1. Analysis and Strategy 1) They can’t all be homers

2. 1: They can’t all be homers The first step in analysis is knowing what to analyze. This means understanding the true objective of the analysis, which usually entails working backwards from the overall goal to the proximate causes of that outcome. This creates a “Factor Map” of causes leading to the main outcome. The power of analysis is in understanding these causes and their relation to the main outcome as well as the inter-relation of factors. For example, in baseball, the objective may be to score more runs than the other team, but that does not necessarily mean that the objective, or value, of each batter is to hit a home run. There are many ways that a batter may contribute to the scoring of runs, and one of the main purposes of the field of sabermetrics is to investigate the causes of runs and the inter-relationships between those causes so that such analyses may aid general managers in team development strategies, managers in game play strategies, etc.

3. 1a: Factor Maps Before examining more formal means for determining the “root causes” or “key drivers” of outcomes, or “problems,” some practice in making these intuitive connections, or Factor Maps, may be helpful: Blackjack, or 21, is a simple game well known to most people. A typical goal, or desired outcome, is to win, i.e. have a financial gain at the conclusion of play. This ignores the entertainment, social, etc., value of the experience, as well as any incidental gains or losses (free drinks, awarded “points” for play, transportation costs, etc.) for the sake of simplicity to facilitate the task here. The first step in this analysis is to clarify what is meant by “win.” Even with the financial constraint simplification “win” is hardly the simple problem that it appears to be, as the issue for many is as much a perceptual issue as it is an economic one. So initially, what is meant by the simplified “win” depends on the perception of the value of financial return magnitude, as well as the definition of the term ”conclusion of play.” There are no absolute answers to these questions; the outcome or problem is relative and idiosyncratic. -How much money is a ‘’win” for you? A good win? These are essentially “utility curve” issues, but in a sense represent “target returns” that will influence strategy. e.g., -----Bad loss-----loss-----small loss-----even-----small win-----win-----good win----- $ 200 $ -100%+* -25 to -100% -10 to -25% + 10% 10-25% 25-100% 100%+ *Lose more than you came with (get additional funds) or were willing to lose -What is the “conclusion of play” for you? One visit? One year? Lifetime? Once you know what “win” means, then you need to understand the factors that impact the outcome. Again, before formally examining the outcomes to develop hypotheses regarding causal factors, we can assume via intuition these factors in order to illustrate the process, i.e., construct a “concept map.” For this discussion, the causal factors are assumed to be: -House Edge-Odds Improvement Techniques -Knowledge of Game-Money Management -Quality of Play-Serendipity -Internal and External Environment

4. Blackjack Concept Map Factors Objective: Achieve at least a small win (>$20) for a single visit (one evening at Foxwoods or Mohegan Sun) within risk tolerance standards (maximum loss $200) Critical Factors: - House (Edge, Dealer): The famous John Scarne first calculated the house edge at 5.9%, but variations in the modern game typically bring the house percentage down to around <1% in many cases. - Knowledge of Game: Game rules are easily understood, but Casino variations may be significant. -Quality of Play: Strategy/Play guides, such as the one on the previous page, are plentiful and provide information on optimum play. Many distractions at the gaming table, the difficulty of memorizing optimum play heuristics, and natural human foibles, create significant potential for deviations from optimum play. -Odds Improvement Techniques: Conventional wisdom holds that there are systems, such as card- counting, that may reduce the house edge. Modern thinking appears to maintain that Casino counter- actions (penetration cut, multiple decks, constant shuffling, pit monitoring, etc.) greatly mitigate potential legal techniques. While there may be some merit to new theories, such as “clumpiness,” most modern strategists now conclude that current odds improvement techniques provide at best minimal effects, if any. -Money Management: When cards are randomly distributed or non-random distributions are unknown, no betting system has been shown to be advantageous since each trial (hand) in independent. Where a non- random distribution is known, differential bets and play position may have some impact. However, as such knowledge is very difficult to attain, of intermittent and short duration, and produces only small probability variations, to have any real effect a very large number of trials (hands) must be played to approach true probability values. Beyond bet management, there are also session money management issues, such as “limit loss” and “lock profit” heuristics. -Serendipity: The greater the number of trials, or hands, the greater the confidence that true probabilities will be approached. Conversely, the fewer the hands, the greater the potential impact of “luck.” For a single visit, serendipity effects are likely to be substantial. -Environment: Internal and external factors interacting and influencing other factors. Examples include alcohol, emotions, “magical thinking,” distractions, memory, etc.

5. Factor Map- Blackjack “WIN” House Serendipity Player (H) Natural Odds (H) Dealer (L) Money Management (L) Knowledge Of Game (M) Quality of Play (H) Odds Improvement Techniques (L) H = High Importance Factor M = Medium Importance Factor L = Low Importance Factor Environment (M)