Poker as a financial investment problem?

high-risk short-term investment

Depending on your commitment and abilities its usually a lower risk long-term investment than the average portfolio, the # of variables you can influence/mainipulate is way bigger. Portfolio optimization could be linked to your poker game (for example @ MTTs) by playing only the "red" tournaments at stars in which your average ROI should be higher than your average MTT of the same buy-in.

2. Using expected utility instead of the standard expected values. The main idea is that we should be more risk averse when the pot/stack is very large and more risk prone when it is very small.

This makes sense, if you can state it as simple as "the deeper effective stacks are the tighter your range for stacking off becomes.

The concept of utility still works for poker, but portfolio theory isn't applicable because hands / tournaments are indivisible (non-scalable). You can mix 50% of one company's stock with 50% of another company, but you can't play 50% of one hand and 50% of another at the same time if you're 1-tabling. When you play two tourneys of the same kind at once, it's two almost independent investments, not a double investment into a single tourney.

I mean, you need to decide for each tournament (or round at a cash table) separately whether playing it improves your expected utility; the only two possible decisions are to play or not to play.

When you play a bunch of rebuy tournaments at once and decide whether to get a double stack at the start or whether to add on, again, the decision depends rather on the EV than on the risk (it's known that those good players who rebuy before the first hand have bigger ROIs than those who don't rebuy, due to having a stack that covers most weak players' stacks when they make mistakes, and due to rebuys not being raked; if you're not comfortable with the risk, play rebuy tourneys one stake lower).

When you play poker, you don't have a fixed capital that you need to invest fully into a ton of games at once; you need to spend only one buy-in at a time (or as many buy-ins as there are tables to be played at once), which gives you the freedom to decide what to do with the bankroll after those games have finished. Poker allows for much more flexibility than traditional financial markets.

However, poker (especially MTT) staking does allow for portfolio optimisation because MTT (or SnG/cash BAP) shares are quite divisible (one can buy as little as 0.5-1% or as much as 25-50% of a player's grind package). I.e. if you'd like to invest, say, $100 in a single evening, it's wiser to buy $10 pieces of ten MTT players' action than to buy a $100 piece of a single, even strongest, player.

A big difference is that you can have 100 stakees at a time, but you can't play 100 tables at once.

The 'utilisation of the capital' is usually much lower than 100% if you only play poker yourself, e.g. it's typical to only need 15 BIs for a session while having an overall bankroll of 50 BIs.

As a consequence, it's a nice idea to both stake (for a small side profit) and play yourself (which is where most of the profit comes from) if you're able to stake profitably (i.e. recognise which players are good to invest into and which aren't), so that the funds that you don't need immediately for a day/week/month of playing poker still 'work' somewhere.

Another, even better imo, idea to make use of low bankroll utilisation is to select tables / MTTs from a few different sites, storing small chunks of the BR at each site. But it doesn't lower the variance like having a diversified portfolio would do; what it does is that it allows for wider game selection, increasing the total utility EV of those games that you can cherry-pick and play at once.