| True Count | Player Advantage (%) | Betting Ratio (%) | $1000 Bankroll | $2000 Bankroll | $3000 Bankroll | $5000 Bankroll | $10000 Bankroll |
|---|---|---|---|---|---|---|---|
| <=1 | <=0 | <=0 | <=5 | <=5 | <=10 | <=15 | <=25 |
| 1.5 | 0.25 | 0.5 | 5 | 10 | 15 | 25 | 50 |
| 2 | 0.5 | 1 | 10 | 20 | 30 | 50 | 100 |
| 2.5 | 0.75 | 1.5 | 15 | 30 | 45 | 75 | 150 |
| 3 | 1 | 2 | 20 | 40 | 60 | 100 | 200 |
| 3.5 | 1.25 | 2.5 | 25 | 50 | 75 | 125 | 250 |
| 4 | 1.5 | 3 | 30 | 60 | 90 | 150 | 300 |
| 4.5 | 1.75 | 3.5 | 35 | 70 | 105 | 175 | 350 |
| 5 | 2 | 4 | 40 | 80 | 120 | 200 | 400 |
| 5.5 | 2.25 | 4.5 | 45 | 90 | 135 | 225 | 450 |
| >=6 | >=2.5 | >=5 | 50 | 100 | 140 | 250 | 500 |
This Kelly strategy table is a guide for blackjack card counting, specifically for determining the optimal bet size based on the True Count and your bankroll.
Key Terms:
- True Count: A measure of the advantage the player has over the dealer, calculated by dividing the Running Count by the number of decks remaining in the shoe.
- Player Advantage: The percentage of advantage the player has over the dealer, based on the True Count.
- Betting Ratio: The percentage of your bankroll you should bet based on the True Count.
- Bankroll: The total amount of money you have available for betting.
How to Use the Table:
- Calculate the True Count: This is done using a card counting system, such as Hi-Lo.
- Find the True Count on the Table: Locate the True Count row in the table.
- Determine Your Bankroll: Choose the bankroll column that represents your betting budget.
- Read the Optimal Bet: The corresponding cell will show the maximum amount you should bet based on your True Count and bankroll.
Example:
Let’s say you have a $1000 bankroll and the True Count is 3. Find the row for True Count 3 and the column for $1000 bankroll. The table indicates you should bet a maximum of $20.
Important Notes:
- This table is a general guide and may not be suitable for all card counting systems or playing styles.
- It’s important to adjust your betting strategy based on the specific rules of the blackjack game you are playing.
- Always gamble responsibly and never bet more than you can afford to lose.
Additional Tips:
- Start Small: When starting out, bet small amounts to test your strategy and gain experience.
- Increase Bets Gradually: As you become more confident and your True Count increases, gradually increase your bets.
- Don’t Chase Losses: If you’re having a bad run, don’t try to make up for lost money by betting more. Stick to your strategy and your bankroll.
By using this table and practicing responsible card counting, you can improve your chances of winning at blackjack.
The Kelly Criterion, often referred to as the Kelly strategy, is a mathematical formula used to determine the optimal bet size in situations where the outcome of a bet is uncertain. It aims to maximize the long-term growth of your bankroll while minimizing the risk of ruin.
Here’s how it works:
The Formula:
The Kelly Criterion formula is:
f = (bp - q)/b
Where:
- f: The optimal fraction of your bankroll to bet
- b: The odds offered by the bet (e.g., if you bet $1 and win, you get $2 back, then b = 2)
- p: The probability of winning the bet
- q: The probability of losing the bet (q = 1 – p)
Example:
Imagine you’re betting on a coin flip. You believe the coin is slightly biased, giving you a 55% chance of winning (p = 0.55) and a 45% chance of losing (q = 0.45). The odds offered are even, meaning if you bet $1 and win, you get $2 back (b = 2).
Using the Kelly Criterion:
f = (2 * 0.55 - 0.45) / 2 = 0.325
This suggests you should bet 32.5% of your bankroll on each flip.
Key Benefits of Kelly Criterion:
- Maximizes Long-Term Growth: It aims to grow your bankroll at the fastest possible rate over time.
- Minimizes Risk of Ruin: By avoiding excessive bets, it helps you avoid losing your entire bankroll.
- Adaptive: It adjusts the bet size based on the odds and your perceived probability of winning.
Limitations:
- Requires Accurate Probability Estimates: The Kelly Criterion relies on accurate estimations of the probabilities of winning and losing. If your estimates are wrong, the strategy could be detrimental.
- Can Be Conservative: In some cases, the Kelly Criterion might suggest very small bets, which could lead to slow growth.
- Doesn’t Account for Emotions: It doesn’t factor in psychological aspects of betting, such as risk aversion or excitement.
In Blackjack:
The Kelly Criterion can be applied to blackjack card counting. However, calculating the optimal bet size in blackjack is more complex than a simple coin flip. You need to consider:
- True Count: The advantage you have over the dealer, which changes throughout the game.
- Bankroll: Your total betting money.
- Table Stakes: The minimum and maximum bets allowed at the table.
While the Kelly Criterion is a powerful tool, it’s essential to understand its limitations and use it responsibly. It’s not a guaranteed path to riches, but it can be a valuable strategy for maximizing your long-term success in situations with uncertain outcomes.