I have done some preliminary research into pre-flop card removal effects in PLO. I simulated 10 million deals of 6-max PLO where the first 5 players fold pre-flop. I then tallied how many of each rank (Ace thru Deuce) were folded. I will compare the results with previous findings of pre-flop card removal effects in NLHE.

We need the following:
- PLO starting hand rankings
- PLO opening pcts by position.

I have used the mathematical based Hutchinson point system to rank all PLO starting hands. Unlike NLHE where starting hand charts are widely available, such is not the case for PLO. A main reason is that there are many more possible starting hands in PLO and putting starting hand recommendations into a chart is not very easy.

People are probably aware that the Hutchinson point system is quite crude. The system assigns points to each starting hand based upon suitedness (a suited Ace is the best, double-suited is preferred), pairs (the higher the better), and ability to make straights. There is a fair amount of discussion on this system here on 2+2 and elsewhere on the internet. I have used the system in the simulation since it is fairly easy to program and (I think) may be the only PLO numerical point system widely available.

In order to make the NLHE vs PLO comparison as apples-to-apples as I can, I have used the same opening pcts (by position) in this PLO analysis as I used in the earlier NLHE analysis. If I remember correctly, I used the recommended opening pcts for 6-max NLHE available on the Upswing website.

The simulation is pretty straightforward. I deal 6 players 4-card PLO hands. Each player in turn (by position) either folds pre-flop or enters the pot. If the first 5 players all fold, I tally the ranks contained in their collective holdings (20 cards in total, 4 each for 5 players).

The following table contains the results (I also include the earlier NLHE results for comparison):

Rank	Avg # Folded by first 5 Players in 6-Max NLHE	Pct Folded by first 5 Players in 6-Max NLHE	Avg # Folded by first 5 Players in 6-Max PLO	Pct Folded by first 5 Players in 6-Max PLO
A	0.32	3.2%	1.44	7.2%
K	0.62	6.2%	1.43	7.1%
Q	0.65	6.5%	1.41	7.1%
J	0.68	6.8%	1.40	7.0%
T	0.71	7.1%	1.43	7.1%
9	0.72	7.2%	1.41	7.0%
8	0.84	8.4%	1.44	7.2%
7	0.88	8.8%	1.44	7.2%
6	0.87	8.7%	1.58	7.9%
5	0.90	9.0%	1.66	8.3%
4	0.91	9.1%	1.73	8.7%
3	0.94	9.4%	1.80	9.0%
2	0.97	9.7%	1.84	9.2%
.
SUM	10.00	100.0%	20.00	100.0%

It is immediately apparent that this preliminary analysis suggests that the card removal effects (on a pct basis) are much smaller in PLO than in NLHE. Looking at the first row in the table shows that Aces make up only 3.2% of the folded cards in NLHE but 7.2% in PLO. Relatedly, the card removal effects are fairly "monotonic" working through the ranks in NLHE but are fairly "flat" at the top end of the PLO ranks. The folded pcts of Aces all the way down to Sevens are remarkably similar. Then a fall-off occurs for ranks below Seven.

I imagine that the reason behind this result is that the ability to make straights is very important in the Hutchinson PLO point system. And middling cards have the best chance to make straights compared to either high or low cards. In the point system, high cards are rewarded for making winning flushes and full houses, but this is offset by their lesser chance of making straights.

Anyway, I post these results as a way to start a discussion, not to be the end of the discussion. I would be interested to hear if anyone knows of another PLO starting hand system that may be available and is easy to program. My first impression when seeing the above results is that they may be driven by the use of the Hutchinson system, but I do not have a feel for what extent that is true.

nice work man, QUICK, HOW MANY MATCH STICKS ARE THERE?


-what are you trying to solve/figure out
-what are the direct applications of this solution
-how did you run these simulations?


unless im missing something, the overall lesson is that ranges are much more evenly distributed, and noone really has much of an equity advantage.

nandez has a really nice excel chart on PF ranges and rankings, but id have to think about how to program them. its about 87 categories, i suppose it would be possible to assign them values if youd like to work together on it.

what youve done is fascinating work, and im really interested in your methodology here, i think there are other areas in poker where it can be applied in a very profitable manner. lets skype or email about it, i get to be tom cruise, though.