This is the first part of a two-part series. You can read the second part here.

Generally speaking, people who have tried the new game Power Up from PokerStars have responded positively. I’m sure there are some who’ve played it and hated it, but I haven’t seen anything written to that effect so far.

There are plenty of people out there who still refuse to try it, however, and I can guess at their reasons. For one thing, it’s PokerStars, and the company has done a great deal in the past couple of years to alienate high-volume and net-withdrawing players. That’s fair enough, and I don’t fault anyone who is boycotting the site in general and won’t try Power Up for that reason.

Others are dubious because of the game’s structure – three players, 25 BB starting stacks, blinds increasing every five hands – and its rake, which is currently 8% for $1 and $3 games and 7% for $7 games. In both these regards, Power Up resembles Spin & Go, which is widely regarded as a very difficult game to beat due to its rake being quite high for such a low-strategy, high-variance game.

Silly games and serious players

Although fun to play casually and popular with recreational players, Spin & Go embodies everything that has made online poker such a miserable experience for those attempting to treat it as a source of income. With stacks that shallow and a structure that fast, players find themselves facing the same basic sorts of decisions over and over again. That means that the game’s skill ceiling is very low, and one must be playing very close to it in order to clear even a small profit, and then play a huge volume to turn that narrow edge into significant income.

The way to go about winning at Spin & Go is to write or purchase software to work out game-theoretically optimal strategies, then to memorize those strategies. When the game begins, for instance, there are certain hands you’ll be opening for a min-raise on the Button and some you’ll be folding. Once you’re into the second level, perhaps some hands become open shoves instead of raises. If you raise and get called, you know which hands you’ll bet and which you’ll check on certain textures, and so forth.

Because of their structural similarities, it’s natural to assume that Power Up will be approachable the same way, if you haven’t actually played it. If you have, however, it should be clear with a little thought that it’s a very different beast from conventional Hold’em, and in a way which means it doesn’t actually get much simpler with shallower stacks. The approaches used to approximately solve Spin & Go and other shallow-stacked formats simply won’t work with Power Up. It’s a qualitatively different sort of problem.

Reducible games

It may sound weird to talk about solving Spin & Go, because No-Limit Hold’em is regarded as being one of the toughest challenges for AI. Technically speaking, it’s an even “bigger” game than Go. But this is because of the continuum of available bet sizes. A bet of 5 big blinds and a bet of 5.5 big blinds are different moves, so branching of the game tree is enormous.

From the point of view of skill levels attainable by humans, however, there’s usually not going to be much difference between those bets. No-Limit Hold’em – especially short-stacked No-Limit Hold’em – is a highly reducible game.

What I mean by that is that it’s a game we can replace by simpler, more readily solvable versions of itself, and the solutions to those simpler games will often be “good enough” to win in play against other humans. In fact, such simplification is necessary in order for human players to put the strategies into practice anyway. It’s hard enough to memorize what your continuation betting range is going to be on various textures; it would be impossible to do so if one was treating A52 and A42 as substantially different boards while also having a 30% pot betting range, a 40% pot betting range, a 50% pot betting range, and so on.

Horizontal vs. vertical reduction

That division of game elements into discrete “buckets” is one part of reducing a game; we round off stack sizes, restrict our betting options to third-pot increments, and lump hands and board textures together into general categories like “broadways” and “middle pairs.” We might call this sort of simplification horizontal reduction, as we’re narrowing the game space and pruning branches off the game tree at the level of our current decision.

There’s a second, equally important type of reduction, however, which we could call vertical reduction. This involves treating sequential decisions as independent games, each with its own goal. For instance, we almost always treat one poker hand as being independent of the next, even though the outcome of the current hand is going to impact our starting chip stack for the next one, which will in turn affect our strategies. It’s impossible to think that far ahead, so we set ourselves the simpler goal of maximizing our expectation value for the current hand and assume that’s going to maximize our long-term profit in a cash game or our chances of winning the tournament.

On a smaller scale, players attempting to find approximate solutions for No-Limit poker approach each street as a separate problem. There are just too many possible lines for us to think a hand through from preflop to showdown. Rather, we think about hand equities and balancing our ranges and so forth. Earlier decisions do factor into later streets as we update our assumptions about the opponent’s range based on the action, but when we’re figuring out which hands to check back on a given flop, we’re not explicitly thinking about what we’ll do on every possible runout against every possible line from our opponent; we’re simplifying the game by assuming that having sufficient equity and a balanced range is good enough.

Trying to reduce Power Up

Power Up may be almost as horizontally reducible as conventional No-Limit Hold’em, in some ways maybe more so. Bet sizes can certainly be “bucketed,” and in fact the sizing of small bets may not matter all that much; the biggest strategic issue is whether a bet is all-in, almost all-in or anything else, since a player being all-in changes the nature of the game, freezing the board and preventing that player from using any further powers. Likewise, most low-quality hands can be treated as identical in many cases, as if we have access to an Upgrade or Reload, we’re unlikely to be holding those same cards at showdown anyway.

It’s vertically that Power Up differs very importantly from all other commonly-played forms of poker. Decisions have impact beyond the current street and even the current hand, in ways that decisions in Hold’em do not. Here are some of the major ways in which Power Up requires planning ahead:

  • Energy and powers held between streets: This should of course be obvious. Chips are wagered in a hand, but energy and powers are spent. Winning a hand in conventional poker is pure gain, but using powers to win one in Power Up means fewer resources in future hands. Thus, the question isn’t always whether a power increases our odds of winning a given hand, but whether the benefit now is likely to be greater than we could reap for the same expenditure in a future hand.
  • Many more information asymmetries: In conventional poker, the amount of hidden information is fixed. The public game state consists only of stack sizes, the pot size, and the actions so far in the hand. Each player’s private game state consists of this plus knowledge of their own two cards. In Power Up, the public game state is more complex, of course, including the use of powers, any information publicly revealed by those powers, plus players’ energy counts and number of power cards held.

    Moreover, there are many more types of private information a player can have, including which powers they’re holding, which cards they’ve discarded, and potentially the top one or two cards of the deck. These all have a profound effect on strategy, as the exact same board and betting action can be extremely different based on whether or not one’s opponent has energy left, for instance, or whether someone knows the next card coming off the deck. Even considering only number of cards held and energy totals for a heads-up situation, what is one game state in conventional Hold’em produces over 3000 distinct game states in Power Up; when all the other new forms of information are included, the difference is likely a factor of a few tens of millions or more.

  • Streets bleed together: The fact that players are peeking at and even manipulating the top cards of the deck means that there is no longer so clear a distinction between streets. If there are only three cards on board but my opponent has Intel active and can see the next one, we’re effectively on a kind of “demistreet,” somewhere in between the flop and turn. When inferring his range from his actions, I have to remember that he’s playing his hand from the perspective of the turn, while he must remember that I’m still back on the flop.
  • The importance of closing the action: So long as one’s opponent has power cards available and the energy to use them, there are certain powers which are much safer to use when closing the action. Engineer is the clearest example, as opponents can see which card you’ve selected to be the next off the deck; if they have a chance to respond, they may end up getting rid of it with Scanner or an Engineer of their own, or even elect to put it into their hand with Reload or Upgrade.

    That means that situations arise where one would like to make a bet and to use the power, but can’t do both without reopening the action for others. This then requires a splitting up of the strategy, either using the power before checking back or calling, with the intention of betting on the following street, or betting with the intention of using the power at the next available opportunity.

All of that should give you the intuitive sense that the techniques used to approach conventional Hold’em won’t prove very successful for attacking Power Up. You might still guess, however, that there are commonly-occurring scenarios which would lend themselves to a brute force approach, like the ubiquitous preflop push-fold scenario. You’d be wrong, though. In fact, unless we get down to incredibly tiny stacks of around one or two big blinds, the only time Power Up becomes simple is when no player has enough energy left to use any powers – in other words, when Power Up isn’t actually Power Up.

This was originally intended to be a single article, but ran very long. In the second part, to be posted tomorrow, I’ll take a look at what happens when we take a standard short-stacked heads-up “push-fold” scenario, and give just five energy and two simple powers to each of the players.

Part 2: A ‘Simple’ Example

Alex Weldon (@benefactumgames) is a freelance writer, game designer and semipro poker player from Dartmouth, Nova Scotia, Canada.