Aces! Your Optimal Number of Opponents?

Aces! You’re optimal number of opponents?


A strategic maxim of Big Pair Starting Hand Play in Stud, is that “a reduction of the number of opponents that your hand has to play against tends to increase the profitability of the hand.


This post contains 3 hand confrontation questions : Each question asks your opinion, as to the optimal number of opponents that you would like to play your pair of Aces starting hand against.


But first I would like to quote the opinions of several authors which are related to the topic, as a means of stimulating debate.


1. Mike Caro‘s “Guide to Super Systems” (p34, e14)

“Sometimes you don’t want to eliminate players.... When you start with 10s through Aces, Do you really want to eliminate players ?”


2. Konstantin Othmer “7 Card Stud“ (p71 g.1) A matematical calculation of the number of opponents vs. Percent Returns for playing a pair of Aces.


When Aces are played against a single opponent the amount of return on each dollar invested is $1.45, When played against two players it is $1.80, Three players $1.95, Four opponents $2.00, Five opponents $2.05, Six opponents $2.08.


3. Konstantine Othmer “7 Card Stud“(p70 pg 4.) “Since big pairs lose value as more opponents enter the pot, the strategy, with large pairs is to play aggressively to limit the field.”


4. Sklansky, Malmuth, and Zee Seven-Card Stud for advanced player’s 21-century edition Chapter “loose games” “Playing large Pairs” pgs 151- 152. If you don’t already know this one, you should look it up.


5. Roy West: Lesson 7 High Pair Play (p30.pg3). The more players drawing against your high pair, the higher the chances of your pair being out drawn.


6. Mohammed Mohammed : “The Science of Poker” (Section 7 card Stud, subsection Big pairs) the relative strength of all big pairs is related to the strength of their kickers with the exception of Aces.


Questions no 1


1. You are playing in a LPMCS (loose passive multiple calling stations game) $4/$8 stud game with a 50-cent ante, The game has been averaging 6 callers per hand. You are in an early position with a (As Ac) 10s as your starting hand. Your spades are entirely live, your Aces are live, and there is one King, and one Jack in the doors of your opponents. If you could choose any number of opponents to play this hand against.(between 0 and 7). You would choose?......


Question no 2


2. You are playing in a tight aggressive $9/$18 Stud game. (Ante $1) There has been an average of 3 callers per hand. 80% of the time the players have been completing the third street bring in. And 10% of the time there have been re-raises on Third Street.


Your hand is (As 8c) Ad and there is one Ace out behind you. Your position is two players from the bring in. The door King on your right has completed the bring in. If you could play this hand against any number of opponents, (from 0 to 7) you would choose to play it against.....No of opponents?


.

Question no 3


3. In the future if you could choose the number of opponents that you will always play against. But it can only be ONE number. And it will always be the same number, each time that you have a pair of Aces in your starting hand from now on. (No matter what the playing conditions are) You would choose which number of opponents? From 0 to 7 it would be?.......


Most Sincerely,

Doc AZ

Doc,


Having a choice I would choose 0 each and evey time. Raise and take the ante money. Free money with no risk whatsoever.


Later,


CJ

well here's my opinion. this is based entirely on a couple thousand hours playing stud, very little math offered to back it up /images/smile.gif


Question 1:

This depends entirely on the emotional state of the players in the game, more specificly, how confident are they in themselves and how confident are they in me. A low value in the first and a high value in the second category(usually based on respective #s of chips and recent wins/loses at this level of play) is, of course, optimal. Given this situation I think I'd like to see 4-5 callers of my 3rd street raise/completion(and I would ALWAYS raise in this situation). I say this because I think some aggressive betting(even without a scare card or two on board) could trim the field to one or two callers at the river(if that much), which, again at this level, leaves me with a good chance to win with just AA.


In a game where things haven't been going well(betting big draws that don't come through, raising middle pairs and being outdrawn, etc.) and the opponents don't have confidence in my raises(or they've been hitting and think they can win any hand) I'd like to have either 1-2 or 6-7 opponents. The first case so I could be a heavy favorite to win the hand while still getting a few bucks for my AA; the second case greatly reduces my chances of winning the hand but if I make Aces-up or trip them and it holds up, as it very well could, I'd have a nice pot. There's more detail on this sort of situation in, oddly enough, Hold-Em for Advanced Players.


Question 2:

Juice it. If there's a draw or under pair out there against you that wants to call the raise+completion cold fine, they're making a -ev play calling that(short of a real monster hand that's going to gut you here no matter what you do) so that makes money for you(whether you win that particular hand or not), and if you get it head's up against the KKs(or any other real raiseworthy hand) that's good for you two. If the K is completing with an underpair trying to get the overcard(you) to fold it's really not functionally that different from having KK so that shouldn't effect his play much(yeah right), and if he's trying to steal it's not like you'd get much money out of him anyway so nothing lost attacking right now. In summary, I'd like to play this against 1 or 2 players(maybe 3 if I'd been raising a lot of middle pairs with big door cards and/or big drawing hands(as I should be) so it isn't so obvious to everyone where I'm at).


Question 3:

Gimme 3 suckers /images/smile.gif. This one I really don't know what I should pick, 2 seems a little thin and 4 is getting to be a bit tough to win a high percentage of the time, so I'm saying 3. No analysis and not much thought but, that's what I'm going with.


enjoyed your question, hope this is helpful(or at least entertaining)

Example one, I'd probably just call and hope someone else bets. Depending where that bet comes from, and how many players see it before it comes to me, I may call (if lots see it and I don't think they'll fold for a raise) or I may raise (if one or two people call). If lots of players limp and then it's raised to my immediate right, I'm reraising to narrow the field. I don't want more than two other opponents after fourth street (although I may change my mind if I hit a ten or spade there - if I hit another ace, I'm checking of course)


Example two, I'm raising here to get heads up against the king. This is a classic hand that's "best now but can't improve much."


Example three, I'm generally happy in the low level games I play if two or three stay for a full bet on third and I get it head up or three way by fourth. If I'm not head up on fifth, I'm not too happy.


Of course, all of these answers depend on what I hit on fourth and what my opponents hit. If I'm against a paired door card and a two flush, I may fold. If I trip up my aces, I may get trappy. If I add a live second pair or add a three flush, I may

not mind that fourth or fifth player as much.

1. IN the first hand i would be happy with 6 callers, but the hand can be played against any number of opponents. It is a case of profit vs. chance of winning. I am not sure what the optimum number of opponents is however.


2. I would choose one opponent especially with the dead card.


3. Is a bad question since to answer the question the kicker is all important.


Pat

Pat, I don't follow wanting six callers here. It's not horrible if that happens, but I'd rather have a smaller number. Aces with a two flush is not so powerful that I want to take it against two three flushes, three lower pairs, and a high straight draw. Playing against this big a field, my hand is best but it's a big underdog against everyone else combined. Personally, I'd like to see six limp to me, then thin it to three callers when I complete.

Yes but at low limits your profit is going up with more callers at a faster rate, (I think and am not 100% sure perhaps better minds than I can pop in here) than you chances of winning are going down. I would rather win a large pot 10 % of the time than a small pot or steal the antes of the time. Or something like that; i do not know the actual odds I am just giving a hypothetical. I could be way off here but that is my impression. Being a dog to win the hand does not matter nearly as much as getting the most profit, and that is a situation that many players have trouble with.


If the players held the hands that you describe then a raise will not likely thin the field anyway, but most games players play lots worse hands than those you describe. I think the post by Doc refers to a low limit type game, where players are probably calling with a lot worse than your hand.


Pat

The issue of having a higher money return when playing aces vs a large number of opponents could apply even at hold'em when starting with pocket aces. But it's difficult to find a player glad to see 9 players (or 7 at stud) calling the preflop or the 3rd street, even if the money return is the highest.


Heads-up is the better option to have a good control of the hand (maximizing at the best point the probability to win the hand, no matter the money return).


Marco

While heads up guarantees that you have the best probability of winning this cannot be the main consideration if you are going to play. You cannot win in the long run if just maximizing your probability of winning is your main consideration. Many times this is the same as maximizing profit, but many times it is not, and in those situations you should be willing to give up some percentage of wins in favor of increased profit.


Pat

Dear Pat,


I admit that the question of kicker strenght variability makes the question a complex one. Actualy the multiple possible variables make it a compound complex question. But as Babbage explained when he demonstrated his recently invented mecanical calculator in 1835 (the same one modified at Bletchley Park to create the proto computer)


" The fact that a question has compound variables or even compound complex variables does not mean that it's answer can not be calculated or that that answer is not valid."


Your friend,


Doc

Dear Pat,

I raised the question about the low limit strong pair sinerio, partly because of MY uncertainty as to the best answer.


The one thing I find most frustrating about Othmer’s Aces vs. callers profitability study is that he doesn’t explain what parameters he used as functions to derive it. (aka how in the hell did he get there, and what the hell does it mean)


But as Angry points out “experience is the great teacher“. Which would explain the marked flattening of Othmers curve after 3 CALLERS have entered the pot. (Potential risk vs. potential profit)


“How do she Know”

I'm a little late to the discussion but here goes.


In the first case of the loose passive game, I would only call from early position. I would hope for other callers and a completion from the King or Jack. I want a family pot with my completely live hand and would stand to get lots of callers even if I make a good hand. After assessing the 4th street cards of my opponents, I can then try to knock out opponents if necessary by raising or reraising the action. It sounds counterintuitive, but I would be more inclined to raise and reraise if I haven't improved then if I had improved. The reason would be that either my live flush draw was no longer live or if another Ace or ten fell elsewhere, my hand can't stand the pressure from so many callers or cold callers. This would signal to me that now is the time to limit the field and make the playing of the A's my main focus.


In question 2, I would reraise the completion of the king and hope that I played heads up with him, I could live with two players, but would be very disappointed in a big multiway pot. One of my A's is dead and the table can see that which suggests to my opponents that I may not have A's and could influence many callers if I only call the completion. Because the A is my door card, I will have to lead the betting which makes calling more tenuous. If I plan on betting out I should reraise now and try to end the action. The other reason that I only want one caller, and preferably the K, is that in this level game I can expect a call to the river even when I improve and a value bet is profitable because a lone pair of K's will call my river bet. Because 1 of my a's was dead he is more likely to assume that I do not have A's.


The difference in the two hands to me is the "liveness" of my starting hand in hand 1 compared to hand 2 and the 2 flush (and inside straight draw). Hand 2 doesn't offer any of these additional outs so I think it should be played more aggressively.


If I had to choose the number of opponents for eternity, with the playing conditions of real life, I would choose 2. Real life means that my opponents play good starting hands, etc. If I was playing in a showdown atmosphere where starting cards didn't matter and everyone just called everybet to the river, I would choose 7.