It seems I was setting the bar too high by trying to make something better than NLHE. But in my opinion, it's possible to make a better game than PLO and this is the one that should do it. If you don't agree with me, please tell me what is so special and good about PLO that makes it such a popular game and better than this ?

At first I thought it's a No Limit game, but when analyzing closer the odds and draws, I realized that it's actually a Pot Limit game. If the hand rankings are mathematically verified with 100% (instead of current 95%), could this game beat PLO ?

Here are the Big Five's advantages in my opinion:

- only 2 hole cards, which makes it much easier to play in a live game
- a lot easier to track opponent's range
- a bit easier to connect with the flop
- easier to get good hole cards
- no useless hands like 444Q or 7777 or 4 suited cards
- easier access for beginners (simple hand rankings)
- better to watch on TV
- and just like in PLO - often multiple draws to better hands


Here's the game:

Multiple draws are one of the strengths of PLO, especially 5 card or 6 card PLO. It may seem that if you have only 2 hole cards and very simple 5 hands rankings, this thing will just go away. It won't. Take a look at this hand, it's not some rare theoretical example. Things like this just sometimes happen in Big Five:

Player 1 - T T
Player 2 - A Q

FLOP - A T A

Player 1 => has already TENS DUPLICATE + runner runner ROYALTY FLUSH draw + FOURTH KIND draw + QUICK RUN gutshot
Player 2 => has already ACES DUPLICATE + ROYALTY FLUSH draw + FOURTH KIND draw

That's awesome. And this game just screams loudly "Pot Limit !". It took me a few days to hear this screaming though. All thanks to a deeper odds and draws analysis.


Another complain could theoretically be about the strength of your hand on the Turn. I dealt 50 hands to check this out and about 45% of the time player had at least a DUPLICATE on the Turn. I think this is a very good score considering there are multiple draws happening with it.


As far as the "solvability" of Big Five, I'm not sure what to think. But there are 40 cards in the deck and it's Pot Limit, so I think it's not easy to solve.

This is how often different kinds of hands play (don't confuse this with rarity, it's a different thing):

LOOSE CARD - about 32% of the time
DUPLICATE - about 36% of the time
QUICK RUN - about 20% of the time
FOURTH KIND - about 10% of the time
ROYALTY FLUSH - about 2% of the time

To measure this I've dealt only 50 hands (2 random cards + 5 random community cards). At the table most of these hole cards would be folded pre-flop.

It's hard for me to compare this to PLO now, but considering that only 7 types of hands usually play in PLO, the hand rankings in Big Five are more fun than they may look at first.

I've shuffled and dealt another 50 hands to see how good the A A starting hand connects with the flop.

SUITED ACES DEALT and
THE FLOP CONTAINED:

One Ace - about 44% of the time

Two Aces - about 10% of the time

One heart - about 40% of the time

Two hearts - about 8% of the time

Empty flop - about 16% of the time


It's worth to mention that one heart on the flop always gives a QUICK RUN gutshot for the suited pocket aces. It's a very strong starting hand although I won't compare it to the best starting hand in PLO - AAKK double suited, because you need a miracle to have this hand, which is actually kind of funny from my point of view.

Yoooooo !!! Post status: "MUST READ" I swear I didn't cheat here ... It's also very unlikely that I made a mistake. Take a look, I think the numbers speak for themselves.

I shuffled the cards and dealt extra 100 hands (2 x 50 hands) to compare how often player connects with the Flop and Flop + Turn in both games. 50 hands per each game. Random hole cards + random flop + random turn.

"CONNECT" = improve to a better type of hand or make additional draw(s) to a better type of hand or improve current draw(s).


Pot Limit Omaha

Connected with the Flop: 94% of the time
Connected with the Flop and Turn: 60% of the time
Didn't connect: 6% of the time


Big Five

Connected with the Flop: 98% of the time
Connected with the Flop and Turn: 62% of the time
Didn't connect: 2% of the time


I trust my hand rankings results (150 extra hands dealt today for this purpose), so combined with THIS it really looks like a better game than PLO !!!!!!

Please tell me what you think about it.

What did the math say? Why do you feel this indicates a better game?

1) We have to wait for the official analytical and precise math calculations, this must be done by someone else than me. But my "practical calculations" were done on a quite large number of hands dealt and most of the results were very obvious, although there was one spot (between Duplicate and Quick Run) that wasn't so obvious at first. I had to shuffle many additional hands to be (95%) sure it's correct. I'm sure the hand rankings are correct for 5 cards and also for the game setup (2+3), so you shouldn't worry about these, unless you totally don't trust me.

2) I've already listed the advantages in post #1, so when you combine them with post #2, #3, #4 and especially post #5 this makes quite a good proof. The only serious advantage I see for PLO is that occasionally this game can build massive pots when two super strong starting hands collide on the flop that's good for both of them. Like the #1 online pot of all time (Antonius vs Blom). Even if we assume that the results from post #5 are identical for both games, this still is a very good sign.

It took a while to calculate this, but there's surely no mistake here:


STARTING HANDS (HOLE CARDS) PROBABILITY:

1. Suited pair - 2,60%
2. Pair - 15,40%
3. Suited connectors - 10,25%
4. Suited - 10,25%
5. Ace high - 24,60%
6. OTHER - 36,90%


Hand rankings are only 95% verified now, but I'm already starting to feel like Alice in Wonderland. Let's not wake up from this cool dream

I wish I could see the odds calculator for my game, this would be super sick. But I'm sure the odds % will be super fun and perfectly set and I'm not worried about those at all.

There will be a lot of similarities to PLO I think, but there must be something significantly different about Big Five's odds and I wonder what it is. Maybe pre-flop, maybe turn will give the answer. It's difficult to guess. My rough estimations only give a sense that it's all in the right place.

Something also tells me that relatively soon, some people will secretly play Big Five without informing me about it

I wrote a poker poem about both games:

Big Five rocks !!! It's so much better
Old one needs to be forgotten
Just like four cards in a letter
Close it, send it, they will shuffle

Deuce and seven, three and ace
To remind you where the Queen is
You must choose the final way
Bet correctly and you'll win it

If you choose the one with error
You will step into the darkness
Where black hunter shoots an arrow
That will crash down your stock markets

Hello !

I'm creating this thread for 3 different reasons:

1. I'm looking for players who have 2 identical decks of cards at home and can look INTO this game more deeply using real cards and share their opinions here.
2. I need to find a person who is able to mathematically and precisely verify the hand rankings.
3. I want to know if poker players would accept completely new hand rankings.

#1 - This game looks very simple at first, but when you deal some hand examples and try to analyze them, things are starting to look more than just interesting.
#2 - Currently the hand rankings are 95% verified with a non-analytical method on a large number of examples for both: 5 cards and 2+3 cards game setup.
#3 - The hand rankings are totally different from the well known 10 poker hands that create a solid basis for most popular poker variants.

Here's the game:





If you want to know more about this game (some statistics, numbers and examples), click the LINK below:
https://forumserver.twoplustwo.com/1...rison-1834604/

G. J.

Hey instead of dealing hands irl how about simulating a couple million hands in code?

Would be better of course, dealing real hands is all I can do now. But the hand rankings results I got with dealing real card examples (in my other "Geometric phenomenon..." thread) are so clear and undeniable that now I know for sure that they are correct. But yes, 100% is always better than 99,9%.

He doesn't do math or play-test. Just thought experiments.

Math is the projection of thoughts.