<![CDATA[Mathieu's Blog]]>https://mathieutorchia.comRSS for NodeThu, 18 Jul 2024 14:13:23 GMT60<![CDATA[Exponential Growth: Investing and Inflation]]>https://mathieutorchia.com/exponential-growth-investing-and-inflationhttps://mathieutorchia.com/exponential-growth-investing-and-inflationMon, 01 Jul 2024 16:00:55 GMT<![CDATA[<blockquote><p>Visit my GitHub page (<a target="_blank" href="https://github.com/mathieutorchia/SP500-Investing-Project">link</a>) to learn more about the python code that made this article possible.</p></blockquote><p>Isn't exponential growth a mind-blowing concept? I remember first learning about it and not thinking much of it. However, the more I thought about it, the more I realized how common it is around us, and how powerful it can be. It's easy to say things like: "<em>Only 42 people have COVID in the United States, what's the big deal?</em> "or "<em>Sure I'll sign the mortgage, the 5% fixed interest rate is not that bad." or "I'll keep my money under my mattress, I don't want to risk it in the stock market"</em>. At first glance, these statements seem reasonable. However, when we consider their compounding nature, they take on a completely different meaning:</p><ul><li><p>In March 2020 (in the US), the number of COVID cases jumped from 42 at the start of the month to 185,000 by the end (a 4400x increase!).</p></li><li><p>Even if the fixed interest rate is set at 5%, mortgages usually last for many decades. This means that 5% is compounded yearly and could end up growing to over 100% of the home's value.</p></li><li><p>If you kept your money under your mattress from 1983 to 2024, it would be worth a third of its initial value (in real terms).</p></li></ul><p>While there are countless examples of exponential growth that affect us in our lives, we will be focusing on it in the context of investing in the stock market. In this article, <strong>we will explore the long-term effects of periodically investing in the stock market</strong>, as well as <strong>how inflation affects your bottom line</strong>.</p><h3 id="heading-inflation">Inflation</h3><p>Before getting into the importance/benefits of investing in the stock market, let's explore the <em>worst</em> thing that was ever invented: inflation.</p><div data-node-type="callout"><div data-node-type="callout-emoji">ðŸ’¡</div><div data-node-type="callout-text"><strong>Inflation</strong> is the term used to describe how the money we have today will be worth less in the future.</div></div><p>One of the ways we track inflation is by looking at the consumer price index (CPI), which <strong>measures the average change over time in the prices paid by consumers for a basket of goods and services</strong>. For example, if inflation was 3% last year, this means that, on average, something that used to cost $100 will now cost $103. In other words, your money is losing value... every. day.</p><p>So, how bad is it? We can plot the CPI in the United States from 1947 to 2024 to help answer that question.</p><p><img src="https://cdn.hashnode.com/res/hashnode/image/upload/v1719626639204/c1158a85-9580-4a36-a607-66f4ccdc87c3.png" alt class="image--center mx-auto" /></p><p>This shows the CPI to be 100 in 1983, in contrast to roughly 300 in 2024. This means that $100 of typical expenses in 1983 would cost 3x that amount in 2024!</p><p>At first, this is terrifying. Thankfully, there is a way to bypass some of the negative impacts that come with inflation, and that is for investors to place their money somewhere it will appreciate in value: real estate, private lending, <s>loansharking</s>, or investing in the stock market.</p><h3 id="heading-the-stock-market">The Stock Market</h3><p>There are many ways to invest in the stock market. For the purpose of this article, we will be looking at investing in an index fund (like <code>TSE: XSP</code>) that mimics the Standard & Poor's 500. The S&P 500 tracks the performance of the 500 largest companies in the United States. In fact, these top 500 companies make up roughly <strong>80% of the total U.S. equity market capitalization</strong> (source: <a target="_blank" href="https://www.morningstar.ca/ca/news/185437/sp-500-or-total-stock-market-index-for-us-exposure.aspx#:~:text=Stocks%20in%20the%20S%26P%20500,the%20presence%20of%20smaller%20stocks.">Morning Star</a>). Investing in an index fund that includes all the companies in the S&P 500 is common advice, even from people like Warren Buffet:</p><blockquote><p>"In my view, for most people, the best thing to do is own the S&P 500 index fund. The trick is not to pick the right company. The trick is to essentially buy all the big companies through the S&P 500 and to do it consistently and to do it in a very, very low-cost way".</p></blockquote><p>Now, let's look into the outcome of investing in the S&P 500 for 40 years, from 1983 to the end of 2023.</p><h3 id="heading-investing-for-40-years-increasing-monthly-investments">Investing for 40 Years - Increasing Monthly Investments</h3><p>Let's imagine an investor (we'll call her Sabrina) who is about to embark on a lifetime of textbook S&P investing:</p><ul><li><p>She has purchased $50,000 worth of shares (at the start of 1983).</p></li><li><p>She is willing to invest an additional $2,000 per month from 1983 to 2023.</p></li><li><p>She is willing to <strong>increase her monthly investment by the inflation rate</strong>. For example, if the inflation rate is 1%, then instead of investing $2,000, she'll invest $2,020.</p></li><li><p>When she receives dividends (once per year), she will automatically reinvest them into the index.</p></li></ul><div data-node-type="callout"><div data-node-type="callout-emoji">ðŸ’¡</div><div data-node-type="callout-text">A <strong>dividend </strong>is a small payment made by a company to its shareholders. In the context of typical indices that track the S&P 500, the yearly dividend was <strong>between 1% and 4%</strong> from 1985 to 2024.</div></div><p>It's as simple as it gets as far as investing goes. It will be interesting to take a look at two main metrics: her <strong>nominal net worth</strong>, and her <strong>real net worth</strong>.</p><div data-node-type="callout"><div data-node-type="callout-emoji">ðŸ’¡</div><div data-node-type="callout-text"><strong>Nominal money</strong> is the amount of money measured in current dollars without adjusting for inflation, whereas <strong>real money</strong> accounts for inflation by measuring how valuable your money is in today's terms.</div></div><p>Essentially, the most important number to consider is the <strong>real</strong> net worth. When planning for the future, we need to understand how much our money will be worth in the future. Therefore, it's crucial to account for inflation and focus on the real net worth. Nonetheless, we can plot both Sabrina's real and nominal net worth after 40 years of investing in the S&P 500.</p><p><img src="https://cdn.hashnode.com/res/hashnode/image/upload/v1719637045237/f1383208-9fff-4b03-ac5a-7facfb4ad706.png" alt class="image--center mx-auto" /></p><p>In the lighter blue, we can see that Sabrina will have a net worth of $17,100,000, which is equivalent to enjoying a 10% year-over-year (YoY) return. However, as explained previously, life (on Earth) is a lot more expensive in the future, and inflation was able to grow at an exponential rate. Once we take into account inflation, we get the darker blue curve, which illustrates that Sabrina has $8,200,000 of "real" money (equivalent to a little less than 7% YoY return).</p><p>There are a couple interesting things to note here:</p><ul><li><p>The <strong>gap</strong> between the light blue (nominal) and the dark blue (true) lines <strong>seems to get wider and wider as time goes on</strong>, even though she is increasing her monthly investments to follow the inflation rate. This showcases the magnitude of the inflation rate, which cuts Sabrina's spending power in half. More on this below.</p></li><li><p>This method of investing is similar to enjoying a 7% YoY return. When people say that investing in the S&P yields roughly 10% per year, this is only true at the nominal level, and therefore doesn't mean much.</p></li></ul><p>For those who prefer tables, we can see the growth in both nominal and real terms, as well as the percentage difference between the two.</p><div class="hn-table"><table><thead><tr><td>Year</td><td>Nominal Net Worth</td><td>Real Net Worth</td><td>Percentage Difference</td></tr></thead><tbody><tr><td>Year 0</td><td>$50,000</td><td>$50,000</td><td>0%</td></tr><tr><td>Year 10</td><td>$680,000</td><td>$538,000</td><td>-21%</td></tr><tr><td>Year 20</td><td>$2,630,000</td><td>$1,780,000</td><td>-32%</td></tr><tr><td>Year 30</td><td>$6,350,000</td><td>$3,830,000</td><td>-40%</td></tr><tr><td>Year 39</td><td>$17,120,000</td><td>$8,180,000</td><td>-52%</td></tr></tbody></table></div><p>As explained by the first bullet point above, inflation does not seem to matter much in the first 10 years. The difference between nominal and real net worth is only about 21% (or $142,000). However, once we allow a lot more time to pass (39 years), we see that inflation has wiped out almost half of Sabrina's spending power (which amounts to more than $8,000,000!). Even though the average inflation rate was around 3.5% in the United States from 1985 to 2024, it was solely responsible for a 50% decrease in Sabrina's spending power...</p><h3 id="heading-investing-for-40-years-stagnant-monthly-investments-and-no-dividends">Investing for 40 Years - Stagnant Monthly Investments and No Dividends</h3><p>Let's imagine two other investors (we'll call them Mark and Donald), who are going to follow the same investing rules as Sabrina, except for two things:</p><ul><li><p>Mark is <strong>not willing to increase his monthly investment by the inflation rate</strong>. He will always invest $2,000 per month for the next 40 years.</p></li><li><p>Donald is <strong>not willing to reinvest his yearly dividends</strong> and decides to spend them on luxury goods instead.</p></li></ul><div data-node-type="callout"><div data-node-type="callout-emoji">ðŸ’¡</div><div data-node-type="callout-text"><strong>Side note</strong>: I called <code>M</code>ark "<code>M</code>ark" because he doesn't increase his <code>M</code>onthly investments, and <code>D</code>onald "<code>D</code>onald" because he spends his yearly <code>D</code>ividends.</div></div><p>To summarize the differences between Sabrina, Mark, and Donald, we can refer to this table:</p><div class="hn-table"><table><thead><tr><td></td><td>Sabrina</td><td>Mark</td><td>Donald</td></tr></thead><tbody><tr><td>Starting Investment</td><td>$50,000</td><td>$50,000</td><td>$50,000</td></tr><tr><td>Monthly Investment</td><td>$2,000</td><td>$2,000</td><td>$2,000</td></tr><tr><td>Reinvesting Dividends</td><td>Yes</td><td>Yes</td><td>No</td></tr><tr><td>Increase Monthly Investments</td><td>Yes</td><td>No</td><td>Yes</td></tr></tbody></table></div><p>What will be the impact of Sabrina and Donald increasing their investments to keep up with inflation compared to Mark, who did not? What about the impact of Donald consistently taking out his dividends to spend on other things? We can look at the next graph.</p><p><img src="https://cdn.hashnode.com/res/hashnode/image/upload/v1719679483831/b6eb1c77-fdfc-4c5c-bad2-5d8114956eb6.png" alt class="image--center mx-auto" /></p><p>As we already know, Sabrina ends up with roughly $8,200,000 of real net worth. This is compared to Mark's $5,900,000 and Donald's $5,100,000. If the primary goal is to save the most money for retirement, the moral of the story is quite clear:</p><ul><li><p>For the periods between 1985 and 2024, investors who increased their investments by the going inflation rate had a large advantage compared to those who did not. In the short term, this meant increasing the yearly amount by only 3% (ish), which is equivalent to $60 (if we're investing $2,000 per month). Those seemingly minor incremental increases (like the $60) was equivalent to over $2,000,000 in the long run.</p></li><li><p>For the periods between 1985 and 2024, even though dividends were between 1% and 4%, reinvesting instead of spending them would have a monstrous impact, increasing total net worth by 61%!</p></li></ul><h3 id="heading-conclusion">Conclusion</h3><p>Exponential growth is a powerful concept that should significantly impact our financial decisions, especially when it comes to investing and dealing with inflation. By understanding how inflation eats away at your cumulative wealth over time, we can make more informed choices about where to place our savings.</p><p>Investing in the stock market, especially in index funds like the S&P 500, can help reduce the negative effects of inflation and grow our wealth over time. As shown above, two key strategies to combat inflation are (1) consistently increasing investments to match inflation and (2) reinvesting dividends. By following these practices, and assuming similar market behaviour in the future, investors can expect upwards of 60% more retirement savings after 35+ years compared to not using these strategies.</p><blockquote><p>Visit my GitHub page (<a target="_blank" href="https://github.com/mathieutorchia/SP500-Investing-Project">link</a>) to learn more about the python code that made this article possible.</p></blockquote><p><strong>Disclaimer</strong>: The information provided in this article is for general informational purposes only and is based on historical data of the S&P 500 from 1983 to 2024. Past performance is not indicative of future results, and the financial markets are subject to various risks and uncertainties. This article does not constitute financial advice and should not be taken as such. Readers are encouraged to conduct their own research and consult with a qualified financial advisor before making any investment decisions. The author and publisher of this article are not responsible for any financial losses or damages incurred from following the information presented herein.</p>]]>https://cdn.hashnode.com/res/hashnode/image/upload/v1719685209843/7e8829d8-2282-4167-b198-2823f4172e30.png<![CDATA[Blackjack: Is It Beatable?]]>https://mathieutorchia.com/blackjack-is-it-beatablehttps://mathieutorchia.com/blackjack-is-it-beatableTue, 11 Jun 2024 04:22:25 GMT<![CDATA[<p>This is my first blog and first Python coding project. I have always been fascinated with casino games, especially Blackjack and Texas Hold'em. The appeal of Texas Hold'em is that if played correctly, it can be beaten. Why? Because your opponents are humans, and humans make mistakes. All I had to do was capitalize on their mistakes to make money in the long term. But Blackjack... Your opponent in Blackjack is not a potentially drunken human staying up too late on a Sunday night. Your opponent is the infamous <em>house</em>, which has supposedly made all the calculations to ensure they will win in the end. No matter how well you play, <strong>you will lose in the long run, they say</strong>. So, I decided to turn my first coding project into a Blackjack simulator to see if that statement holds true.</p><hr /><h3 id="heading-player-and-dealer-logic">Player and Dealer Logic</h3><p>This section will explain the various choices that were made to make a good attempt at modelling the game of Blackjack. Here are the main important points:</p><ul><li><p>There is an number of cards (we do not assume a finite number of decks)</p></li><li><p>The dealer stands on soft 17</p></li><li><p>A blackjack pays 3 to 2 (unless the player split aces)</p></li><li><p>The player can double</p></li><li><p>The player can split equal cards as many times as they'd like</p></li><li><p>The player can only split aces once, and can only receive one additional card for each ace</p></li><li><p>The player cannot surrender</p></li><li><p>The player plays the <em>optimal strategy</em> as shown in <a target="_blank" href="https://www.blackjackapprenticeship.com/blackjack-strategy-charts/">this</a> diagram.</p></li><li><p>The player bets $10 per hand</p></li></ul><h3 id="heading-simulation-logic">Simulation Logic</h3><p>Once we have the logic of the game properly coded, the rest is easy: <em>just press run 100,000 times and manually record the results with a pen and paper</em>. Kidding, of course. We can simply write a little bit of code that will run the game as often as we'd like, while recording the relevant information. But what kind of "relevant information" do we need? We decided to record the following information for every hand that was played:</p><ul><li><p>The sum of the player's first two cards</p></li><li><p>The sum of all the player's cards (when he is done playing)</p></li><li><p>The dealer's first card</p></li><li><p>The sum of all the dealer's cards (when he is done playing)</p></li><li><p>A boolean where <em>true</em> signifies that the player split his cards during this specific hand, and <em>false</em> signifies that the player did not split his cards</p></li><li><p>The result (W, L, T)</p></li><li><p>The money won or lost</p></li><li><p>The cumulative total money won or lost for a given player</p></li></ul><p>There are three other things that we record for every hand, which can be confusing to explain, so I would like to take the time to elaborate on it here. Here they are:</p><ol><li><p>The simulation number (one game)</p></li><li><p>The hand number</p></li><li><p>The meta simulation number (one player)</p></li></ol><p>The <strong>simulation number</strong> is used to track which iteration of the game we are currently on. For example, let's say the player is playing his 54th game (in other words, his 54th simulation), and is showing an [8,8]. He then decides to take one more card and gets to [8,8,5] for a total of 21. In this case the simulation number would be 54 since this was the 54th simulation for this particular player.</p><p>Using the example from above, his <strong>hand number</strong> would be "0", since this was the first hand he played in the 54th simulation number. Most of the time, the hand number will be "0", since players usually play one hand per game. However, for example, if a player is showing an [8,8] and decides to split his cards, he will then be given 2 hands: [8,3] and [8,5]. Now the [8,3] will be categorized as hand "0", and the [8,5] will be categorized as hand "1".</p><p>Finally, the <strong>meta simulation number</strong> categorizes a given player. As you'll see in the next section, we simulate the game of Blackjack for 100 different players, or, in other words, we have 100 different meta simulations. Let's say player 3 is playing his 55th game and has a [6,5,10], his meta simulation number would be 3, the simulation number would be 55, and the hand number would be 0.</p><p>Putting everything together, we get a table that looks like this:</p><p><img src="https://cdn.hashnode.com/res/hashnode/image/upload/v1717993361272/ed324eeb-7b8c-417a-b06f-099cf86e2de6.png" alt class="image--center mx-auto" /></p><p>To help read it, the first row shows that for meta simulation number 1 (or player 1), for their first game (first simulation number), and for their first hand (hand 0), their first two cards gave them a total of 16. However, since the dealer was showing a 10, this made them have to "hit" which put them at a total of 26. The final result is a "L (since their sum went above 21) and so the player lost $10, and is currently sitting at -$10 in cumulative earnings.</p><hr /><h3 id="heading-results-first-simulation">Results - First Simulation</h3><p>The first simulation runs the Blackjack game 100 times (100 <strong>simulations</strong>), records the results, and then does this 100 times (100 <strong>meta simulations</strong>). Therefore, in total, there are 10,000 simulations being played (with 10,293 hands since the player split a total of 293 times throughout the simulation). The purpose of running the simulation this way is twofold:</p><ol><li><p>To mimic a scenario where a single person plays for 2 hours, which comes down to approximately 100 hands</p></li><li><p>To simulate observing 100 different people, each playing 100 hands</p></li></ol><p>With each coloured line representing a given player in the figure below, we plot the total profit per player over 100 hands, assuming the player bets $10 per hand:</p><p><img src="https://cdn.hashnode.com/res/hashnode/image/upload/v1717916027481/c39df27d-66db-46cf-baba-87164a7a76c1.png" alt class="image--center mx-auto" /></p><p>It's interesting to note that the graph doesn't clearly show that the house has an edge. There are a lot of players that are above the $0 line (meaning they secured a profit at the end of the 100 simulations). In fact, in this simulation, we find that out of the 100 players:</p><ul><li><p>45 made a profit , where the average profit was $0.87 <strong>per hand</strong></p></li><li><p>54 made a loss, where the average loss was $0.87 <strong>per hand</strong></p></li><li><p>1 broke even</p></li></ul><p>From the points above, it looks like the player wins 45% of the time. However, this is not the case, since the following shows the amount of individual hands that were won, lost, tied, and the average profit:</p><div class="hn-table"><table><thead><tr><td>Result</td><td>Count</td><td>Count (%)</td><td>Average Profit</td></tr></thead><tbody><tr><td>Win</td><td>4,449</td><td>43.22%</td><td>$11.84</td></tr><tr><td>Loss</td><td>4,895</td><td>47.56%</td><td>-$10.93</td></tr><tr><td>Tie</td><td>949</td><td>9.22%</td><td>$0</td></tr><tr><td><strong>Total</strong></td><td><strong>10,293</strong></td><td><strong>100%</strong></td></tr></tbody></table></div><p><strong>QUESTION</strong>: Even though the Player wins at a lower rate than the dealer (43.22% vs 47.56%), the average gain is greater than the average loss ($11.84 vs $10.93). So what's the final result? Are we profitable?</p><p>To answer that question, we can plot the distribution of the <strong>average profit per hand</strong> for every player. Essentially, we look at a given meta simulation <em>i</em> (which represents a player), and we apply the following formula:</p><p>$$\frac{\text{(Total Profit or Loss)}_i}{\text{(Total Number of Hands)}_i}$$</p><p>So, if a player ended with a profit of $50 after 100 simulations (and 105 hands), then his average profit per hand would be:</p><p>$$\frac{$50}{105\text{ hands}} =$0.48\text{/hand}$$</p><p>We do this for each player (each meta simulation), and we plot them in the following bar chart:</p><p><img src="https://cdn.hashnode.com/res/hashnode/image/upload/v1717919095116/94e20971-f15a-4b32-abb9-0acd4cdd3af4.png" alt class="image--center mx-auto" /></p><div data-node-type="callout"><div data-node-type="callout-emoji">ðŸ’¡</div><div data-node-type="callout-text">Keep in mind these values are at the "per hand" level. So if the average loss per hand is $3, then this would come to roughly $300 total loss if a player played 100 hands.</div></div><p>In the plot above, we can see at the most left point, for example, there are roughly 2.5% of players that ended their night with an average loss per hand between -$3 and -2$. However, the red dotted line shows that the average result is a $0.08 loss. We can now answer the question from above.</p><p><strong>ANSWER</strong>: There are two opposing dynamics: the dealer tends to win more hands, but when the player wins, their winnings are typically larger. The question is, which dynamic has a greater impact overall? Unfortunately, even though the player wins more money during a winning hand, <strong>the dealer wins too many hands for the player to remain profitable</strong>, which is why we see an average loss of $0.08 as shown in the figure above.</p><p>You may be wondering, isn't the sample size of 10,000 total simulations a little small? Maybe this is just a fluke? You may be correct, so let's run this simulation 1,000,000 times.</p><h3 id="heading-results-second-simulation">Results - Second Simulation</h3><p>In this new simulation, we keep everything the same, except we allow each of the 100 players (meta_simulations) to play 10,000 simulations (instead of 100). This will give us a more accurate depiction of the long-term reality when playing Blackjack.</p><p>Let's start by plotting the profit per player across the 10,000 simulations:</p><p><img src="https://cdn.hashnode.com/res/hashnode/image/upload/v1717956858777/5e3bbc4f-741b-452a-ab8b-d410f1db586c.png" alt class="image--center mx-auto" /></p><p>In contrast to the first time we ran this graph, we can more clearly see that there are more cases where a player seems to end in the area below the $0 profit line. In fact, in this simulation, we find that out of the 100 players:</p><ul><li><p>25 made a profit , where the average profit was $0.08 <strong>per hand</strong></p></li><li><p>75 made a loss, where the average loss was $0.13 <strong>per hand</strong></p></li></ul><p>This also shows that the more hands a player plays, the less likely it is that they will end the day with a profit. Even though the casino's edge is very small, it adds up quite quickly in the long run.</p><p>When we rerun the distribution plot (as shown below), we also see a similar result, where the average loss per hand is steadily at $0.08 per hand.</p><p><img src="https://cdn.hashnode.com/res/hashnode/image/upload/v1717957250920/5a540219-3e98-4022-b3fd-5f801d8abe47.png" alt class="image--center mx-auto" /></p><p>The distribution is significantly narrower compared to the previous simulation. Earlier, the average profit per 10 hands ranged from -$4 to +$4. Now, it fluctuates only between -$0.30 and +$0.20. This reduction in variance is due to the increased number of simulations played (10,000 versus 100). With more simulations played, the results tend to cluster closely around the true average profit per hand.</p><p>Consider this analogy: if you flip a coin 10 times, its believable to get heads more than 70% of the time (7 or more heads). The probability of this occurrence is roughly 5%. However, if you flip the coin 1,000,000 times, it becomes virtually impossible for heads to appear more than 70% of the time (700,000+ heads). The probability is nearly 0%, as this outcome would be around 400 standard deviations away from the mean. This is an example of the <a target="_blank" href="https://www.britannica.com/science/law-of-large-numbers">Law of Large Numbers</a>, which was proven by the Swiss mathematician Jakob Bernoulli in 1713, and is widely used in the field of statistics, economics, mathematics, etc.</p><h3 id="heading-conclusion">Conclusion</h3><p>Our analysis shows that, for this specific type of Blackjack game and assuming the player uses the optimal strategy described <a target="_blank" href="https://www.blackjackapprenticeship.com/blackjack-strategy-charts/">here</a>, players will, on average, lose $0.08 per $10 hand. <strong>This indicates a house edge of about 0.8%</strong>. This edge is highly specific to the conditions outlined at the start of the article. If any of these conditions changesuch as a 6 to 5 Blackjack payout, the number of decks used, or restrictions on splittingthe house edge will also change. However, regardless of the Blackjack variation, the house will always have an advantage. The only way to potentially shift the odds in your favor is through card counting, which allows you to adjust your strategy based on the current state of the deck. Implementing a card counting feature in the code could be an interesting next step to explore when it turns the profit in favour of the player.</p><p>Thank you for reading the very first blog to be posted on mathieutorchia.com. I am excited to explore more questions and learn new methods on Python along the way. Follow my <strong>GitHub</strong> <a target="_blank" href="https://github.com/mathieutorchia/blackjack_simulator">here</a> to see the Python code that made this article possible (I am still learning the ins and outs about GitHub so please bear with me - if anyone has any suggestions, I am all ears). And of course, feel free to reach out if you have any questions or comments!</p>]]>https://cdn.hashnode.com/res/hashnode/image/upload/v1717960418739/5dc9cade-58ec-4a7c-bad4-fac6566645be.png