Can we make poker great again?

[Admin]

While texas holdem is a very good card game and is still relevant it is definitely showing its age now with it being easy to use real-time assistance to cheat against other players.

The game is also overly analyzed with does take a bit of fun out of it. It's less interesting when you can simply plug it into a solver and get the exact perfect play.

 

[Admin]

8 card poker
For the same stacks and betting format this game (NLP8 A variant) is around 23 million times harder to solve than NLHE if the number of players is 2.

See attachment poker8_99 for more details.

https://app.box.com/s/w1ws365yhewl2cdwm052te7z19h3unbq

 

[Admin]

Increasing the number of community cards does make it harder to solve
If we take texas holdem and increase the number of hole cards to 3 and reduce the flop to 2 cards the game becomes around 14 times harder to solve. While this may seem like a significant improvement it really doesn't help much given how powerful computers can be.

If we get rid of community cards completely and also have one of the 3 starting cards be visible the game becomes around 173 267 640 times harder to solve. That is assuming 2 cards are added to each player next betting round and then 1 card added per round until a total of 7 is reached for every player (of which 5 is selected for a hand).

 

[Admin]

Tweaking blinds/ante
The way blinds are set up in texas holdem make the game prone to having just 2 players after the fllop (if it even reaches the flop) since limping is generally bad outside of the small blind.

What if we instead had the player at the BB position have the standard blind and randomized it for everyone else? (up to a full big blind) that would make the game more dynamic instead of you following preflop charts to tell you what to do every time.

Another interesting option is to have ante only so no forced betting at all. Results in all players reacing the flop if nobody raises.

 

[Admin]

Stack depth and the number of betting rounds
Having more betting rounds or deeper stacks does make the game significantly more complex to solve.

Unfortunately for texas holdem that game doesn't work too well preflop if it's too deep and this depend on the number of players where more players means that the game will function worse as it gets deeper. Other poker games that start with more hole cards (PLO, NLP8A, NLP8C, etc) does not however have that issue preflop (standard omaha has postflop issues though).

I would estimate the following max depths (before significant issues emerge) for various games (heads up):

NLHE: 360 BB
NLP8C: 6 000 BB
NLP8A: 700 000 BB

Note that the max depth is inversely proportional to the number of players so NLHE with 6 players should not be deeper than around 120BB.

 

[Admin]

The AI threat
Unfortunately it is always possible to develop AI to master some poker game even if you cannot brute-force your way through the game via a solver.

https://en.wikipedia.org/wiki/Pluribus_(poker_bot)

 

[Admin]

Live poker
It is significantly harder to cheat via an AI/solver in live poker where other people can see you directly. That however does not eliminate the possibility of cheating, it simply makes it harder. There are plenty of cheating scandals involving live poker with private games being especially problematic.

https://www.youtube.com/shorts/MWl-Vb2LQ6Q

 

[Admin]

The notion that computer hardware is going to magically improve to solve all poker variant is very much false.

Let's take no limit poker8 (variant A) with 8 players.

Each player starts with 5 holecards

flop: 3 community cards added
turn: 2 community cards added
river: 1 community card added.

Number of card combinations (including equivalent hands) = FACT(52)/FACT(3)/FACT(2)/FACT(5)^8/FACT(6)

217 112 426 596 910 000 000 000 000 000 000 000 000 000 000 000

Then you have to multiply that with the size of the game-tree from the betting which is enormous even if you use a very simple tree with only one allowed bet-size (way more than a billion if everyone has like 256 times the initial pot and only 50% pot-size is used. If a bet called by N player is of the size 1(N+1) we get 22 088 403 073 ways the betting can be done if everyone starts betting on the river (50% bet-size used instead if it results in all-in, assuming no folds prior to all-in).

1000 billion computers checking 1000 billion combinations per second would need 6 880 024 652 437 833 years to check all the combinations.

It's not always practical to use a brute-force approach to solve a game. In the case of go very strong artificial neural networks eventually solved it properly.