We are interested in looking at the existence of gambling strategies because it allows us to validate some of the ideas behind theoretical predictions. We search for strategies that are path independent and path dependent, allowing us to verify the types of gamblers in Barberis’ casino model . However, we will observe that it is impossible for us to observe sophisticated, committed gamblers from an empirical standpoint, as we do not know what devices are used by them.
In our dataset, we are unable to evaluate gamblers that follow proportional betting standards, as it is not possible to parse their wallet data exactly at the times they bet. Because of this, we do not have access to their total wealth information, and thus we cannot search for proportions they bet at. In response to this, we will evaluate gamblers that bet at a fixed wager in place of proportional bets. Also of interest is the betting system in which a gambler continuously bets at a high probability (analogous to the bet everything system). This is one of the most common systems. Additionally, we will be able to evaluate gamblers who bet with negative progression, staking betting systems. We will evaluate one of the most common systems: the martingale. This is because gamblers following the martingale always return to their original stake, making it easier for us to detect the usage of this system. We also aim to see if gamblers have a mixture of systems, such that they transition strategies over some timescale. The reason why we choose these systems for our analysis is because it allows us to possibly observe time inconsistencies in both path-independent (fixed wager/fixed probability/high probability) and path-dependent (mixed) strategies.o find more simple systems, such as fixed probability, fixed เว็บพนัน UFABET wager or high probability betting systems, we will use Python’s pandas package for data analysis. To classify fixed systems, we convert our data, stored in csv files into pandas dataframe, and search for gamblers who have zero variance in their probability choice and wager sets (see Dataset and methods for details). To classify high probability bettors, we choose any bettor who bets only at tuning the probability of winning p > 0.9.
We also will only apply these methods to gamblers who have sufficient gambling data, e.g. whale bettors (bettors with over 100 total gambles). Additionally, we assume that the initial reference frame for these gamblers, once they enter the online casino, is the beginning of the day their betting session starts at. In this way, we will be able to detect possible time inconsistencies in daily data. With this as our reference point, we found many gamblers that behave similarly to the hypothesized path-independent betting, naive gamblers who are unaware of the time inconsistencies. However, we observe some interesting path-dependent betting strategies as well (such as the martingales), or some mixture of betting strategies.The most common and popular ‘strategy’ found in this population is the fixed probability betting strategy. In this strategy, the gambler chooses some probability, usually p > 0.5 and continually bets. In evaluating gamblers who bet with fixed probabilities or wagers, we can observe what happens when a gambler has no strategic time inconsistency (irrespective to exit strategies). In a very heuristic way, we can label these kinds of gamblers as more risk seeking if p < 0.5 and less risk seeking if p > 0.5.
An example of this strategy is found in the betting history of the individual labelled as professional #5619 in our dataset (figure 12). Through the three-date periods of 23 November 2017 15.17.43—23 November 2017 19.54.43, 24 November 2017 8.22.40—24 November 2017 23.30.14 and 25 November 2017 8.20.38—25 November 2017 22.04.12, this gambler gambled 147 (whale) times, all at p = 0.49. This is an example of a simple, path-independent strategy. No matter what his/her results are, the gambler sticks to his/her initial chosen betting strategy. Upon entering the casino, the gambler commits to this strategy, and even upon accumulating losses, this individual continues to gamble at a suboptimal probability. In gambling, at p < 0.5, this gambler is taking significant risk—in the long run the expectation runs negative rapidly.