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Eg if you say "I bet i'll have pocket 7s next hand" you'll be correct 1 in every 221 times.
If you say "I bet i'll have a pocket pair next hand" you'll be correct 1 in 17 times.
Limped in with A,10o, and J,Q,K hit the board. Re-raised all-in in response to a hefty raise and was called. The oppo had pocket kings. Ouch! - I felt for him.
A timely reminder why I limit my play to low level SnGs and have given the cash tables a wide berth. It's the sort of odd incidence that can cost you a bundle - who wouldn't have shoved with everything in front of them flopping a set of kings? At the risk of mis-typing a figure again, what about this?
Odds of flopping a 10-A straight odds of flopping a set from a pocket pair
1/305(ish) x 2/50 x 3/1 (again ish).
So the odds of an end of range straight being up against a set (from a pocket pair) after the flop
1/305 x 2/50 x 3/1 = 6/15,250 = 1/2,542; 2,541-1
After the event, his dilemma in calculating the chances of me holding 10,A?
16 (possible combos for A,10) * (51-5 * 52-5) five cards are known.
1 2 to account for A,10 v 10,A
= 1/68 (ish); 67-1
As pointed out above, the consideration should change based on the cards now on the board, although bearing in mind the odds the judgement call probably won't. If all three cards on the board were suited, the odds of a set being dominated at this stage change considerably of course.
Looking on the bright side he dropped 30p. It could have been so much more. I can't remember who s/he was, but I wish her/him better cards in the future.
Of course you are quite right . . . its not just about the obvious draw on the board but the probabilitiy of ending up on the business end of other combinations s/he might lose to. From my point of view I did consider the number of cards that would mean my ace high straight was overtaken - 1xK, 3xQ, 3xJ; anyone of which would have had the last laugh (7/47 x 2/1 = 14/47 or a tad more than 3-1).
Where someone wrote above something to the effect that the odds change, what I think they meant was that the factors to consider change, and these factors' probabilities will have different odds from those of the the initial instance? - which is a fair point to make. A matter of terminology perhaps? Sometimes when people refer to the the "odds changing", it's linked to nonsense like the great Gamblers Fallacy.
So how do you work out the "equity" of a range of hands?
Hands that beat you: 65, A5, possible, some villains you can expect to fold pre. Sets are in nearly all villains ranges , 2p is sometimes a possibility although many villains fold them pre. An odd time you see slowplayed QQ+ but not often
Of hands you are ahead of Ax with flushdraw will have slightly more than 50% equity v you, any pair with an A kicker, 55 also have good equity, you need to decide is villain likely to play them this way. You crush smaller overpairs, lots of villains go broke here with them some dont though. He may raise air sometimes
You need to calculate your equity v best guess at villains range. Pokerstove is a good tool for this, download it for free. Play around with it and you will get good at estimating your equity in certain spots
1. if you are a sadist,work out your equity v each hand in his range and average it out using number of combos of each hand. This would be pretty difficult even if you approximate equities using rules of 2 and 4 etc
2. plug the ranges into pokerstove
Two other questions fall out (sorry if I sound thick) - firstly what is "equity" (what does it measure)? Secondly, how is it quantified, therefore enabling diffferent instances to be compared (in order to do this you would need to calculate it, hence my question above).
Why not take me through a simple example?
Apologies to all of the true Area51ers, as I've taken this thread off topic I think - perhaps we should start a new one somewhere else?
Im not really capable of doing a full equity calc tbh. It would involve finding the odds of all boards for all different hands in villains range beating the hand you have. If he beats you 1/4 of the time you have 75% equity etc. You might find a full calc somewhere if you google it. Use pokerstove to calculate for you, learn off the basic important one, eg pair v i over pre, two pairv fd on flop etc, even doing this you have to weight the possible combos
sorry cant be more help but just play around with pokerstove is my advice
It would seem to me that we've all been talking about the same thing . . . . although perhaps in different terms.
The description of having an "equity" share of any pot, is a difficult one to visualise, as it is basically a longer term measure of success; with x hand equating to 75% "equity", then over the longer term you could expect to win 75% of chips in pots when these hands show over the longer term. Trouble is, the longer term is a long time coming, and with the flux of variance the averages may never actually average out.
If taking as an expression of probability of winning - from the example above if the odds dictate you'll lose one out of every four hands (on average) then you have 75% equity - then it is easier to comprehend. So the equity could be the possibililty of winning the hand, based on the likely hands an oppo might have and is willing to play. In my discussions above, I've been considering the possibilities of the oppo having hands and drawing certain cards that could turn it into a winner - expressed as odds rather than %ages. Convert my possibilities into %ges, and take them off of 100%, to arrive at the "equity" you've both discussed.
The difference is, I endeavour to do my calculation on the fly, with the thing between my ears (part of the challenge of the game) although the 15 seconds, less network lags, SkyPoker allow isn't sufficient time to consider every single possibility and factor in the impact of it - so it's mainly the most probable of the possibilities that might occur, with a fair amount of rounding involved. As I've said above though, some of the finer points won't really have any impact on a playing decision.
I'll give your comments some thought may write again in due course.
Good cards.
Whilst the logic is clearly explained, the examples you give do seem to be taking the scenic route to arriving at a call or fold decision. To some degree assigning specific hand ranges is somewhat academic as well (although I can see it will assist when considering the playing behaviour of different oppos) If you shove with a pair of aces, and the oppo calls with a pair, the actual value is irrelevent as it's an overpair v an underpair and the odds are exactly the same to suckout, regardless of whether the underpair is KK or 88. Likewise if, the call is two different undercards, regardless of what they are the odds will remain the same in drawing to two pair or better - suited cards will throw it as there's a higher chance of hitting a flush, and suited connectors open up further possibilites. If there is a chance that someone might have a better starting hand, what are the odds of that? More likely the lower your cards are. In the overpair v underpair pre-flop contest, there's still a 60%-ish chance that neither player will draw and the higher pair will take it.
Working out the odds on the most common draws to lose is fairly easy and can be done on the fly, in contrast to having an open window on the desktop and asking a software programme what you should do - I'm sure some players do this. I personally haven't gone down this route, although my reasons for playing regularly are probably different to your own and other members. I play once a week in a live two table tourney, and I think it'd be seen as a tad anti-social to slap a laptop on the table just as the chips were being divvied up. Also, common situations occur time and time again and you don't have to work them out each time as they become ingrained in your memory - I know that someone chasing a set from a pair after the flop has around an 11-1 chance of hitting it, and therefore play accordingly based on all of the other considerations in the game.
Playing against software and 'bots online is probably the reason that most seasoned players I speak to tell me it's become a lot harder to make money at the game than it was, say, five years ago? Can't comment myself as I've never set out to make money and have only been playing (again) since January.
Thanks for your efforts in writing your post.
and there was me thinking its a fix