: 460/1135-460 = 460/675 = 0.68 odds.
So, the OR is 0.57/0.68 = 0.83.
Note, this is very close to the RR (0.89) but is a slight overestimate of the effect on the outcome. This is always the case with the OR compared to the RR - it overestimates the effect.
Take the example of supination-flexion vs hyperpronation for nursemaid’s. The risk of failure for SF was 96/351 vs. 32/350 with HP. Let’s convert this to odds.
SF: 96/351-96 = 0.376 odds
HP: 32/350-32 = 0.10 odds
The OR is 0.376/0.10 = 3.7
Note, the OR overestimates the RR, which was 3. Although one could say the risk of failure using SF is 3 times greater than HP, one could not say, based on the OR, the risk was 3.74 times greater. The OR and RR are not the same. What could be said is that the odds of failure is 3.74 times greater.
Risk Ratio vs Odds Ratio
Whereas RR can be interpreted in a straightforward way, OR can not. A RR of 3 means the risk of an outcome is increased threefold. A RR of 0.5 means the risk is cut in half. But an OR of 3 doesn’t mean the risk is threefold; rather the odds is threefold greater. Interpretation of an OR must be in terms of odds, not probability. Again, the OR will always be an overestimate compared to the RR. However, the RR and OR will be similar for rare outcomes, <10%. But the OR increasingly overestimates RR as outcomes exceed 10%. This is easier to understand with an example.
Pretend a new vape, Vapalicious, is associated with cancer.
80/100 people who use it get cancer.
20/100 who don’t use it get cancer.
The risk of getting cancer is 4 times greater in Vapalicious users. RR = 0.8/0.2 = 4
Note how distorted the OR becomes in this example. OR = (80/20)/(20/80) = 16
What if Vapalicious rarely caused cancer?
5/1000 get cancer with Vapalicious vs 2.5/1000 for non-users.
RR = 2.
OR = 2 as well (actually 2.005)
With rare outcomes, the RR and OR are very similar.
Why Does This Matter?
This matters because we often equate the OR and RR. Unwary researchers, reviewers, or news media might report a 16-fold increased risk of cancer from Vapalicious. In fact, there was a 4-fold increased risk of cancer from Vapalicous. Not that I plan to use Vapalicious (or any other vape), but a 16-fold vs 4-fold increase is a gross overestimation of the effect.
What Does the OR Mean?
So, what does an OR mean? Here it is in plain language.
An OR of 1.2 means there is a 20% increase in the odds of an outcome with a given exposure.
An OR of 2 means there is a 100% increase in the odds of an outcome with a given exposure. Or this could be stated that there is a doubling of the odds of the outcome. Note, this is not the same as saying a doubling of the risk.
An OR of 0.2 means there is an 80% decrease in the odds of an outcome with a given exposure.
Summary
Odds Ratio is a measure of the strength of association with an exposure and an outcome.
OR > 1 means greater odds of association with the exposure and outcome.
OR = 1 means there is no association between exposure and outcome.
OR < 1 means there is a lower odds of association between the exposure and outcome.
If the 95% confidence interval for the OR includes 1, the results are not statistically significant.
OR and RR are not the same.
OR always overestimate RR, but…
OR approximates RR when the outcome is rare but markedly overestimates it as outcome exceeds 10%.
References
The odds ratio by Bland and Altman, of Bland-Altman plot fame
Wikipedia aka source of all statistical knowledge
Survey, Harvest & Hunt Data, Draw Odds for Big & Small Game
Population survey data and draw and harvest statistics are provided below. Please note that as a result of software and technology changes, the Department is changing how the harvest and survey data are presented. As of 2018, the data will no longer be provided as a consolidated Hunt Arizona book. Individual summaries will be posted as available.
It is very important that hunters return their hunter questionnaires. The hunter surveys are a critical component of the hunt recommendation process, and the information helps us accurately estimate species harvest and set permit levels.
2020 Harvest Summaries
- 2020 AZ Spring Javelina Harvest Summary PDF
- 2020 AZ Spring Turkey Harvest Summary PDF
- 2020 AZ Bighorn Sheep Harvest Summary PDF
2019 Harvest Summaries
- 2019 AZ Fall Javelina Harvest Summary PDF
- 2019 AZ Bighorn Sheep Harvest Summary PDF
- 2019 AZ Black Bear Harvest Summary PDF
- 2019 AZ Fall Turkey Harvest Summary PDF
- 2019 AZ Elk Harvest Summary PDF
- 2019 AZ Draw Deer Harvest Summary PDF
- 2019 AZ Pronghorn Harvest Summary PDF
- 2019 AZ Deer OTC Archery Harvest Summary PDF
- 2019 AZ Mountain Lion Summary PDF
- 2019 AZ Bison Harvest Summary PDF
- 2019 AZ Bighorn Sheep Survey Summary [PDF]
- 2019 AZ Elk Survey Summary [PDF]
- 2019 AZ Javelina Survey Summary [PDF]
- 2019 AZ Mule Deer Survey Summary [PDF]
- 2019 AZ White-tailed Deer Survey Summary [PDF]
- 2019 AZ Pronghorn Survey Summary [PDF]
2020 Draw Odds for Big Game
- 2020 AZ Bighorn Sheep Hunt Draw Odds PDF
- 2020 AZ Bison Hunt Draw Odds PDF
- 2020 AZ Deer Hunt Draw Odds PDF
- 2020 AZ Elk Hunt Draw Odds PDF
- 2020 AZ Fall Turkey Hunt Draw Odds PDF
- 2020 AZ Javelina Hunt Draw Odds PDF
- 2020 AZ Pronghorn Hunt Draw Odds PDF
- 2020 AZ Spring Turkey Hunt Draw Odds PDF
2019 Draw Odds for Big Game
Odds Are Parents Guide
- 2019 AZ Bighorn Sheep Hunt Draw Odds PDF
- 2019 AZ Bison Hunt Draw Odds PDF
- 2019 AZ Deer Hunt Draw Odds PDF
- 2019 AZ Elk Hunt Draw Odds PDF
- 2019 AZ Fall Turkey Hunt Draw Odds PDF
- 2019 AZ Javelina Hunt Draw Odds PDF
- 2019 AZ Pronghorn Hunt Draw Odds PDF
- 2019 AZ Spring Turkey Hunt Draw Odds PDF
Cementum Age Results
- 2019 AZ Deer Harvest Age Results PDF
- 2019 AZ Elk Harvest Age Results PDF
No data available except for bighorn sheep, bison, black bear, and mountain lion. The hunter survey response rate for 2018 was poor, to the point that the harvest and hunter success data were not useable.
- 2018 AZ Bighorn Sheep Harvest Summary PDF
- 2018 AZ Bison Harvest Summary PDF
- 2018 AZ Black Bear Harvest Summary PDF
- 2018 AZ Mountain Lion Harvest Summary PDF
2018 Hunt Arizona Book sections for Big Game (Includes 2013-2017 data)
- 2018 AZ How to Use Survey and Harvest Data and Bonus Points By Species Section PDF
- 2018 AZ Bighorn Sheep Section PDF
- 2018 AZ Deer Section PDF
- 2018 AZ Mountain Lion PDF
- 2017 AZ Pronghorn Harvest Summary PDF
- 2017 AZ Elk Harvest Summary PDF
- 2017 AZ Bison Harvest Summary PDF
- 2017 AZ Black Bear Harvest Summary PDF
- 2017 AZ Mountain Lion Summary PDF
2017 Hunt Arizona: 208-page publication PDF (Includes 2012-2016 data)
Poker Odds Guide
2016 Hunt Arizona: 205-page publication PDF (Includes 2011-2015 data)
2015 Hunt Arizona: 209-page publication PDFRevised
2014 Hunt Arizona: 212-page publication PDF
2012 Hunt Arizona: 198-page publication PDF
2011 Hunt Arizona: 198-page publication PDF
2010 Hunt Arizona: 192-page publication PDF
Expenditure Guidelines Odds
2009 Hunt Arizona: 184-page publication PDF