Is it worth counting cards?
To answer this question, we need to have enough data points. It would not be realistic to manually play and record thousands of games. So, this is where Python simulator comes in to play. I have generated 100,000 samples by simulating 1000 cases of 100 consecutive rounds for each scenario.
Scenario 1 — Use basic strategy table and use a fixed bet size of $25
Scenario 2 — Use basic strategy table and vary bet size by counts; bet $12.5 for counts under -10, $25 for counts from -10 to 10, and $37.5 for counts above 10
Pool size of $1000For every simulation, the player starts off with full shuffled decksThere is only one player on the table throughout the gameNo insurance or side betsBlackjack payout ratio of 1.5Deck size of 6
Does varying bet sizes help?
After playing 100,000 hands under scenario 1, I have rearranged samples into 3 groups of counts (Below -5, from -5 to 5, and above 5) to compare the win ratios. The chart above illustrates that the player has a higher chance of winning with higher counts. When the count is above 5, there is a 43% chance of winning a hand while the chance of winning falls to 41% when the count falls to below -5. This suggests that betting with higher blackjack simulator wagers for high counts and smaller for low counts increases the player’s expected payoff. (Betting more with less risk and betting less with higher risk)
Why do higher counts have higher win ratios?
This intuitively makes sense. When there are more high cards left in the deck, the chance of a dealer to bust increases as the dealer does not have discretion on when to stand. On the player’s side, it increases the odds of having a good initial hand like a hand value of over eighteen.
Let’s compare changes in the pool sizes
According to the above statistics, we can conclude that varying bet sizes with Hi-Low count system has improved results: 43% of 1000 samples were in profit with counting strategy while 38% without counting strategy. Also, the expected pool value at the end of 100 games has increased by $27 with counting. Thus, players who have been adjusting bet sizes based on counts will likely yield higher profits on average.
Is Hi-Lo System Good Enough to Beat Casinos?
No, it is not good enough. Although the result has been improved with Hi-Lo counting strategy, this does not fully reduce Casino’s edge. The chart on the left illustrates linearly decreasing expected pool size over time as the player plays more rounds of games.
Hence, individual gamblers will only lose in the long term and should never risk an unaffordable amount of money.