The Challenges of "solving" 4 & 5-Card PLO

Omaha is a more complex game to solve than No-Limit Hold'em. The higher number of hole cards expands the possibility of getting dealt a specific starting by a significant factor.

In Texas Hold'em, there are 1326 preflop combos you can get dealt. In 4-Card Omaha, this number increases to 270'725, and in 5-Card Omaha to 2'598'960 preflop combos.

Because of the high complexity of Omaha, current solvers aren't solving the game to the same degree of accuracy as No-Limit Texas Hold'em. So instead, in Omaha, a solver simulates every possible node in the game tree, including every possible starting hand, in pursuit of finding the Nash equilibrium. This is a process that, in theory, has an ending point. But unfortunately, we don't have the technology to solve Omaha entirely and reach a Nash equilibrium.

Therefore current Omaha solvers use abstractions to simplify the game. For example, a solver groups hands that share traits in character to lower the game's complexity. In essence, this makes the output not as accurate but gives humans an approximation of what a game theory optimal (GTO) strategy might look.

In solving Omaha, even with abstractions, a solver with modern technology can't solve every node to nash equilibrium. Therefore when scrolling through solver output, you might encounter some misleading information. For example, sometimes expected value (EV) might not match the recommended action, or sometimes a specific combo chooses an unorthodox line, which isn't congruent with hands of similar strength.

In this case, you must look at the bigger picture and compare individual combos with a more significant subset of hands. For example, if KK72 rainbow calls a 3-Bet, but any other combos of rainbow Kings with disconnected side cards folds, then KK72 represents an outlier and should fold more likely than not.

Frequently occurring situations in the game, for example, button raises first-in, are solved to a higher degree of accuracy than infrequently occurring nodes. Therefore you might encounter more outliers or misleading information in spots such as, "EP raises, MP calls, CO calls, Button 3-Bets, Small Blind next to act".

Because the solver uses a primitive method of playing through each scenario one by one, it has a lower chance to play through less frequently occurring spots and solve these to nash equilibrium.

Therefore, you must carefully analyze these few spots, especially when filtering into individual combos. The best practice is to filter for a more significant subset of hands to understand better how to play a particular type of hand instead of a specific combo.

A simplified solution can help us understand some of the more complex situations in the game, such as making profitable preflop decisions, finding stack-off thresholds, and finding good blockers to make a bluff or light call-down.

However, we must understand that we're still far away from completely solving Omaha, even within the constraints of a simplified model with abstractions.

This should come as a reminder of not blindly following solver suggestions but using them as a guidance tool to make better-informed decisions. The most valuable tool to improve your game is still your brain and should always question any outside source of information.

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