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These Aces...
Originally Posted by pti
A simple question every one has to know the answer to. But it may turn that no one knows it
Follows my letter to givememyleg_flopturnriver.com, which advised me to open a thread.
Good reading and good thinking.
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Hello,
Please, see what is my problem. I want to know which are the pocket cards that play the best against Aces. All these more than 15 years that I play Hold'em, I thought that these are 87 suited. Yes, but when accidentally tryed on PokerStove some 65s they turned to be better. I was tottally astonished and tryed some calculators.
Here are the results (in %) I obtained:
1 - CardPlayer (PokerListing is the same but work very slowly)
2 - PokerStove (PokerRanger gives the same results but arounded to the hundredth)
3 - CardsChat
4 - Old FlopTurnRiver (as a couple of months ago)
5 - New FlopTurnRiver converter
1 2 3 4 5
JTs 21.55 21.717 21.88 21.35 21.42(0.35 tie)
T9s 22.61 22.765 22.43 22.50 22.66(0.33)
98s 22.47 22.623 22.11 22.40 22.27(0.30)
87s 22.87 23.021 23.33 22.97 23.02(0.28)
76s 22.87 23.033 23.55 22.73 22.88(0.34)
65s 22.87 23.056 23.23 22.51 22.87(0.39)
Also I tryed your plain text odds calculator but received some error - Backend error:
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Well, it is of no practical importance these tenths, or hundredths of the percentage, but they have its theoretical meaning. I know that you use some optimization methods (I had red the source code of PokerStove, which is no more supported, and the author used some pre-calculated tables for faster obtaining the results), but the truth has to be one! And I expect you to help me to find it.
Also, I had found this thread "Why is 56s best hand against pocket Aces?":
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( Use a search for me not to give a link to an other forum)
Have a good day and all the best.
Т П
P.S. I lost one hour to cope with this software. That is why I rarely post anywhere!
The question is not so bad one, once we go to EV /expected value/. I will present three examples in two main categories: 1) crippled stacks and 2) multi-way hands, where more than a player can have positive EV.
(Only after I finished this post, I realized that had not said that in this post is mostly spoken about MTTs. But all is the same, including the mathemathics
1) In a satellite we are very (2-3 people to be burst) close to the bubble. Blinds 50/100 no ante. Me on the SB with thousands am qualified for sure and am dealt 6s5s. The BB has 60 (was severely crppled) after the post. Because it was SH 6-table we often were left in hands-up. If I am TAG, he is super-TAG. I never tryed to steal his blind and to irritate him as I prefered him on my back than some maniac. Even after he suffered a bad beat and was crippled I started to muck decent for the SB hands. This time I called, knowing that he is qualified. If I had remembered this hand it is because of the insanity he did - he pushed all his chips! Aces for sure! Even not Kings. Absolutely frustrated, what had I not did for him to survive and he - splash! On the turn he already packaged his knapsack. If Dan Harrington gave us a simple case where the Aces are to be folded pre-flop, this one is a more than obvious case where the Aces are to be slow played - check till the showdown, even if they lose, you have 50 for the next SB and the remaining 10(!) would have saved your life! But these are Aces Aces, sure, but they are not invincible...
An other thing that chocked me and made me laugh half an hour non stop, when analyzing this hand, was that I am on the edge. My EV=0 is at 85 chips. Had he had and pushed 86, not 60 chips, my right play with my 3,300 chips is to FOLD, and no one could blame me for dumping! Can you imagine this to happen at a cash table? Expelled with kicks and banned forever not only from my casino, but all casinos in the country, even around the world (One more half an hour non stop laugh)
2) Crippled stacks ofen occur in long MTTs when a few - 2,3,4, players are remaining with a few chips, even partial a chip (Yes, there are tournaments won by a player, who at some moment had had a fraction of a chip!) Here all mesure are in chips (SBs) in this example (100 entries, 1500 starting chips, 36th level - 15K/30K, 10 min per level, 6 hours play, four remaining - more than normal). The situation is reversed - the 65s is the short stack. Four player still alive, blinds 1/2, no ante. Player A(SB) puts 1, B(BB) - 2, C raises. You with just one chip (1/2 BB) left, have 65s. Do you call? Against Aces you have 23% chance to win, or EV -0.08 chip. The next hand, UTG, you have the chance of 25% to be dealt the winning hand, but in the pot there will be only 2 chips, or EV +0.50. A further one more hand you are forced all-in on the BB with EV +0.50, if two passes. Call now?
Let the players be not 4, but 5. Same situation, but there is a player (the dealer) behind you. He may be forced, being cripled, or decide that such a big pot is worth to call. As we will see in 2), you have the same more than 20% chance to win the hand (AcAd/AhKh/6s5s is 63.5%/12.5%/24.1% ! We are not to expect such big clashes - AA vs. AKs too ofen when 4-handed but this is mostly theory.) but your EV +0.16 - clear call.
No one has the time to make these calculations on the table. He is to make them beforehand at home, sitting in a confortable chair, with a paper sheet and a pencil in hand (it is faster than calculators), listening a quiet, relaxing music.
Here is my homemade. It depends of 1) the prize structure (sometimes the difference between the 1st and 4th sums is in times, other times it is flat like this - $10, $8, $7, $6) and the amount of the prize itself ($10, $100, $1000 ?) in relation to my bankroll (I always follow the rule to have 20 buy-ins.) I assume the scheme $10, $7, $5, $4. In general (4-handed), if the 1st prize is less than my bankroll (20 buy-ins), I made it till now well (4th prize has to be no lesser than 5 buy-ins, usually that put you a level higher), it is worth a push - call with 65s, but fold with, what may look better for some people - QJs (19.7% win, EV -0.21) and KQo (13.7%, EV -0.45). If the 1st prize is bigger than my bankroll, I did it very well till now, am in big money and every place up means new big money - fold with at best EV -0.076. If the prize structure is very flat, I call in both cases - that may be my day, I do not play so many tournaments
For the 5 handed table in both prize/bankroll cases, if we assume that the dealer will call with 50% probability, which means 3,5 pot, our EV +0.04; if he wll call in 25% of the cases, pot 3,25, EV -0.02 -> no one can know 50% or 25%, so call. If I am the dealer and he had already called, it was said above - EV +0.15 on 4 pot and call. In the latter case, pot 4, I would call even with QJs - EV -0.015. The suited connectors from 54s to JTs are with positive +EV, if in a sperate suit. (Difficult against 4, 6 or 8 cards, but I am not going to make the exact calculations. Someting like 18,5% /EV -0,075/ if one card in the 65s suit and 18,0% /EV -0,10/ if two cards, instead of the needed >20% /EV 0.0/. You decide the risk!) Examples:
1) AcAd : KhQh : 5s4s . pass . pass = 60,6% : 17,8% : 21,5%
2) AcAd : KhQh : 5s4s : 9d9h . pass = 49,1% : 14,7% : 20,6% : 15,6% ........... EV +0.03
3) AcAd : KhQh : 5s4s : 9d9h : AhJd = 41,7% : 13,2% : 23,0% : 17,2% : 04.9% ... EV +0.15
but
4) AcAd : KhQh : 5s4s : 9d9h : 7h2s = 43,6% : 14,5% : 18,7% : 15,7% : 07.6% ... EV -0.065
5) AcAd : KhQh : 5s4s : 9d9s : 7h2s = 43,6% : 15,8% : 17,0% : 16,1% : 07.6% ... EV -0.15
The math behind my reasoning is very simple. At this stage of the game, final 10 and lesser players remaining, it is not the EV in chips that counts, it is the EV to Win the Tournament (EVWT) that is the essential. Let in the example above player A has (before the posts) 2 chips (SBs), B - 3, C - 4, Me - 1. My EVWT is 10%.
EVWT = my chips / all chips = 1 / 10 = 10%
If I win the main pot (the other pots do not interest me) I will have 4 chips for EVWT = 40% or a gain of 30%. The same way as for the EV in chips, the question is - if I put my 10% in the pot of 30% what are to be my chances/probabililies (0 < X < 1) to win the pot for that not to be a losing move? We are to resolve the equation:
(30% * X) - (10% * (1 - X)) = 0 X = ?
The anwer is X=0.25, or in percentages - 25%. In the above hand (AcAd/AhKh/6s5s) I am very close - 24.1%. So I call in some situations. But not with QsJs - 19.7%.
Let me sumarize. Supposing that I have full 25% to win the hand in the above example. Every 4 hand I win once 40% EVWT and thrice lose my 10%, for the sum of 30% lost EVWT and in the long lun I am left with my inital 10% EVWT. Neutral play - neither winning, nor losing. The EVWT is based on chips, but it is far more meaningful to say: "This hand I won 10% EVWT and I am 53% EVWT now.", than: "I won 100 (1,000 or 1,000,000?) chips." or: "I went 3 places up." In a MTT with 100 entrants and starting chips 1500, there are 150,000 chips. If some idiot (they still exist and reproduce themselves doubles up (two idiots are needed the very first hand, he gained 1% EVWT and now has 3,000 chips and 2% EVWT no matter how many other idiots on the other tables went home
We may return some day to this example on an other place. Most of this hand, my decision and the tournament depends of the stack of player B. Is it in practice 2.9 or 3.1 chips(SBs)? Remember the first example.
2) In a multi-way pot, many players involved in, more than one participants may have +EV, so good reason to play. Let us look at the following percentages to win and EV of the hands. All the participants have 100 chips and are all-in. Not so unprobable, if we remember that along, and even before, the No Limit Hold'em there is the Fixed Limit one. The settings are the most favorable for the 65s (and the Aces, too!) - all the pairs are in the black suits, the 65s are red. The 65s is last to bid. Given are only the numbers for the AA and the 65 (the first column), the other are irrelevant and far lesser than that of the 65.
AA : 65 ....................... 23.1% : 76.9% ...... EV -53.8 ... +53.8
AA : KK : 65 .................. 23.0% : 61.2% ...... EV -31.0 ... +83.6
AA : KK : QQ : 65 ............. 23.0% : 47.9% ...... EV -08.0 ... +91.6
AA : KK : QQ : JJ : 65 ........ 22.6% : 37.7% ...... EV +09.4 ... +88.5
AA : KK : QQ : JJ : TT : 65 ... 22.3% : 29.5% ...... EV +33.8 ... +77.0
It is not needed to comment how the one staying with the same percentages, go up in value, while the other one falling like a stone down in percentages, mark time on (almost) the same value.
In these examples, that may look forced, I tryed to show why is it important to know how different pocket cards play against Aces. One thing is the 65s 23.056% win, an other one is the 72o 11.024%. All the other pockets are somewhere in between these two extremities. That give us a notion of how strong is our possession as compared to a sole standard - AA.
As a matter or fact 65s plays not so bad against the range of the 5.3% best hands (12 in number) - 88+,AJs+,KQs,AKo - 29.0% : 71.0%. For comparision - QJs has 34.8% win, KQo has 33.1%, 72o has 19.5%.
No, in no way am I anxious about the fate of the mediocre hand that 65s is:
65s : rnd ..... 43.13% : 56.87% rnd = random hand
65s : rnd : rnd 30.21% : 34.90% : 34.89% ............ etc.
I am interested of how the situations look like from the position of the strongest hand - the Aces. Now we know their most tenacious opponent - 65s. What next?
See you an other time at an other place.
Buy.
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