The "7% rule" or the "5 and 10 rule"
I've seen in a few places, including the Lee Jones article in the latest CPPM, authors mentioning 7% of their stack size as (roughly) the maximum they are willing to limp in for or call a pre-flop raise with in no-limit with hands like small pocket pairs.
Ciaffone & Reuben mention the same kind of thing in "Pot-Limit and No-Limit Poker", which they refer to as the "5 and 10 rule". That is, they say they're willing to call pre-flop in most cases (with hands like small pairs) when the bet to them is less than 5% of their stack size, they'll fold in most cases when the bet is more than 10% of their stack, and "it depends" within the 5% to 10% range.
What are your thoughts about these guidelines? What do you think is the reasoning is behind the 7% number (or 5%-10% range)? What kinds of hands exactly do you think this kind of reasoning applies to? Just pairs? Suited connectors? Suited Aces?
[I'm assuming that these authors are referring to "stack size" as the maximum amount they could win from each player. For example, thinking of the case where everyone has you covered, or at least, that's roughly so.]
ScottyZ
Ciaffone & Reuben mention the same kind of thing in "Pot-Limit and No-Limit Poker", which they refer to as the "5 and 10 rule". That is, they say they're willing to call pre-flop in most cases (with hands like small pairs) when the bet to them is less than 5% of their stack size, they'll fold in most cases when the bet is more than 10% of their stack, and "it depends" within the 5% to 10% range.
What are your thoughts about these guidelines? What do you think is the reasoning is behind the 7% number (or 5%-10% range)? What kinds of hands exactly do you think this kind of reasoning applies to? Just pairs? Suited connectors? Suited Aces?
[I'm assuming that these authors are referring to "stack size" as the maximum amount they could win from each player. For example, thinking of the case where everyone has you covered, or at least, that's roughly so.]
ScottyZ
Comments
The 5-10% rule is an application of “implied odds.†What can I win if I hit my hand? The 5-10% is based upon the assumption that if I hit my hand I will be able to take my opponent for his entire stack or all of mine (whichever is lesser). And yes, the 5-10% rule applies your stack or your opponents. For instance, if you opponent only has $20 and best $5 but you have $100 yes, that’s 5% of your stack but the implied odds are not very good since all you can win is $20 (the $5 he has bet plus the $15 still in his stack). This is by way of background and I am sure is nothing new to ScottyZ.
So… what do I think about these guidelines?
Let’s look at a medium pair. You will flop a set 11% of the time. If we assume that you will always double through when you flop a set then you about 10% of your stack is perfectly reasonable – 10% of your stack for an 11% chance of doubling through. Of course, this is far from certain. You will, however, win some smaller pots without flopping a set. For instance your pair of 8’s might take A-K of a hand when the flop is 7-6-2. So, all in all I think that the 5-10% rule is probably about right.
Codicil: You must have a good handle on your opponents. If you routinely play off 10% of your stack based upon implied odds you better be right about those implied odds. That means you had better be right about HOW YOUR OPPONENT plays since that is the assumption upon which you are basing your call.
What kinds of hands does the reasoning apply to? In my case, if I feel that I have a strong handle on my opponent I will consider any pair, suited connectors, suited one gap, and suited two gap (excluding Q-Js, Q-Ts, and Q-9s). Frequently I will also play suited aces but I am a little more leery about them because I know that I have trouble laying down an ace when I flop top pair. So, if I feel in top shape I play them and if I feel like I am off my game I avoid them – they are harder to play than pairs and suited connectors.
Why suited one and two gap? My small amount of research tells me that there is very little difference between suited connectors and suited two gapers when you are trying to take a big stack for his whole stack. In fact, a suited two gapper might even be better since he might put you on 7-6 but he will NEVER put you on 9-6.
Also note that against some opponents it is profitable to call with ANY two cards provided that the circumstances are correct. Again, you better be right about the circumstances because woooweee we are talking about a high variance approach to no-limit.
I love these hands too. Brunson says pretty much the same thing in Super System. What do you have against the queen-high connectors, one-gappers, and two-gappers though?
Keith
I guess that this is sort of what I was thinking of. Let's take a pair for example. Odds of flopping a set are 8-1, and the 7% rule is giving you implied odds of around 13-1 or 14-1 under the assumption that you get a double up every time you hit. Clearly this is excellent if the assumption is valid.
However, I was thinking that there will be a good number of times that you will hit and *not* get any action. You'll sure win a few small pots in this way, but you're going to be losing more than enough bets along the way every time you miss to more than make up for that.
What I was wondering is if there is any way to (even very roughly) estimate the percentage of the times that you do get paid off given that you hit your set. This seems impossible to "calculate", but do you have some intution of this? Obviously this depends on a lot of things: your opponent's skill level and playing style, your own skills at extracting large value bets (slowplaying, etc), what the board cards are. But I was wondering if you had any rough long-run ideas about how much of the time you'll get paid off when you hit your small pair.
This is very important to get a handle on I think. If you're getting a double up 100% of the time, it looks like a 7% call is going to be a solid play. If you think you'll get paid off only 50% of the time, it's much more dodgy.
Under some (massively) simplifying assumptions, if X is the percentage of time you'll get paid off given that you hit, then I think a rough way to calculate the EV break-even decision point for X is
Amount of call / Odds of hitting a set
since the numerator is exactly equal to your implied odds in the cases when you are fully paid off.
That's about
0.07 / 0.11 = 0.63
So, I think you can call 7% of your stack with a pair *in terms of EV only* when you figure you'll get paid off more than around 63% of the times that you hit.
Also note that this is simply the EV break-even point. You're probably going to want some extra value beyond this to compensate you for the Variance, and also: for the times you hit and lose, the bets you lose along the way when you don't hit, or what happens when you flop hands like straight draws or medium-sized overpair and might have to pay off some small bets.
My intuition is that you're going to have to expect to get paid off almost *all* the time, maybe at least 75%-80% of the time, in order to justify calling a full 7% of your stack with a speculative pair. That doesn't seem that realistic to me as a general rule, and my intuition personally is that the 7% guideline might be too high.
Also note that the exact bet size you need to call makes a huge difference. Facing a limp-in of 20 with a 1,500 stack size (e.g. PokerStars), then you only need to expect to get paid off for the full stack (again, in terms of EV only) about 12% of the time, under some simplifying assumptions. This seems like a much easier call.
And one other thing is for sure. It can almost *never* be right to be calling off a percentage of your stack (if the active chip stacks are deep) which is greater than, or even pretty close to, the odds of hitting your hand. So, the 10% upper band (i.e. the "never call" limit) of the 5 and 10 rule definitely seems sound to me.
ScottyZ
I'm not so sure about this. Those "small pots" really add up. This is the entire strategy behind Super System.
If you are going to get no action when you hit, then you should be able to pick up the pot when you miss. Having position on the guy certainly helps here.
Keith
I guess that in order to make the original analysis tractable, I am making a *lot* of simplifying assumptions. I'm virtually ignoring anything that happens post-flop besides assuming
1. you'll somehow get all the chips in when you hit a set (but a rough idea of the percentage of time your opponent comes along is the question I'm trying to get at), and
2. that you'll fold every time you miss.
There is a *lot* going on post-flop in reality. Your set may not turn out to be good. Your opponents may turn out to be on a draw. You may turn out to be on a draw instead of hitting. You may be an overpair to the flop. You may hit a set and win part of your opponent's stack instead of all of it. You may be up against 3 opponents and quadruple-up when you hit instead of just doubling-up. An opponent might outplay you and cause you to fold in a case where you hit your set and it was good. And, of course, as you point out, you can try sometimes making a play at the pot in cases where you do miss.
Obviously, there are a lot of specific things wrong with the simplifying assumptions. I guess I'm really just trying to get some sort of framework going to try to get a rough idea of how often you're going to double-up, given that you hit your set, and how this might relate to your implied odds in general, or the 7% rule specifically.
ScottyZ
But is this the sort of scenario the 7% rule is talking about? For one thing, against such an opponent you don't need to have any specific type of hole cards. (Although, a hand with potential obviously gives you an extremely important "extra" way to win.) Also, against this kind of an opponent, aren't you possibly willing to commit a few more chips pre-flop? Maybe 10% or 15% of your stack? Of course the trouble with committing *too* many chips (besides just putting more chips at risk than might be appropriate) is that now you're starting to get into the realm of the opponent who is showing that much strength being more likely to have a big hand. Or even running the risk of getting the opponent into pot-committed situations (or simply giving them the right pot/implied odds to draw) you may not want them to be in on later streets.
So, the 7% rule might not be a bad guideline in either case. But I definitely see the point about knowing your opponent. If you mix up the two situations (opponents you can pick up pots against, vs. calling stations who might pay you off big-time when you hit), you're going to up some kind of creek with no outboard motor.
I'm going to make sure to be betting about 8.6% of my opponents stacks on a pre-flop steal from now on.
Thanks for the input guys!
ScottyZ