Both Bob and Mr. Theymos make wiser decisions but if you ask which one of them is the wisest one I'd choose the DCA way method of purchasing Bitcoin since it doesn't involve a high risk than investing all at once.  However, the process may take longer waiting for the price until will dump to execute the DCA method because DCA spreads your investment over time, reducing the impact of short-term market fluctuations on your overall investment.  The problem here is those investors often struggle to predict optimal entry points when they're planning to invest all at once at a time.

Both are the same in gaining profit but the question of Bob, when Bob enters the market, is he an early investor?

in my opinion, there is no concrete answer on this particular question because we don't know what the market will look like so there are so many factors in play to determine which option would be the best one. from what i understand, we are talking about profits here, right?

so if you want to really determine which one will give you the most profits, you need to consider a certain time frame and consider those 3 options and see what you will get. the option with other alts alone is quite difficult because it depends on the alt itself. the movement is also tough to predict. whereas, even if you decide to choose with btc, the variable of price itself is the factor.

but if we are talking about the risks involved, i can opt for number with the DCA method. at least you are taking action according to the market movement. on the other hand, if you go all in with btc all at once, it means, you are taking all the risks that comes with it before you cash out your btc.

also, if i may add. if a person will choose any of this type of investment. he should also consider what kind of dedication he can give into this. because if he has little to no time, of course it is easy to choose. just go for option 1. but if you have time to observe and make analysis of the market, you can go for either option 2 or 3.

I assume they are investing based on the same time frame since they are investing the same amount of money too. Additionally, I think the aim of this question is about the investment strategy used, not the time. And with that, there is an answer and it’s Mr Bob who is wiser because  he went straight to Bitcoin without having to put his money where he doesn’t know or elongate the time for him to do his investment.

I wouldn't be able to guarantee that this is the most profitable method, but If I have $10,000 just laying round and all my needs is fulfilled, then I would go with Miss Alice, 50% on Bitcoin and 50% for random altcoins, or I could change the proportion like 70% bitcoin and 30% split in some altcoins. I won't go with Bob because I like my portfolio diversified, and I only do DCA if the funds comes from my monthly salary, but if I have some big money laying around I just invest it all at once.

I think it depends on the time when you invest. Right now DCAing sounds better, but when BTC was below $20,000 it was better to invest 100% of that in it.

I support all three of the attitudes mentioned here. Mr. Bob who goes 100% into Bitcoin will have to wait a long time and if the market grows very fast, he will have a lot of success. On the other hand Miss Alice who goes 50% to Bitcoin and 50% to Altcoin is a very good investment strategy. For example among altcoins (Ethereum 50%) it is a very good investment. Then Mr. Theymos who invests $100 per week must invest continuously. Investing using DC is very smart.

Well, the point is that Alice is gambling not investing. But she can hit the lottery and make a x1,000 with some alt, which does not mean that she is a good investor, but that she has been lucky.

Regarding the example raised, in the OP with the other two cases, it seems to me too simplistic because it does not take into account the personal situation and other issues. For example, for me the answer of who is wiser between Bob and theymos depends on whether apart from what they invest they have an emergency fund and other assets. If Bob has a paid house and an emergency fund of 6 months of expenses, apart from what he is going to invest in Bitcoin and theymos has nothing, the wiser is Bob, but if the situation is the opposite, the wiser is theymos.

DCA is the wisest strategy. That doesn't necessarily mean Theymos will be the most profitable. Bitcoin and alts could triple in value and in that situation Theymos will be buying at a higher price while the other investors reap massive profits. If the inverse happens and there is a huge crash then Theymos will have lower losses than the rest. $10,000 is enough to DCA for 2 years. Over a long stretch of time like 5 or 10 years this strategy will have payed off because you will be better prepared for bear markets. You don't have to gamble on altcoins or FOMO into Bitcoin. Having patience is the key to a strategy that will have significant rewards.

Forget the market, forget the current situation let me tell you the fact.

Mr. Bob's playing it safe, going all in on bitcoin.

Miss Alice is taking a gamble, splitting between bitcoin and random altcoins.

Meanwhile, Mr. theymos is staying consistent with a smart DCA.

Now from above theymos is having a balanced and disciplined approach. Be like theymos.

Remember: "Bitcoin is no longer a get-rich-quick scheme; instead, it's a way to avoid getting poor slowly."

Without any sentiment as an investor, I say this without any doubt that Miss Alice is the wisest of them all. By investing in Bitcoin and altcoins, she's already diversified her portfolio and will continue to mean that she can't miss out on both Bitcoin and altcoins investments. Investing a whooping sum of 50% ($5000) in Bitcoin is big enough and there is no way she can miss out on any advantage possible in Bitcoin, this is inclusive of the situation where her altcoins investment fails her.  However, this is highly unlikely if she carefully selects her altcoins/tokens. The same goes for the altcoins as well.

That said, There is a high possibility that she will win more than what she could earn in Bitcoin with her altcoins, that's the reason for investing in the altcoins at the same time as Bitcoin. This has ever been the wisest option in investment, and you can attest to it as some altcoins moved significantly in the last few months where Bitcoin has not doubled its value since that time.

However, all of these guys are doing good, after all, they invested in cryptocurrency and time is the best judge of who will make the most money out of their investments.