Have you ever watched the movie 21 (2008)? Or have you heard of the MIT Blackjack Team, a group of students from MIT, Harvard, and other top universities who used card counting techniques to beat the blackjack game? Do you know what the term "card counting" means?
If you're familiar with these concepts, you already know how a brilliant group of students used blackjack to outplay casinos and make money. They followed a relatively simple strategy: by counting the number of high and low cards remaining in the deck, they increased their bets whenever they believed there were more high-value cards left.
This concept, known as card counting, was first popularized by mathematician Edward Thorpe in his book Beat the Dealer. Thorpe’s groundbreaking discovery was that the probability of receiving certain cards changes over time based on which cards have already been played. According to his calculations, when played perfectly, blackjack gives the casino only a 0.21% advantage, meaning the casino earns 0.21% of every wager over time.
However, when specific cards are removed from the deck, the casino's odds shift. For example, the more high-value cards (Ace, King, Queen, Jack, Ten) that are dealt, the higher the casino’s winning probability. But Thorpe discovered the opposite is also true. In his book A Man for All Markets, he explains:
"However, removing lower-value cards such as 2, 3, 4, 5, and 6 significantly benefits the player. The best scenario is when all four 5s are removed, shifting the casino's win probability from 0.21% to the player’s advantage of 3.29%."
This means that under optimal conditions, the player's long-term losing probability of 0.21% can be reversed into a 3.29% winning probability. Although this percentage shift may seem small, it had a tremendous impact, allowing the MIT Blackjack Team to develop a system that led to millions in earnings and even inspired a Hollywood movie.
I often think about Thorpe and his calculations—not because I love blackjack, but because this framework can help us in investing. Recently, a reader asked me:
"I am retired and following a 4% withdrawal rate. My question is whether it is better to withdraw 4% of my portfolio at the start of the year or spread the withdrawals evenly throughout the year. Which strategy is likely to generate more wealth in the long run? Let's assume my portfolio consists entirely of U.S. index funds."
This is an excellent question. To determine which strategy is more advantageous, let’s compare two different approaches:
Lump-Sum Withdrawal at the Beginning of the Year: Withdraw 4% of the portfolio in January and leave the remaining funds fully invested in stocks. Repeat this process every year.
Quarterly Withdrawal Strategy: Calculate the total withdrawal amount based on the January portfolio value and then withdraw equal amounts in January, April, July, and October. Repeat annually.
By testing these two strategies, we found that while both involve the same withdrawal amount, the timing of withdrawals differs. One method sells everything upfront, while the other spreads it out over time. So, which strategy wins?
If we compare these strategies over different timeframes, we find that quarterly withdrawals outperform lump-sum withdrawals in the majority of cases, with win rates ranging from 65% to 100%.
For example, if we test these strategies annually from 1926 to 2021, we find that the quarterly withdrawal strategy ends the year with more money than the lump-sum strategy. Over a five-year period, the quarterly strategy wins 62% of the time. Over 30 years, it wins 100% of the time.
However, beyond just win rates, we should also consider how much more wealth is generated. Unfortunately, the performance difference is not huge. Regardless of investment duration, the quarterly strategy outperforms the lump-sum strategy by an annualized 0.1%–0.2%.
Despite this small performance gap, the advantage compounds significantly over time. For example, on a one-year basis, the quarterly strategy outperforms by 0.05%. Over 10 years, this increases to 0.72%, and over 20 years, it grows to 1.54%. Remember that Thorpe’s blackjack strategy gave players only a 1%–2% edge, yet it still led to massive earnings over time.
This small advantage may seem insignificant, but it is not. If you were playing a fair game where the odds were perfectly 50-50, you would have zero advantage. No matter how long you play, you wouldn't gain an edge over your opponent. But if you have even a 1%–2% edge, your profits will compound over time. Whether in blackjack or investing, the principle is the same.
You might wonder why the quarterly withdrawal strategy outperforms the lump-sum withdrawal strategy. The answer is surprisingly simple: markets tend to rise over time. Because of this, the best theoretical and practical action is to sell gradually over time. By delaying the sale of income-generating assets, you capture more market growth than someone who sells everything upfront. This logic also explains why lump-sum investing generally outperforms dollar-cost averaging.
This logic applies not only to index funds but also to individual stocks. Unless you have a compelling reason to exit a position quickly, selling gradually over time is usually the smarter approach for long-term success.
