EnigmaAP
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April 20th, 2026 at 1:47:48 PM permalink
Hi everyone,

I’m looking for data on the effect of single card removal in UTH, and also the EV to all players for each card appearing in the dealer’s hand.

CAA has EV for each card in player’s hand and in the community cards, Jacobson has (slightly different) figures for EV if each card in players hand, and I’ve not been able to find anything anywhere else.

Does anyone have this data or would be willing to calculate it for me?

Many thanks

Enigma
MDawg
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April 20th, 2026 at 1:56:18 PM permalink
If I understand what you are getting at, that is the way I approach all card games, but you have to be able to calculate what that means at each instant, too. By means of course I mean what advantage is at play at that moment, and why.

That requires both knowledge (including unerring math crunching ability) and a perfect memory, to do it to the utmost.
I tell you it’s wonderful to be here, man. I don’t give a damn who wins or loses. It’s just wonderful to be here with you people. https://wizardofvegas.com/forum/gambling/betting-systems/33908-the-adventures-of-mdawg/
aceside
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April 20th, 2026 at 2:03:11 PM permalink
This question is questionable. Poker is not like a blackjack shoe game. If four aces in a deck is removed from a shoe, there are no more naturals in the remaining shoe, but the game of blackjack still goes on and on. There is no such an instance in poker. So, why do we calculate this?
EnigmaAP
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April 21st, 2026 at 4:40:59 AM permalink
MDawg- I don’t know what you think I’m getting at, but judging by your answer, it appears that you don’t. That’s ok though, I’m just looking for someone who has the data I’m looking for, or is willing to calculate it for me. If that’s not you, it’s fine :-)
EnigmaAP
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April 21st, 2026 at 4:45:34 AM permalink
Aceside - Again, if you don’t understand why I’m asking that’s fine. I’m just looking for someone who has the data or is willing to calculate it, which obviously isn’t you. No worries.
aceside
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April 21st, 2026 at 5:06:45 AM permalink
I actually know someone who can easily give you the answer. His name is Mental. However, I don’t understand what you are getting at? Are you trying to cheat in a home poker game by secretly hiding one card from the playing deck? Or, mark one card?
EnigmaAP
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April 21st, 2026 at 7:32:44 AM permalink
As per the title of the thread, I’m talking about UTH. The casino game, Ultimate Texas Hold ‘Em. Nowhere have I mentioned home poker games.

No, I’m not trying to cheat.

As above, other authors in the AP world have published data on the EV for each of the 13 potential values of a single card in the player’s hand and the EV to each player for each of the 13 potential values of a single card in the community cards.

I’m looking for two things: firstly the EV to each player for each of the 13 potential values of a single card in the dealer’s hand and also the EOR of each of the 13 potential values of a single card to all players. (In other words, what is the effect to the house edge on removing a deuce from play in the next round versus a 9, and what is the effect of that deuce or nine being in the dealer’s hand instead of being removed from play, as an example).

I’d appreciate it if you could put me in touch with your friend, thank you.
Last edited by: EnigmaAP on Apr 21, 2026
aceside
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April 21st, 2026 at 9:19:09 AM permalink
I still think this question is invalid. The game of UTH is different from blackjack, where suits do not matter. In UTH, if an Ace of hearts and a king of hearts are removed from the deck, the EV will be different from other suit combinations of these two cards. So, what do you want to achieve if knowing these values? You need to be specific.
gordonm888
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April 21st, 2026 at 10:46:02 AM permalink
The change in player EV when seeing a card in the UTH dealer's hand (hole carding) has been published, I believe, by Eliot Jacobsen in his book Advanced Advantage Play.

Mental is the WOV Forum name of an individual; you can send him a personal message. He has not been dropping into the forum lately.

There are many of us who can do the EOR calculation, but it's complicated and requires a lot of work - 9 cards modeled per hand and 3 decision points. Most of the gaming analysts are serious people who aren't interested in putting in the work to do such a calculation because the pre-deal EOR is not of great interest. People are more interested in the EORs for specific post flop decisions.

- a collusion strategy for UTH that uses cards seen by the player to optimize decisions is published on the Wizard of Odds website as well as on Steve How's website called Discount Gambling.


Regarding pre-deal EORs for UTH:

Obviously, the presence of A, K, Q in the deck are important to the player because they create the opportunity for player to Bet 4X on various pre-flop hands in which the player has a positive EV.

The rank with the largest positive EOR on pre-deal EV will be when a deuce is removed from the deck. The removal of the deuce increases the odds of making a 4X wager preflop or a 2x wager post flop.

But beyond that there's not much of interest in a pre-deal EOR calculation for UTH.
Last edited by: gordonm888 on Apr 21, 2026
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EnigmaAP
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April 21st, 2026 at 12:33:00 PM permalink
Hi agan Aceside.

I understand that you don’t see the value of EOR in UTH.

That’s fine, and in that case this question isn’t for you as it’s pretty obvious you aren’t able to help here. Have a nice day and all the best.

Good skills and positive variance

E
EnigmaAP
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April 21st, 2026 at 12:42:12 PM permalink
Hi Gordonm888

I’m not talking about HCing, I’m well aware of the value of HCing UTH as I own and have read Grosjean’s CAA.

I’m talking about the EV to the players from the simple fact that a dealer has a 2-9 in their hand.

No, Jacobson hasn’t published that data in his book, or on his site. The closest is a table publishing the EV to the player for each of the 13 card values being held in the player’s hand (not the dealer’s). Grosjean has also published this table in CAA (albeit with slightly different values) and also a table of the EV to all players for each of the 13 card values being on the flop.

Common sense dictates that a 2-9 appearing in the dealer’s hand will help the player, I’m trying to quantify that.

I’m aware of Stephen’s site and have been for some time. I’ve also contacted him via the site with the same request.

I’m also trying to establish if the house edge can be overcome by removing a single card (most likely a deuce, trey, etc but hopefully anything up to a 9) from the next potential round of UTH.

I appreciate that you think my question is pointless. TBH, I’m kind of glad that you do… the more people that think like you, the better.

I’ll reach out to your friend and see if they will help me. Obviously I’m happy to pay for their work.
aceside
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April 21st, 2026 at 1:55:33 PM permalink
Actually, I myself is able to find all these numbers from Eliot’s work. It only takes some patience and statistics skills; however, I leave this as a homework to others.
Mental
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April 21st, 2026 at 3:19:07 PM permalink
Quote: EnigmaAP

Hi everyone,

I’m looking for data on the effect of single card removal in UTH, and also the EV to all players for each card appearing in the dealer’s hand.

CAA has EV for each card in player’s hand and in the community cards, Jacobson has (slightly different) figures for EV if each card in players hand, and I’ve not been able to find anything anywhere else.

Does anyone have this data or would be willing to calculate it for me?

Many thanks

Enigma
link to original post


https://wizardofvegas.com/forum/gaming-business/game-inventors/24259-ultimate-texas-hold-em-face-up-cards/
Look at my comments on this thread and you will see what my UTH program is able to do. The more cards are known, the faster the calculation is.
Last edited by: Mental on Apr 21, 2026
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
Mental
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April 21st, 2026 at 5:37:37 PM permalink
Eliot has an updated article date Nov 19 2025: https://www.888casino.com/blog/novelty-games/ultimate-texas-holdem-collusion
The article is still presenting a very poor estimate of the collusion advantage based on a sample of only 500 hands. This number of hands is totally inadequate. If Eliot would have done statistical analysis of the spread of EVs within his sample, he would probably realize this himself. To be fair, he write: "Here are the (very approximate) results for six-player collusion at UTH:", but he never estimates the uncertainty in his 'approximate' answer.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
MichaelLandon
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April 22nd, 2026 at 4:20:33 AM permalink
Quote: Mental

Eliot has an updated article date Nov 19 2025: /blog/novelty-games/ultimate-texas-holdem-collusion
The article is still presenting a very poor estimate of the collusion advantage based on a sample of only 500 hands. This number of hands is totally inadequate. If Eliot would have done statistical analysis of the spread of EVs within his sample, he would probably realize this himself. To be fair, he write: "Here are the (very approximate) results for six-player collusion at UTH:", but he never estimates the uncertainty in his 'approximate' answer.



500 is only useful for determining a ballpark figure.

For any kind of exactitude you should basically throw the data out.
Mental
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April 27th, 2026 at 5:16:10 AM permalink
Quote: aceside

Actually, I myself is able to find all these numbers from Eliot’s work. It only takes some patience and statistics skills; however, I leave this as a homework to others.
link to original post



Are you able to download the XLSX files linked in Eliot's article? https://www.888casino.com/blog/novelty-games/ultimate-texas-holdem-hole-card-play-one-dealer-card

When I try to open these files, I get a message saying the files are corrupted:
https://www.888casino.com/blog/sites/newblog.888casino.com/files/inline-files/uth_dhc_computer_perfect_strategy.xlsx
https://www.888casino.com/blog/sites/newblog.888casino.com/files/inline-files/uth_dhc_grosjean_strategy1.xlsx

If you have any of these detailed results, I would love to get a copy so I can compare my calculations in detail.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
Mental
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April 27th, 2026 at 7:11:06 AM permalink
Quote: Mental


Are you able to download the XLSX files linked in Eliot's article? https://www.888casino.com/blog/novelty-games/ultimate-texas-holdem-hole-card-play-one-dealer-card

When I try to open these files, I get a message saying the files are corrupted:
https://www.888casino.com/blog/sites/newblog.888casino.com/files/inline-files/uth_dhc_computer_perfect_strategy.xlsx
https://www.888casino.com/blog/sites/newblog.888casino.com/files/inline-files/uth_dhc_grosjean_strategy1.xlsx

If you have any of these detailed results, I would love to get a copy so I can compare my calculations in detail.
link to original post


Eliot sent me a link to a page with all the XLSX files: https://advancedadvantageplay.com/downloads/
He knew that 888 had somehow corrupted the files linked from their site. The direct links work fine for me.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
aceside
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April 27th, 2026 at 10:01:46 AM permalink
I downloaded them several years ago. Thank you! Actually, I have studied most of these files.
Mental
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April 27th, 2026 at 2:23:06 PM permalink
Quote: aceside

Actually, I myself is able to find all these numbers from Eliot’s work. It only takes some patience and statistics skills; however, I leave this as a homework to others.
link to original post


Now that I have the files, I can confirm this. I just sorted Eliot's whole UTH_DHC_Computer_Perfect_Strategy.xlsx file by the column that has the dealer hole card, then split it into thirteen sub-lists for each dealer rank. Then, I use three simple formulas to sum the permutations column and weighted 'Optimal EV' column and divided the two to get the EV for computer-perfect play when you know one dealer hole card. This took me five minutes.

I had a minor bug in my new program which I found and fixed by comparing my results to the XLSX file. Now, my results are agreeing with Eliot's to seven significant digits that I use in my output. These are the EVs for dealer deuce through ace:

0.6242647
0.5266145
0.4321708
0.3381928
0.2860220
0.2284905
0.1615280
0.0856705
-0.0124859
-0.0817021
-0.1625157
-0.2582048
-0.4010560
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MichaelLandon
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April 27th, 2026 at 3:08:54 PM permalink
There are some serious methodological problems with Jacobson's work on this. You need a more reliable source on this to test your numbers against.
Mental
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April 27th, 2026 at 4:47:39 PM permalink
Quote: MichaelLandon

There are some serious methodological problems with Jacobson's work on this. You need a more reliable source on this to test your numbers against.
link to original post


I disagree. We are both calculating computer perfect play, and we should both agree on the exact number. Our calculation do agree, now that I debugged my new code.

This is not an EV that is attainable by players just using their grey matter at a table. Nobody could possibly remember of all the deviations from basic strategy when the dealer is known to have an six and you have a marginal post-flop decision.

The pre-game EV advantage that he calculates knowing that the player will have a 6c in the hole is essentially the real-world EV the player accrues, because he simply needs to play basic strategy well to achieve it,

What specific methodological problems do you see?
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
MichaelLandon
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April 28th, 2026 at 12:12:44 AM permalink
Quote: Mental

Quote: MichaelLandon

There are some serious methodological problems with Jacobson's work on this. You need a more reliable source on this to test your numbers against.
link to original post


I disagree. We are both calculating computer perfect play, and we should both agree on the exact number. Our calculation do agree, now that I debugged my new code.



You will end up with the same numbers if you replicate the same flaws.

Remember Jacobson is a casino consultant. I don't want to encourage casinos to find any errors in his work, or encourage them to stop paying for faulty and exploitable analysis. Sorry I can't go into this further for obvious reasons.
EnigmaAP
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May 2nd, 2026 at 1:02:26 PM permalink
Hi Aceside, Michael and Mental.

Firstly, I am grateful to you all for contributing to this, and for the time and effort that you have spent in both calculating and posting.

This information (the EV to the player from the dealer having each one of the 13 values, and the playing altering their play accordingly) is very useful (although I would be keen to discuss further with Michael regarding the accuracy concerns).

However, I am still looking for the two sets of data in the original request to this post:

1) The EOR for each of the 13 card values to the player’s EV

(in other words, if a player had the ability to prevent a 6 from being dealt in the next round, what would be the EV to all players, even if they just played basic? What would it be if they removed an A instead?)

2) The EV to each player for each of the 13 card values in the dealer’s hand.

(In other words, if a player were to be able to somehow control one of the dealer’s two cards, what is the EV to all players for each of the 13 cards merely being in the dealer’s hand, even if they just played basic because they might not know any better?)

As posted above, Grosjean provides the EV for each value appearing both in the player’s hand and on the flop, and Jacobson provides the EV for each value in the player’s hand. I’m simply looking for the obvious omission.

I’d be very grateful if someone is willing to assist with calculating these sets of data and am willing to pay for the information or hire them to calculate it.

(Aceside - I do not believe this data is obtainable from Jacobson’s excel sheet. Feel free to prove me wrong, however…)

Thanks again

Enigma
Last edited by: EnigmaAP on May 2, 2026
aceside
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May 2nd, 2026 at 6:41:05 PM permalink
For your question #1, I fully understand it. Even if you remove a deuce from a deck of 52 cards, you probably will not overcome the house edge of 2.185%.

For your question #2, I kinda understand it. So this is hole carding. Mental has listed the EV of each of the thirty ranks above. The problem is players cannot change their ante+blind bet amount after seeing the dealer hole cards, so the player EV gain is still very limited. I haven’t found any opportunities for hole carding in any casinos around the world.
Mental
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May 2nd, 2026 at 7:31:39 PM permalink
Quote: EnigmaAP

Hi Aceside, Michael and Mental.

Firstly, I am grateful to you all for contributing to this, and for the time and effort that you have spent in both calculating and posting.

This information (the EV to the player from the dealer having each one of the 13 values, and the playing altering their play accordingly) is very useful (although I would be keen to discuss further with Michael regarding the accuracy concerns).

However, I am still looking for the two sets of data in the original request to this post:

1) The EOR for each of the 13 card values to the player’s EV

(in other words, if a player had the ability to prevent a 6 from being dealt in the next round, what would be the EV to all players, even if they just played basic? What would it be if they removed an A instead?)

2) The EV to each player for each of the 13 card values in the dealer’s hand.

(In other words, if a player were to be able to somehow control one of the dealer’s two cards, what is the EV to all players for each of the 13 cards merely being in the dealer’s hand, even if they just played basic because they might not know any better?)

As posted above, Grosjean provides the EV for each value appearing both in the player’s hand and on the flop, and Jacobson provides the EV for each value in the player’s hand. I’m simply looking for the obvious omission.

I’d be very grateful if someone is willing to assist with calculating these sets of data and am willing to pay for the information or hire them to calculate it.

(Aceside - I do not believe this data is obtainable from Jacobson’s excel sheet. Feel free to prove me wrong, however…)

Thanks again

Enigma
link to original post



I pointed out the earlier thread where I did a boatload of calculations on exposed cards and collusion in UTH. The clear result of that thread is that there is very little EV change for a single card removed from the deck EVEN WHEN YOU PLAY OPTIMALLY. If you play basic strategy when you know a deuce is removed from the deck, the EV change will be even less. My program plays optimally. I suppose I could do a bit of work to have the program calculate the basic strategy for every hand and then recalculate the EV with a card removed from the deck. This means doing 22 trillion hands twice for each card removed from the deck, so 44 x 13 = 572T hands. I doubt it is worth the effort, but I might think about how I could code this without too much effort. I am cruising in the Mediterranean, so maybe it is something I can do to to amuse myself on a sea day.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
Mental
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May 3rd, 2026 at 4:54:19 AM permalink
I can easily calculate the optimal strategy EV for UTH played with a single deck that is missing a ace of clubs, etc. You seem really fixated by getting the EV for basic strategy, but you cannot play basic strategy perfectly. No human can.

A basic strategy would contain every optimal decision for every possible player hand, flop, and river. (52 choose 2)*(50 choose 3)*(47 choose 2) = 28,094,757,600 ways. If you specify a basic strategy for UTH without compacting it, it will not fit in RAM. A program to calculate UTH EVs will typically calculate the strategy on the fly and then discard it to avoid consuming memory. If you have a compact basic strategy in mind, the programmer could calculate the EV for that strategy. I think I could also calculate the basic strategy in smaller chunks and then apply it to the deck missing one specific card.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
EnigmaAP
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May 3rd, 2026 at 9:50:28 PM permalink
.Aceside:

1) I disagree.

2) No, it’s not holecarding.

Incidentally though, not being able to increase your bet after seeing the HC is irrelevant in HCing anyway…that’s not how an AP obtains an edge on a HC play.

As per my previous post, it’s clear you aren’t able to help with this query.

I don’t expect you to be able to answer my questions, and wasn’t placing you under any obligation to offer your opinions on them either.

Please be assured that there is no need to trouble yourself by continuing to reply to the thread with your valuable contributions.

All the best and I wish you well
Last edited by: EnigmaAP on May 3, 2026
aceside
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May 4th, 2026 at 7:52:54 AM permalink
I’m still trying to understand your second question. If I don’t understand it, most readers here will not understand it either. How about you restate your question in terms of high school math?
EnigmaAP
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May 4th, 2026 at 9:30:22 AM permalink
Aceside-

This question isn’t meant for someone who doesn’t understand it.
Especially when that person feels they can offer their unsolicited opinion that the OP was invalid and questionable, and when that person tries to suggest that the data will be used for cheating or deception in a home poker game, or when they resort to trying to taunt the OP with the childish claim that they easily calculated the data required themselves but aren’t willing provide it.

These are just a few examples, and the reader will find plenty more above. Despite all of the provocations from you, I’ve been nothing but polite, courteous and respectful towards you in my replies, every single time.

I don’t know if you are intentionally trolling or sealioning here, or if you are genuinely curious about trying to figure out an Advanced play that you aren’t aware of and trying to pick away until I tell you, but neither of those things are helpful or conducive to this thread.

As before, I wish you all the best, despite your behaviour towards me. But that’s it, no more engagement now, I’m not prepared to waste any more time and energy with you.

I’m obviously happy to engage with people who are able to help me and even if they aren’t, people who are prepared to discuss this seriously.

I am going to block you now, to prevent me from seeing your inevitable reply which will no doubt be attempt to troll / sea-lion further. Most likely ‘I was only asking the question…’, I would imagine.
Last edited by: EnigmaAP on May 4, 2026
EnigmaAP
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May 4th, 2026 at 9:36:05 AM permalink
Hi Mental,

Condensing both your posts into one reply for thread tidiness:

1) I’ve read through that thread and whilst it is very detailed on collusion play and the minimal impact of increased EV obtained through that additional information, I don’t see any data on the impact to EV from the fact that a card cannot appear in your hand at all.

To phrase it another way, my understanding of that thread is that you have calculated there isn’t much EV gain from noting that one of the outs linked to one of your cards is live or dead.

What it doesn’t cover is the EV gain from the fact a specific card cannot appear in your hand in the first place.

Correct me if I’m wrong, but I cannot see any data on this in that thread

2) Thank you, I’d be grateful if you could calculate that, although I understand you are on a cruise at the moment.

Incidentally, when I use the phrase ‘basic strategy’ for UTH, I am using it in a loose sense and am referring to either the Wizard’s version or Grosjean’s (both of which are very similar and provide an edge very close to computer perfect). I appreciate that true computer perfect BS is impossible for a player to achieve, and never meant that.
aceside
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May 4th, 2026 at 9:50:56 AM permalink
You posted this question for people to question. I just figure out what you want to calculate.
Mental
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EnigmaAP
May 4th, 2026 at 11:27:48 PM permalink
Quote: EnigmaAP

Hi Mental,

Condensing both your posts into one reply for thread tidiness:

1) I’ve read through that thread and whilst it is very detailed on collusion play and the minimal impact of increased EV obtained through that additional information, I don’t see any data on the impact to EV from the fact that a card cannot appear in your hand at all.

To phrase it another way, my understanding of that thread is that you have calculated there isn’t much EV gain from noting that one of the outs linked to one of your cards is live or dead.

What it doesn’t cover is the EV gain from the fact a specific card cannot appear in your hand in the first place.

Correct me if I’m wrong, but I cannot see any data on this in that thread

2) Thank you, I’d be grateful if you could calculate that, although I understand you are on a cruise at the moment.

Incidentally, when I use the phrase ‘basic strategy’ for UTH, I am using it in a loose sense and am referring to either the Wizard’s version or Grosjean’s (both of which are very similar and provide an edge very close to computer perfect). I appreciate that true computer perfect BS is impossible for a player to achieve, and never meant that.
link to original post


I agree that the collusion thread is addressing a slightly different question. Whether you know about a specific dead card before or after you size your bet is different for practical purposes. Knowing you will become aware of random dead cards after the deal is different than knowing a specific card is out of play before the deal. It is also more valuable. I think I see a way of calculating what you want efficiently. We try to sightsee all day and dance all night when we are cruising. I have a sea day coming up on the 7th and I will try to do some work on this.
BTW, we have cruised to 110 different ports and will add 17 more ports this year.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
EnigmaAP
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May 5th, 2026 at 1:43:34 AM permalink
Thanks again for your continued help, I really appreciate it. And please don’t feel obliged to do this instead of enjoying your cruise!

Enigma
gordonm888
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May 5th, 2026 at 6:34:06 AM permalink
I also have figured out your reason for asking this question. It would not be appropriate for me to mention it publicly. May I send you a PM?
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
EnigmaAP
EnigmaAP
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Joined: Apr 20, 2026
May 5th, 2026 at 8:32:47 AM permalink
Quote: gordonm888

I also have figured out your reason for asking this question. It would not be appropriate for me to mention it publicly. May I send you a PM?
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Please do! And THANK YOU for your discretion. It’s a pleasure talking with people that realise the way this kind of thing needs to be handled.

Enigma
aceside
aceside
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May 5th, 2026 at 11:25:34 AM permalink
Quote: gordonm888

I also have figured out your reason for asking this question. It would not be appropriate for me to mention it publicly. May I send you a PM?
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I actually haven’t understood what OP is asking. Please PM me too to let me know, if you can.
Mental
Mental
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EnigmaAP
May 8th, 2026 at 2:19:07 AM permalink
I calculated 8 of the 13 EOR cases for removing a specific card from play. As I speculated, the EOR is quite small. For a deuce, EV = -0.013, for a queen EV= -0.029. I did not pay for ship internet, so posting from a train station in Cinque Terra. Will have full results tomorrow.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
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