Introduction/Disclaimer

When I first thought about doing a COTW, I had a number of ideas but at the time I was experimenting with pre flop bet sizing, and hence thought it would be a great idea… … … but then, when I actually started the research I realized that preflop bet sizing is probably one of the best analyzed topics on 2p2. So, me being me (not who you might call a pro), I had quite a task in front of me. Hence I ask you not to judge too strictly.

“4BB+1BB Per Limper” Mantra

I think that every modern player must have heard or knows of the 4BB+1BB mantra, and indeed there is a lot of topics about it, for instance a very good discussion back in the archives:

http://archives1.twoplustwo.com/showflat.php?Cat=0&Board=ssplnlpoker&Number=616675 7&fpart=1&PHPSESSID=

However, in my experience a lot of people still argue that 3BB+1 or any other lower (Than 4BB+1BB) alternative is feasible as a standard bet. This, is where I disagree and one of the main points of this COTW is to make it very clear why 4BB+1BB per limper is “correct” (I know, I know… it still depends, and we shall address this later).

To get to this point, let us first look at the following example with the computer hand or what one may consider the average NLHE hand:


Poker Stars $0.10/$0.25 No Limit Hold'em - 9 players
2+2 Hand Converter Powered By DeucesCracked

UTG+2: $10.00
MP1: $9.65
MP2: $25.70
CO: $83.70
BTN: $4.55
SB: $25.00
Hero (BB): $52.35
UTG: $25.00
UTG+1: $26.00

UTG+2 posts a big blind ($0.25)

Pre Flop: ($0.60) Hero is BB with Q 7
2 folds, UTG+2 checks, MP1 raises to $0.75, 4 folds Hero ???


Now then, how do we go about a decision to call? First of all we need to know what are our odds to hit on the flop and then to evaluate our pot odds and estimate how we are doing against the villains range. For example our odds to hit are:

Chance of getting 4-of-a-kind on the flop: 0.01%
Chance of getting a Full House on the flop: 0.09%
Chance of getting 3-of-a-kind on the flop: 1.57%
Chance of getting 2 Pair on the flop: 4.04%
Chance of getting 1 Pair on the flop: 26.94%
Chance of getting a Four Flush on the flop: 2.24%

(Courtesy of http://www.texasholdem-poker.com/calculator)

All in all, we have a chance of around 34.89% (Odds of 1.86 to 1) of the time. Now then, the villain only raised to 3BB and there was a limper in the hand giving us pot odds of 27.027% (Odds of 2.7 to 1). So we are clearly getting the correct odds to call. Moreover the equity without any further betting against any other non-pair hand is 31.89% (Odds of 2.14 to 1).


equity win tie pots won pots tied
Hand 0: 68.109% 67.90% 00.21% 223217964 700158.00 { AKs, AKo }
Hand 1: 31.891% 31.68% 00.21% 104144088 700158.00 { Q7o }

Thus, we can see that if we make our raise sizing too small then we are allowing villains to call with too wide a range, profitably and without making a mistake.

Let us generalize this scenario. With any non-paired hand the odds of hitting at least one pair on the flop is 32.4% or 2.1 to 1. (Source) If we add a little bit of % for flops where we hit something better than a pair, or something playable… then it is clear that one needs to offer pot odds that are worse for the big blind (as he has already put the BB into the pot and thus has the best pot odds amongst the players) than 2.0 to 1 namely, I am going to suggest this number to be at least 1.9 to 1. There are some details here which can argue for both offering slightly worse or slightly better odds, I think they cancel out but feel free to discuss and argue this point!

By doing a little bit of math with a help of my friend (Who for now shall remain known as PoorLeno), who doesn’t play poker but is rather good at math, we came up with the following formula:



This gave us the following result (In big blinds):


As you can see the 4BB+1 mantra holds fairly well. However with a number of limpers increasing, one may consider increasing the raise amount slightly. For example with three limpers, I might suggest that it may be advantageous to bet 7.5 big blinds. (Also note that by raising 3.5BB+1BB will always offer 2 to 1 odds)

The effect of a different betting structure.

Not all games run under the assumption that one big blind is equal to two small blinds. In some games such as 25NL, 1 BB = 2.5 SB. Let us take a look at how that will change the situation:


The difference, as you can see is pretty miniscule and could generally be disregarded. However what I want you to take from this is the following: with increasing ratio of the structure in regards to SB to BB ratio, you will need to bet LESS pre-flop.

RAKE?

Now then, while we were at it, we thought to see how does rake affect this scenario. Given that rake formulas are different for different sites and even between stakes, we decided to greatly generalize and just did a calculation for 4% rake. This analysis assumes that there will be no further betting of course.

The result can be displayed in a graph:

X-Axis -> Required bet amount. (In small Blinds) Y-Axis -> Pot Odds, with the yellow line being the needed 1.9 to 1.

The red line is the needed bet amount without rake and the blue line is with rake. As you can see the with rake taken into effect, the needed bet amount is slightly less. However the difference is very small indeed, but would be greater with higher rake %.

ANTE Games

With the introduction of ANTE games at PS, I feel like this section might be of most use to players. Lets jump right into it. We have analyzed two scenarios, first where ante is 25% of the BB and then where ante is 20% of the BB, as this is typically the range for ante, you can guesstimate for higher and lower ante values from the analysis. The results are:

Ante at 25%



Ante at 20%



From these graphs you can come up with your own betting system, but personally I would suggest 6.5BB+1BB per limper for 25% antes and 5BB+1BB per limper for 20% antes. One thing to note here would be that with increasing number of limpers, one may need to add more than 1BB per limper to correctly adjust.

Conclusion:

All of that being said, don’t forget to think about the table, specific players and all the other variables when choosing your bet sizing. This post is intended just as a guideline to help you start thinking about how the pre flop betting size can be analyzed under different game structures. This can be taken further and extended to pre-flop betting depending on position, adjusting to calling stations and nits. For instance one may choose to raise 5bb+1bb per limper on loose tables running 25VPIP+ while make it 3bb+1bb per limper on 8VPIP tables. Moreover there are strong implications for further streets. One other thing I’d like you to think about and maybe discuss is how bet sizing affects stealing situations, and how you can use the combined VPIP of the SB and BB in order to capitalize on stealing opportunities. One other thing you might want to think about is the fact that the small mistakes that you can allow yourself to make pre-flop can be too small to count at later streets with competent opponents. This COTW is mostly intended as a starting point with a strong discussion to follow, and hopefully I will be able to make a few replies with further analysis.

Aknowledgements:

Along with my 1000th Post, this is one of the first serious strat posts that I have made, its been a nice journey from a complete beginner a year or so again, to becoming a reg. Although I have only played around 150k hands meanwhile, I feel like I’ve gained a lot of understanding in poker and thanks to poker (Which I talk a lot about in my 1000th post). For this, I would like to thank everybody who has been helpful in my poker education. Special thanks to PokerRon for helping me greatly in my journey, to JLBorloo for taking a look at my draft and giving me suggestions. Also, I would like to express my gratitude to my best friend, PoorLeno for helping me with the math behind this post. PoorLeno asked me to forward this to you: “If you would like us to tackle any interesting poker and math related research, please do let us know and if we have the time we shall try to deliver.” (PM me if you have good ideas) Thanks to all previous COTW writers as well.

On a side note: Yesterday when playing one of the SCOOP tournaments, I forgot to follow my own advice and while being a short stack, raised to 2.5BB with 66, the BB called. I pushed on a A27 flop and he called with T7o 

Resources that have covered Pre-Flop aspects previously:

Basic Theory Discussion -

http://archives1.twoplustwo.com/show...fpart=all&vc=1

Playing PP’s –

http://archives1.twoplustwo.com/show...rt=&PHPSESSID=

http://archives1.twoplustwo.com/show...fpart=all&vc=1

Suited Connectors –

http://forumserver.twoplustwo.com/78...ectors-705585/

http://archives1.twoplustwo.com/show...1&fpart=2&vc=1

Positional Awareness –

http://forumserver.twoplustwo.com/78...p Re-Raising –

http://forumserver.twoplustwo.com/78...sizing-574867/

Stealing –

http://archives1.twoplustwo.com/show...Number=5348855

ISO –

http://archives1.twoplustwo.com/show...Number=6073737

Playing from the blinds -

http://archives1.twoplustwo.com/show...=0#Post7459990

These are just some of the resources, there is plenty more out there, also if any link does not work for some reason, do let me know.

Nice!

almost first!!!!!!

Someone writing a lot of good and long stuff recently.

Calling a raise with Q7o in your example is going to lose money whether it is 3bb+1 or 4bb+1, there is more than your expressed odds preflop to consider. Naturally it loses more in the latter case but if the first is more likely to be called then that should be what you raise.

fancy maths. Nice post.

Not to be an *** but doesn't that mean that it would be better to raise 5x+1bb per limper? What about 6x? Why not more?

Yeah there are other considerations that we need to address like how big the resulting pot will be relative to stacks, and what is the impact of our open raise size when we get 3 bet?

Nice post, ty.

Stop the madness! There are enough preflop donk shovers already.

nice stuff dude.

Yeah, I don't have much time for an analysis of pre-flop play that uses pot odds because the sums of money involved pale in comparison with those involved in the implied odds. Q7o is a terrible hand to call oop with against a pre-flop raiser.

I really feel like that Q7o AK thing is flawed. The obvious point is if you are facing a taggy player open from MP to 3bb and you are sitting in the bb do you call with Q7o. Of coarse not.

There are a few reasons for this.

First you are not playing against just AK you you are playing against a range and you are doing worse against his range than against Ak because of all of the pairs and dominations.

Also flopping a pair or better doesn't mean you win. It just means you are oop with a pair and a bad kicker with no initiative. Doesn't sound that profitable.

There are situations where 4+1bb opens are best. They are generally loose passive games where there is a lot of c/f on the flop. I play 6max so I am not sure how much this comes into play in FR but you really only need one semi competent light 3better to make your life hell if you are opening that big.

You also are not taking into account position or skill advantage. when I am playing I usually assume at least some (if not a great) skill advantage at my limit until proven other wise and by raising smaller ip I get to play with a bigger SPR which benefits me as the better player. I also get a bigger SPR ip which means more money could potentially go in with me making more informed decisions

Baluga Whale does a good job explaining this in the new Coaching Kristy videos when he talks about the fact that if you have about 50/50 equity say AQo v 77 the player ip will win in the long run by a pretty big margin. He goes on to say that you can probably get away with even as much as a 35-40/60-65 disadvantage as long as you are ip.

Not trying to flame the OP or to say I know better. I am just trying to put forth at least some counter argument to the premise of the post

Thanks for getting us started OP

nice post thanks for the thoughts

math is sound, but it assumes that post flop play is non-conditional.

Great post, but I disagree with the 4xbb+1bb mantra due to several reasons.

I was trying to think of a way to respond to this COTW in a way that wasnt harsh, but explained what I was feeling. This response...is what I would have said