Allin or Fold Poker

Hi,
does anyone familiar with the variant game of poker that is called "Allin or Fold"?
The game is as follows:
- 4 or less players
- Each player has a stack that is usually constant and 8 BB
- BB = 2 * SB
- The players play in order: Cutoff-Dealer-Small blind-Big blind
- Each player can pick between only two actions: {Allin, Fold}

Therefore there are relatively small number of possible states see table below:

Player	History
Cutoff	---
Dealer	CO-Fold
Dealer	CO-In
Small Blind	CO-Fold, DE-Fold
Small Blind	CO-In, DE-Fold
Small Blind	CO-Fold, DE-In
Small Blind	CO-In, DE-In
Big Blind	CO-Fold, DE-Fold, SB-Fold
Big Blind	CO-Allin, DE-Fold, SB-Fold
Big Blind	CO-Fold, DE-Allin, SB-Fold
Big Blind	CO-Fold, DE-Fold, SB-Allin
Big Blind	CO-Allin, DE-Allin, SB-Fold
Big Blind	CO-Allin, DE-Fold, SB-Allin
Big Blind	CO-Fold, DE-Allin, SB-Allin
Big Blind	CO-Allin, DE-Allin, SB-Allin

Seems to me that this can be solved analytically, a solution that looks like: <State, 2 Cards> -> Action for pure strategy and maybe even have probability as the action for mixed strategy.
Dose anyone know any attempts to solve this game?

Thanks,

Is this a casino pit game or poker room game?

I’m not sure what you’re saying in your chart.

For the record, sometimes, when a poker tournament runs long and a deal has been made for most of the money, players will play all in or fold to resolve it for the title and maybe a little bit more money. Note this rarely, if ever, happens on a televised tourney.

A couple months ago, the Wizard wrote an article about a heads up all in or fold game on DraftKings.

https://wizardofvegas.com/forum/gambling/poker/37948-hart-race-hold-em/

A place by me had a version years ago. Cheap rebuys and the all-in rule only lasted so many levels. It was not popular enough to last.

Quote: DJTeddyBear

Is this a casino pit game or poker room game?

I’m not sure what you’re saying in your chart.

For the record, sometimes, when a poker tournament runs long and a deal has been made for most of the money, players will play all in or fold to resolve it for the title and maybe a little bit more money. Note this rarely, if ever, happens on a televised tourney.
link to original post

I saw it online so i am not sure to which category it's fit.

The table is just for showing all the possible states the you can encounter in game so both to clarify the problem and to show it's a simple game.

Yes I am familiar with that tactic but in this case it's not a tournament, it's a cash game.

Quote: DJTeddyBear

A couple months ago, the Wizard wrote an article about a heads up all in or fold game on DraftKings.

/forum/gambling/poker/37948-hart-race-hold-em/
link to original post

Yes, it's actually similar to the idea of the game.
The main difference is that you play against a player without knowing his strategy. So first i guess you have to find the equilibrium, and maybe given history of the player you can find optimal strategy given the player strategy.

Quote: AZDuffman

A place by me had a version years ago. Cheap rebuys and the all-in rule only lasted so many levels. It was not popular enough to last.
link to original post

I saw it in a couple of online poker software and there were hundreds of players in the tables so I guess it's making a comeback.

Is this the game you are talking about?
https://pokerfuse.com/news/poker-room-news/218846-play-four-hand-all-or-fold-poker-exclusively/

Quote:

What Is All-In or Fold Poker?
All-In or Fold (or AoF) poker is a brand new variation of real money online poker available only at GGPoker Ontario. The game is played at four-handed Texas Hold’em tables and is offered at micro, low, mid, and high-stakes.

True action junkies who love poker will fall in love with AoF, as the format provides relentless non-stop action that leaves no room for tanking or wasting time.

The initial buy-in for AoF games is a maximum of eight big blinds at all stakes, and you are allowed to take any chips you accumulate past 8 big blinds off the table.

This means you will never need to risk more than eight big blinds in a single hand unless you want to, and you will be able to play nearly perfect poker with some training and discipline.

The short time bank each player is given to act and the ability to choose between only two options makes these games lightning-fast, allowing you to get the maximum number of hands per hour at all times.

With only four players at the table, you can apply the basics of All-In or Fold Poker charts, which have been around for a long time, to play a profitable strategy. Fortunately, such charts are readily available, and you should be able to master them in no time at all.

Finally, playing AoF means being in contention for the AoF Jackpot, available at each level of play.

Quote: Hannibal96

Quote: AZDuffman

A place by me had a version years ago. Cheap rebuys and the all-in rule only lasted so many levels. It was not popular enough to last.
link to original post

I saw it in a couple of online poker software and there were hundreds of players in the tables so I guess it's making a comeback.
link to original post

It probably works better online as rebuys will slow a live game.

Quote: Mental

Is this the game you are talking about?
/news/poker-room-news/218846-play-four-hand-all-or-fold-poker-exclusively/

Quote:

What Is All-In or Fold Poker?
All-In or Fold (or AoF) poker is a brand new variation of real money online poker available only at GGPoker Ontario. The game is played at four-handed Texas Hold’em tables and is offered at micro, low, mid, and high-stakes.

True action junkies who love poker will fall in love with AoF, as the format provides relentless non-stop action that leaves no room for tanking or wasting time.

The initial buy-in for AoF games is a maximum of eight big blinds at all stakes, and you are allowed to take any chips you accumulate past 8 big blinds off the table.

This means you will never need to risk more than eight big blinds in a single hand unless you want to, and you will be able to play nearly perfect poker with some training and discipline.

The short time bank each player is given to act and the ability to choose between only two options makes these games lightning-fast, allowing you to get the maximum number of hands per hour at all times.

With only four players at the table, you can apply the basics of All-In or Fold Poker charts, which have been around for a long time, to play a profitable strategy. Fortunately, such charts are readily available, and you should be able to master them in no time at all.

Finally, playing AoF means being in contention for the AoF Jackpot, available at each level of play.

link to original post

Yes, exactly.
Are you aware of any mathematical analysis that someone made on this game?

If everyone at the table had exactly 8BB at the start of the hand, it would be fairly easy to develop a strategy for any hand, position, pot, and prior action. As you say, there are a rather small number of states to consider. You could start with a a guess at correct strategy and then refine the strategy iteratively using a poker solver and game theory.

If I understand the rules, though, players could buy in for more than 8BB or allow their stacks to build up. If you have four players with four different stack sizes, the solution is substantially more complex. The fact that you cannot bet a fraction of your stack certainly reduces complexity. It is not a problem that I would be tempted to tackle..

The simple 8BB problem is very much like fixed limit holdem games that have been solved completely. Heads LHE up was solved 8 years ago. https://www.runitonce.com/other/hu-limit-holdem-is-solved/

Quote: Mental

If everyone at the table had exactly 8BB at the start of the hand, it would be fairly easy to develop a strategy for any hand, position, pot, and prior action. As you say, there are a rather small number of states to consider. You could start with a a guess at correct strategy and then refine the strategy iteratively using a poker solver and game theory.

If I understand the rules, though, players could buy in for more than 8BB or allow their stacks to build up. If you have four players with four different stack sizes, the solution is substantially more complex. The fact that you cannot bet a fraction of your stack certainly reduces complexity. It is not a problem that I would be tempted to tackle..

The simple 8BB problem is very much like fixed limit holdem games that have been solved completely. Heads LHE up was solved 8 years ago. /other/hu-limit-holdem-is-solved/
link to original post

That's looks great i will look into it.
But anyway despite the possibility of increasing your stack usually everybody automatically remove the wins and have 8BB during the game.

Quote: Hannibal96

That's looks great i will look into it.
But anyway despite the possibility of increasing your stack usually everybody automatically remove the wins and have 8BB during the game.
link to original post

I believe if everybody has 8BB except one person who has more than 8BB, then the GTO strategy will be the same. The extra chips will never play.

Is there an option to have the site automatically cash out and remove the excess bets beyond 8BB?

Are the tables usually full? How long are you allowed to sit out hands before you are bumped off the table? The GTO strategy depends strongly on the number of players.

Yes this option exists and almost everyone remove the wins.
The tables are some times can be played with only 2 or 3 players for some time but I don't see how is it different from playing with 4 players and the CO folded.

Quote: Hannibal96

Yes this option exists and almost everyone remove the wins.
The tables are some times can be played with only 2 or 3 players for some time but I don't see how is it different from playing with 4 players and the CO folded.
link to original post

If the CO has folded, the deck is slightly richer in high cards than if there are only three hands dealt in the first place. All three players should be making tiny adjustments. This probably isn't a big difference compared to the change in the number of errors ordinary players make by not adjusting to the number of players in the hand.

I am sure you don't want to be playing against 3 GTO bots, so I agree with your point.