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Many advantage-playing friends often ask me how to control fluctuations, how much capital to prepare, how much to bet, and how long it takes to see returns.
Asking these questions indicates a lack of expertise! Being able to calculate expected value (EV) alone is insufficient. Without understanding proper bankroll management, one only scratches the surface without grasping the essence.
In reality, managing capital as an advantage player is not about economics, statistics, or management studies—it's about mathematics!
Firstly, I pose a simple question: Is there a betting strategy that ensures you'll never go bankrupt even if you keep losing?
Take a moment to think about it, then consider the answer below.
The answer lies in using proportional betting, ensuring you never go bankrupt!
For instance, if I bet 10% of my total capital each time, if I lose, I wager 10% of the remaining 90%, thus always retaining 90% of my previous bet, ensuring I always have money left.
Now, the question is, what percentage of total capital should one bet for optimal results?
Let's examine a game with a neutral outcome.
Playing two rounds, losing one and winning one, if I bet 10%, regardless of whether I lose first (retaining 90%, then betting 10% of 90% = 9%) or win first (retaining 110%, then betting 10% of 110% = 11%) the result remains 99%. The formula is (1 + 10%) * (1 - 10%) = 99%, only losing 1% of the initial capital!
Now, let's assume we're playing a game with +EV, meaning we win more often than we lose. In a game where we win 101 times out of 200, if we use the same proportional betting strategy, will we make a profit?
Playing 200 rounds, losing 99 times and winning 101 times, if I bet 10%, the result is (1 + 10%)^101 * (1 - 10%)^99 = 44.7373%. While this is better than the neutral game, it's still not profitable.
However, if we bet 1%, the result is (1 + 1%)^101 * (1 - 1%)^99 = 101.005%, finally discovering a strategy that ensures both solvency and profitability.
But is this the best strategy? Let's save time and take a look at a table illustrating the relationship between betting percentages and profit outcomes.
From the table, we can draw some conclusions:
1. For a game with +EV where we win 101 times out of 200, betting between 0% and 2% ensures profitability.
2. Betting 1% yields the highest profit for a game with +EV where we win 101 times out of 200.
3. Accurate calculation of remaining capital after each bet is crucial. Betting too much or too little inaccurately reduces returns.
The Kelly criterion is derived from this principle, suggesting that for a game where the odds are even, one should bet 1% of the capital, for a game with +2% EV, bet 2%, and so on. However, Kelly's calculations are based on 1:1 odds. Different games with varied odds may not align perfectly with EV. Nevertheless, creating a simple Excel spreadsheet can help determine the optimal betting ratio.
I hope this helps beginner advantage players who are unfamiliar with betting strategies. |
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Post time 16-3-2024 07:37:18