While using Excel & VBA, to create a poker analysis/training program I was able to calculate card removal effects for any given live range as well as it's negative or folding range (all combos not in the opening range).

I'm not sure if anyone else has been able to solve this since Micro-Bob first mentioned it. I had plans to create this long ago but Black Friday took the wind out of my sails until now. I did see a post using software that ran Monte-Carlo deals for a small samples across a decision tree for pre-flop folding. From memory I remember thinking the results didn't make sense. The example given was for players folding to the SB and calculating for a shove with 32o vs a given BB calling range.

In that example CR supposedly improved SB shove equity with 32o but I'm certain it should be just the opposite since more chances of 3's and 2's in the muck and higher chances of big cards being in BBs hand. Also the effects appeared to be way to small for combined effects of 4 or 5 ranges folding. I'm guessing it was an issue of non convergence for a small Monte-Carlo sample. They seemed incredibly small to me at the time. Like 4000 hands or something which could account for a micro deviation.

Now after working on mine, I can see that it would be unlikely for the Monte-Carlo method to take card removal weighting effects into account. I'm fairly certain that the Monte-Carlo deals ignored the folding ranges of previous nodes and they only dealt with live ranges and known cards.

I could be wrong about this and I'll be looking it up again to dbl check.

Here is an example:
22% Range(based on vs 3 random) you get an opening range as follows:
66+, A3s+, K7s+, Q9s+, J9s+, T9s, A8o+, KTo+, QTo+, JTo

If the player opens the CR effect from his live hand will mean the stub will average out to:
A)3.559 K)3.697 Q)3.724 J)3.724 T)3.724 9)3.848 8)3.890 7)3.931 6)3.945 5)3.986 4)3.986 3)3.986 2)4.000

If the player folds the CR effect from his mucked hand will average the stub to:
A)3.927 K)3.888 Q)3.880 J)3.880 T)3.880 9)3.846 8)3.834 7)3.822 6)3.819 5)3.807 4)3.807 3)3.807 2)3.803

Nothing too surprising and pretty much what everyone's first guesses would be. Folding a top heavy range leaves fewer big cards in the stub and vice-versa. Oddly, the more speculation about the matter the stranger ideas became.

I think most greatly underestimated the results however. I kind of felt that the effects would be pretty high because I reasoned that if you look at 8 folds for example. That means there are 16 cards removed from 52 so the effects must be proportional.

Also if you look at some live games where you get family limps. It checks down such a large proportion of the time not just because of the fear of bluffing into several players. It's also because everyone's in the same range of hands. i.e. suited connectors or small pps, when a board of high and baby cards come out nobody has anything to bet on except for 3rd pair or something.

I started bluffing with any high card on the flop or turn in these situations and it's worked extremely well. Figuring there might be some late over-calls with weak As or Ks, but most would open muck early position and maybe take a stab late position adding to the CR effects.

While not a guarantee of being correct, there are several factors that kind of self-validate these results:

Note the examples add up to 50 each accounting for the hand in question. Using the live range only 2s are not included in that range which is shown to be the case here. Folding range on the other hand includes combinations that contain all card ranks so you see reduced numbers across all rankings.

Also notice that for tighter ranges, the effects are more pronounced than for looser ranges. This is due to the fact that the wider the range, the portions of the 2 cards are more widely distributed over more combinations diluting the effect.

In this example the tighter opening range of 22% vs the folding range of 78% can be seen illustrating this effect.

Unfortunately there are issues in dealing with weighted combinations or cards such as with equity calculators or combintorics calculations involving factorials. Still I can provide several examples where they can be extremely useful and in fact I had started incorporating CR into my game based on assumptions long before I could see results. For example when players make quick and easy mucks postflop on certain wet boards and I have a borderline draw. Those mucked cards were discounted from the stub in my calculations but any third player would discount my draw obviously.

Here's a ton of empirical data about what actually happens with card removal effects, part 2 in particular.

http://www.spadebidder.com/category/flop-analysis/

Part 7 there breaks down 290 million flops.

More about multiple folds here:
http://www.spadebidder.com/statistic...-claim-part-2/

Thanks for the links, there seems to be some interesting data there that's worth investigating further.

However, this isn't really solving card removal. It's only studying the effects card removal has on boards in general for 100 bb full ring online games at least assuming those were the games that were studied.

By calculating CR effects on a hand by hand basis which would include adjusting for all players ranges regardless of hands that were folded or hands that were still live. I'm sure you will be able to identify many cases where the standard calculations are off by a considerable margin.

Id also expect to find many situations that could be highly exploitable especially when the stub will be biased to a larger degree just as a ten rich deck can be exploited in black jack.

Subscribbed interesting thread.

Lol at the site name spadebidder.

I'm still barreling through the first link. Has anyone vetted the calculations?

Not yet. I wanted to finish the calculations for accumulating the effect over multiple ranges first.

It was a bit tricky but finally got that done a couple days ago. Then I accidentally created some kind of loop and caused a bunch of ref errors lol. Shouldn't take long to fix, just been too busy to get back to it. Excel's just touchy that way and I'm not an Excel expert.

I had to make some estimates that were a little indirect. One example was to get the percent chance a certain card was in a given range, I counted all combinations that contained that card within the range and divided by total combinations (1326) to get the percentage. Notice that it comes out to 200% because each combo needs to be counted twice but its correct because your counting for 2 card combos.

It's a little vague and I know that I could have confused my logic but all the math works out perfectly to end up with 2 cards getting removed.

Here's an example of 8 open fold ranges and 1 open raise range. To get a realistic effect, ranges were based on PokerStrategy's default ranges for 10-max with an assortment of loose, standard, tight ranges based for each position.

First let me say, with apologies to Micro-Bob, that I'm calling this process a range removal effect so that I could differentiate it from the card removal of known cards which is handled very differently.

Each row represents a player's range and the numbers represent the number of cards on average after each range is accounted for. For player 1 there was no change because in my hand simulator within the same program I'm creating, player 1 is the hero with known cards. I took out the card removal for those two cards so you could see the range removal effect effect more clearly.

Please note, these results actually contain an error I'm aware of. Again directly calculating numbers back into a complete array was tricky. I had to start with the results from the last player, and derive a full combo array again with all combos adjusted. It wasn't as simple as reversing the process because we started with a partial array i.e. the players range.

A good example would be even if I know that there will be 3.872 aces in the deck on average, try to get the number of AA combos there are based on this formula:

Since factorials must use integers, again I had to use a round about method. After coming up with the new method then applying removal for the next range I actually saw results that accumulated to be too high but they should be that way because of the error I mentioned.

For example If I were to use all open raise ranges (not folding), while it's not a realistic scenario because each player would adjust their range, it is a theoretically possible scenario but the results would end with -0.15 aces which should not be possible except for the error which we already know about accounts for this quite nicely.

I believe I have a method to make these adjustments and hope to be able to provide you with the new results soon.

BTW, I didn't account for suits and only calculated for 16 unpaired combo group and 6 paired combos per group.

Intuitively, you may think that suits didn't matter because they don't matter when we make decisions in our ranges. For example AcKs is treated the same as Ah,Kd. However there may be some information there as well but I'm not certain.

The information I'm thinking about is that we do differentiate from suited hands vs unsuited hands so maybe A8s is playable but A8o is folded. My reasoning is that when we fold A8o vs A8s, this makes fewer suited hand combinations possible in the stub because A8o requires 2 suits while A8s involves only 1 suit. While the effect is small the impact on flushes may magnify that again because only a single suited combo out of 16 for a given unpaired hand will work towards a flush for a 3 card flushed board.

I know the logic there is difficult to follow because I skipped a bunch of steps to jump to a conclusion but when I worked on the single card removal some time ago, I could see it was true. I just can't explain it easily and I'd need to devote a new thread for that topic.

I think suited hands per se cannot matter much when several players are folding, because even though each suited hand removes a pair of one suit, all non-suited hands remove one each of two suits. It's hard to believe the slight 'chunkiness' in suit removal due to suited hands being played more often will make much difference to the net suitedness of the total cards removed, though it might increase it very slightly.

(However, you must of course take into account the likelihood of the A8 combo in a player's range even if most of them come from A8s. But you probably just need to include the right total amount of A8, both suited or offsuit.)

For the most part, I think you're correct, however for wider ranges the number of suited hand combination groups will be far more than the off-suit groups. While each grouping of off-suit hands is 3 x that of it's suited counterpart (12 vs 4) the actual number of suited combinations begins to rival that of the off-suit combinations at about a 50% range. This would mostly occur with deep stack 6-max games where players are using exploitative styles with super wide ranges. I'm still uncertain to what degree.

Currently all combinations suited or otherwise are accounted for in the estimated removal of each rank, but not suit which I hope to change at some point.

2-D heat map displayed on 13x13 hand grid array.

Card removal for 2 hole cards with range removal of 8 folds and 1 raise. Note that I created a seperate heatmap for suited, off suit, and pps to get a more relative effect. Otherwise the offsuit combos offset too much from the rest and you lose the details.

really interesting thread

I think the best way to view the importance of the concept of range removal is to think of the movie 21 and the concept of variable change demonstrated in the movie.

Lets say you have a perfect play strategy card. With no other information, it's the best strategy we can use to play the best black jack possible. However after we add the information of the card count, we can now make a more informed decision with the new information and using the strategy card is no longer the best method. We use the count and find that when a lot of small cards are removed the many tens in the deck gives us an edge mostly by allowing the dealer to bust whenever he shows a 2- 6 as his up card. The more tens that are left in the stub, the bigger our advantage and the larger our bet should be.

With range removal we can see what is left in the stub, on average, by removing all players folding ranges, calling ranges, and raising ranges. (assuming our range estimates are reasonable) we've just gained a ton of new information to make better choices.

Remember, with 8 opponents, range removal contains the information of 16 cards. That's 16 cards out of 50! so we should be able to refine the way we calculate our odds by quite a bit.

While poker is indeed a game of incomplete information, there's been a big chunk of that missing information that has been right in front of our noses all along in what we call the muck. An appropriate name because it was generally thought to be too difficult to work out that information in the past through the muck of all the different combinations, and ranges, and playing styles, and positions and yada yada yada. So much so we just had to assume the muck is random and calculate based on 50 random cards.

Every Poker Stove ever done for an all in decisions, every EV calculation we ever did for post hand analysis, every time we calculated odds for set mining, or implied odds for suited gappers, or pot odds calculation, or combinatorics analysis, etc. etc. can now be done more accurately.

It's not that how we analyzed play before was wrong just like using a perfect strategy card wasn't wrong in black jack. It's just that we can do so much better with this new information that I've just now quantified just as a card counter uses the count to make better decisions.

Granted that information is not completely recovered. We clearly still can't put most players on single hand ranges when they fold or play. Therefore our decisions are not improved by 16/50 ~ 32%. Well some of us who can read souls maybe but for the rest of you, just how much improvement can we expect.

This can be seen and demonstrated by the size of each range. For example, we believe we have a pretty good understanding of player ranges which have been the basis of every poker analysis ever done. So lets assume we have a very nice HH collection of all players and can assign reasonable pre-flop opening ranges to players. Unfortunately most players muck pre-flop for on-line 100bb poker but this still provides a range to assign them which is simply every combination that wasn't in their opening range. So for a player who has a vpip of 20% for a given position, when he folds he has a folding range of 80%. My program can break this range down by average % of each card rank removed or by % of each hand combination removed. So now instead of pluging in whole numbers into our probability equations or using combination counts of 12/6/4 into our combinatorics analysis, we simply plug in the newly weighted numbers to get more accurate odds, probabilities, etc.

Poker calculators are still a problem since they simply use brute force methods of dealing out millions of hands and they cant deal out hands based on 3.8 aces for example. However they can be modified to save some statistical data of the results and the weightings can be applied to that data. For now until I or someone does this it's still some ways off. We can do some tricks for the time being however. For example we can remove specific cards to approximate combo weightings but I'm drifting off topic, back to ranges and how they effect the stub or other ranges for that matter.

I always like to start with the extremes, a player who only has AA in their range can impact the stub with the clarity of known card removal (minus suit considerations) leaving only 2 aces in the deck or one other AA combo, or 8 Ax combinations instead of 16. Great that's pretty concrete information we can use. On the other hand, folding everything including AA such as for a satellite bubble where he can fold his way to a seat with a better than 80% chance of success. This range doesn't offer any help since his folding range is now evenly distributed over all 169 hands. It's just white noise.

For a more realistic range, lets say a player in late position has a 20% opening range and 80% folding range. The folding range is distributed over 80% of all combos while the open range is only distributed over 20% of all combinations. This means that while a 20% range can make fairly significant adjustments for fewer hands the 80% range will make adjustments of only 15th the size and over 4x as many combinations.

Furthermore when multiple ranges fold or multiple ranges play, their effects will be cumulative just as can be seen in some of the examples I've posted. I think you might see as much as a 1 card differnce in the stub between 2's and aces, 8 folding rangsfor example which is pretty significant since that's a 25% change from 4 aces to 3.

Enough rambling for now, I need to grab some sleep.

Thanks, I'm glad someone appreciates it. I'm not sure if people are having trouble with believing that the stub is not actually random or if they just don't believe my data is valid.

Perhaps I'll post some of my test range results that I used to verify my data. I used tight ranges where you can actually count what the removal effect should add up to and compare it to my results.

They are actually nearly 100% accurate when counting 1-4 of each card with only minor exceptions exist under extreme conditions which shouldn't show up in the real world where extremely tight ranges stackup up to sometimes create an odd result or two and decided it wasn't enough of a priority right now to make adjustments.

The only rough estimates I did were for pocket pairs where I made linear approximations for very non-linear data but I did this to very small portions of the data to keep the effect small.

The impact will eventually be bigger than card counting was to black jack so I'm not sure what the hesitation is in this thread.

It may be that people may not yet realize how this data can be applied at the table but I can assure you, that I can provide many applications. I also display the data in in a very intuitive format over what should be a very familiar hand grid array to players such that simple and intuitive adjustments may be done in the moment when playing.

Was this calculated using the 22% range you described in the OP?

I think that was calculated with accumulated data from 8 folding ranges for players in various positions and who had loose opening ranges as defined by PokerStrategy.com and one raising range is also included for someone in the CO pos I think. Not certain about this though, I didn't save the table layout.

It wasn't based on any real hand, I just needed some realistic range data to measure.

+1

Juk

Thanks, it's very nice to hear. Especially from someone who's been around as long as you have

People are gonna start thinking we're the same person, lol.

BTW, I was referencing the fact that we had the same join date. I probably shouldn't assume that people would automatically pick up on this.

Where do you see this having the greatest impact on current analysis methods?

Preflop range construction is just my guess but judging by your previous posts it seems like you think that later streets can benefit as well.

Do you think post flop range considerations are dominated by betting information that over shadows range removal effects?

Sent from my SCH-R760 using 2+2 Forums

As both the stub and villains range may be adjusted, it will impact all streets. Which streets it will impact more is mostly dependent on how deep the effective stack size is.

Range removal will only give you more accurate information as far as how often villain should have hit various types of made hands, combo draws, draws, air. All information must still be taken into consideration and you must still make decisions based on what you know about villains range and betting patterns. It only gives you more accurate information to base your decisions on.

It may also reduce or increase the odds of making draws which can also change how you should play the hand.

Finally, given the action pre-flop, you may see that certain ranges that may have a higher/lower percentage chance of hitting allowing you to adjust your own range when acting behind.

I haven't had much chance to evaluate these differences yet myself and expect to find more situations where it will help.

In general, eventually you should have a better feel for where you are at over your opponents.

Range Removal is now Verifiable. using Monte Carlo

Without a second method to compare results I was unable to backup any claims which left me in an awkward position especially given that few knew the impact of Range Removal in the first place and there fore cared little about it.

For this reason, I'll follow up with a more detailed analysis for this hand shown. There's so much more going on than you realize.

I'll show the results of comparing Range Removal results to Monte Carlo Simulation.

Since the back story behind discovery is also an important factor when validating claims I'll follow up with my back story in a new post.

If your still not convinced.
I can provide the 25,000 hands used to validate the RR effect upon request.

email me at takeniteasy@msn.com

I can:
send the validation data for the hand shown
or run an analysis for a hand of your choosing. Note you must provide all range data for ALL players including folding ranges. I will also include validation data.

As long as you agree to post your findings here.


I realize that 25K is not a lot for Monte Carlo but I did include the data for the first 1K, 5K hands as well to demonstrate the type of convergence it was getting.





MC(1K), MC(5K), MC(25K) represents the Monte-Carlo results after that many hands dealt. I chose to include 3 disperate numbers so that you could gauge for yourself the amount of convergence there was.

The actual hand which only merit for selection was that it happened to be the last simulation run for testing my pre-flop bots, was 7 folds, hero on the button (seat 1) was obviously holding TT. BB 3 bets, button 4 bets and takes it down.

My original solution was solved through algorithms. Therefore achieving the same results via Monte-Carlo is a pretty strong validation.

First 10 lines in the table represents how each players range will impact the distribution of cards left in the stub.

The big green stripe reflects the fact that the hero, in seat 1, was holding TT in this example

Bottom 3 represent Monte Carlo results after 1,000, 5,000, and 25,000 hands dealt in order to give you some idea of the kind of convergence that even these small runs were getting.

Awesome work!

Do you have any ideas for creating more generalized tables that could by applied in actual play (or at least show some examples of how actual play could be affected by range removal)?

Thanks, I appreciate it.

As far as more generalized tables, well I'm not sure what you mean but the tables I create generally focus on getting a better understanding and feel for what's actually going on so that you can make the best decisions as each situation comes up.

Sometimes practicing what you learn is the best way to truly get the best understanding. This is why I'm putting so much effort into the training simulation.

If you ever purchased a poker tool, I'm sure you tried it out, played around with it and then thought, OK now what? The problem is you need to apply a hand to analyze. Maybe you can think of something but usually not.

It's great for when you wonder if you played a difficult spot but it's after the fact and only a single situation that probably won't come up again for a long time.

I'm hoping that by generating many realistic flops, you'll be able to click through them and analyze many hands instead upfront instead of just a single hand after the fact.

Since you'll be able to generate a large db of flops, maybe I can work out some kind of tag, filter, or library system using a tool that could recognize specific flop patterns.

Maybe I can provide tutorials that are more meaningful to players by using this tool.

As far as training goes. My goal is always based on
1) to get the best possible understanding of a concept.
2) Then learn how to best quantify it
3) Then work through examples to get the best feel for any given spot.

I also have plans to make it a research tool as well for studying more advanced concepts I've been thinking about.

I believe this is the best way to get the most benefit of what you learn. Poker is just too diverse and always changing with the ups and downs of the poker economy. Unfortunately there are very few rules of thumb that work in all or even most circumstance and they often need to be adjusted. If you understand the principles involved you'll be able to adapt to more situations more quickly which is really the key to a long life in poker.

The only thing I know for sure is that I wont have the time to incorporate all the features I'll want myself.

Do you have any examples in mind of situation where some action is best if you were ignorant of range removal but if you were aware you could figure out that some other action is better?

Anything involving an ace will show a huge difference vs calculations that assume a random stub.

I need to get some sleep now. I'll try to include an example tomorrow.

Cheers!