Okay, ajrenni, work was slow, so I spent a fair amount of time contemplating the implications of this chart and I agree, I was a bit too harsh in criticizing it once I realized it wasn't showing what I thought it was: how much FE one needs when making various bet sizes to increase their equity in the hand. However, after thinking about it, I do see the value of this chart. It shows what bet sizes and corresponding fold %s will yield an EV of 0. Since folding has an EV of 0, then it would be preferable to exploit even a tiny bit of FE or set the price of continuing our draw using the values in this chart, even if doing so means we sacrifice our current equity IF we're certain villain is going to bet such that we are not going to be able to continue our draw.

So, my understanding is that this chart shows what bet sizes we can make such that making that bet yields the same result as a fold; however, if we feel we have implied odds, then it would be okay to sacrifice our current equity by making a bet with an EV=0, right? I think? I believe you're correct when you say this information is more useful for deciding if/how we should use a blocking bet.

I just started working on a chart that sets EV=to our current equity in the pot, then I'm going to calculate what fold %s we need for various bet sizes to maintain our current equity. It seems to me this would be pretty handy to have pulled up while playing, as you could consult it when considering a semi-bluff, and if it says you need a fold X% of the time to maintain your present equity, then you would then bet that amount IF you felt it would lead to villain folding more than the the breakeven %

E.g., Hero holds 9 outs for the flush, meaning he needs a return of 4:1 to breakeven because hero's equity is 19% of the pot. Turn didn't bring the flush, so hero is considering making his standard 3/4 pot turn bet.

Ugh, just realized I already used this example lol. I really like FDs
.19P = fP + (1-f)[.19(P+0.75P)-.81(.75P)
.19P = fP + (1-f)[0.3225P-0.6075P]
.19P = fP + (1-f)(-0.285P)
.19P = fP - 0.285P + 0.285Pf
.475P = 1.285Pf
f = .3694
f = 37%

I'm also going to set EV=.50, giving hero 50% combined equity in the pot, so:
.5P = fP - .285P + .285Pf
.785P = 1.285Pf
f = 61%

Imo, this part of the chart will be more useful for selecting bet-sizes when semi-bluffing; if you're torn between betting 3/4 pot or just jamming for 1.5 pot, you could assign an estimated fold % to each bet-size and refer to the chart to see which one is more likely to boost your overall equity to +50%, given your estimated fold %s for each line.

As I already mentioned, Dwarrior's chart shows that hero needs 20% FE to breakeven, but not maintain your equity. So, in practice, you could refer to the chart I'm working on to see if you can add value to your hand by semi-bluffing, whereas you could refer to Dwarriors to see if a particular line is preferable to C/F-ing to villain's bet, since the EV for folding is 0, his chart is really comparing the value of various lines compared to folding imo.

Cool story, huh?


3 of the dorkier posters in this forum, I'll concede There are certain posters that I'll attempt to bleed/milk dry before I let them escape a thread, however, and renni/zad are definitely on that list.

But it does!!! Just not much of it. Very, very little. Tiny amount. But it does exist. That's the reason I'm trying to go all book smart on the topic lol. I'm sick of over and underestimating my FE. But many players have posted graphs with breakeven or positive redlines as low as 2NL (though most redlines seem to get healthier @ 10NL+, I'll concede). Those respectable redlines are not entirely due to smart hand selection preflop. They're also attributable to rare, but timely, bluffs and intelligent c-betting (c-betting is exploiting FE, tis why we do it) imho.

I concede I haven't played much below 10NL (not a brag, as my poker education cost me more than it should have), but I know for a fact that FE does exist @ 10NL and above. I, and others, wouldn't be able to play so loosely and c-bet 70% of flops and 40% of turns profitably if it didn't.

Just one more point at this time, I don't think "breakeven relative to folding" is a good measure of breaking even, or deciding when a bet is in order. That's why I think "instant profit," "+ev," or "breakeven" should be measured relative to *not betting*... especially when we're trying what to do when it's our turn to act, and there is no bet in front of us. This is a meaningful way of considering the value of semi-bluffing/bluffing, or even value-betting.

I think there exist other reasons for betting in poker, including blocking bets, setting up action for another betting round, etcetera, but I think those fall outside the scope of what we're measuring. We shouldn't try to turn this into a chart of "all the times you should bet, for any reason."

I agree. When you're in position checking is going to be best for you a lot of the time. But there are a lot of standard spots where you are in high FE/decent equity when called situations, such as when you raise pf on the button and miss on a dry flop; or delayed c-bet situations; or when you float the flop and pick up outs on the turn (or the turn brings a scare card) and Villain checks to you. In these spots the combination of FE and equity when called can be very powerful. That was really my point in my first post ITT when I said that the principle is more important than the chart.

Okay, so I started analyzing what fold %'s are required to maintain one's current showdown equity based upon various bet sizes by hand because I'm not clever enough to do so in Excel; I quickly realized that it was really boring, so I wound up crunching way less numbers than I'd intended, but I still think I generated a useful chart. Once I figure out how to enter my formula into Excel, I'll finish up. I also only analyzed numbers for one street and used the equities one would use for analyzing flop to turn action, whereas this chart is probably more useful for deciding if you should bluff on the turn; however, the difference is slight, so this shouldn't throw the numbers off too much. Once I figure out how to get Excel to crunch my #'s, I'll create a more complete chart with 2-streets.

Feel free to spot check my math as I did this on very little sleep (and I sux @ the maffs). I set my EV calcs equal to hero's present equity in the hand to determine what fold %'s are required for various bet sizes for hero to preserve his current SD equity. I.e., if villain were to call at exactly the percentages listed, then hero would be completely ambivalent toward betting, because it would yield the same EV as checking behind.

Current SD EV= Pf + (1-f)[SDwin%(P+B) - SDlose%(B)]
(See my FD example from a previous post itt)

Where f=villain fold%, (1-f)=call%, SDwin%=showdown win, SDlose%=showdown lose, and B=bluff. I entered bluff in terms of pot.

For the last 2 columns of the chart, I set my EV calc equal to .5P, so the values in the chart show the fold% hero needs to claim overall equity of 50% of pot. These last 2 columns would be useful if you were debating potting on the turn or jamming your remaining stack in, or wandering if neither is profitable. For you nits, I put Don't Bother semi-bluffing with 6 outs, as it's really more of a bluff with a tiny bit of equity than what I deem a semi-bluff, and I got tired of math.



I recommend using this in conjunction with the charts you can find here.

CLIFFS: If my math is correct, anytime you hold X # of outs and estimate a bluff of a certain size will lead to villain folding X% of the time, you can refer to this chart: If you estimate villain will fold > often the correlated percentage, you can profitably bet that amount (i.e., increase overall equity). The last 2 columns show how often villain must fold to a pot-size/1.5 pot-size bet for your overall equity (FE+pot equity) to equal 50%.

NOT SO NINJA EDIT: Okay, I have to declare the chart a pure rough draft. It suddenly hit me that a FD+GS has 12 outs and it really didn't make any sense for me to include a 10-outter, but not a FD. So, once I figure Excel out, I'll be fixing those mistakes. Makes me wonder how many more there are...

My brain failed earlier, so I came back to it, just spot checked the figure for 1/2 pot bet with 15 outs, one card to come, and came up with same result (rounded up from 20.5%).

It's an interesting idea to chart it against outs, though I'd think that would be a sort of *supplement* to the main chart, which would simply chart percent chance of winning a showdown. However, I'll admit that I find this interesting mainly as an illustration of a concept, and perhaps as a way to get an objective guage of the value of semi-bluffing... whereas I would probably not personally consult the chart regularly... I just don't think about poker that way, and enjoy this mainly as an exercise in theory. But some hold'em players might actually employ this chart regularly.

Anyway, as I was hinting, if you follow the format of percent chance to win, it generalizes the concept to ANY poker or poker-like game, particularly those with a big bet format (i.e., it could apply to NL single draw 2-7 lowball, or PL-Omaha hi). The outs chart works mainly for a specific NLHE scenario.

I was the original creator of the chart in OP and I did indeed make a huge mistake in comparing our equity to 0 instead of to our showdown equity.

AcesFullMoon has the correct equation:
Current SD EV= Pf + (1-f)[SDwin%(P+B) - SDlose%(B)]

and since I'm pretty good with Excel, I have revised revised my chart to reflect the correct fold equity for a break-even bet:



So yeah, it gets closer to the original chart as our showdown equity goes to 0 and diverges as our showdown equity increases.

Although this is probably a good estimate of our required fold equity, there are several problems with it:
1. Our win% for a check is not the same as our win% for a bet. This is because our bet will presumably fold out most of the hands we're ahead, whereas checking keeps them in the range. So for example, it's probably fine to check down a weak pair if we don't think villain will fold any pairs, as our bet just folds out the hands we best and keeps the hands we're behind. But if we have a 6-high, then we might get K-high and A-high to fold (plus all 7-high etc), and so our it's possible for our win% to remain about the same.

2. This obviously ignores villain responses other than calling or folding, as well as future streets. We may get bluff-raised, or we might get check/raised with FD and have to fold, whereas if we check behind we get the next card. On the flip side, betting our draw allows us to get value easier once we hit, since the villain may not expect us to semi-bluff.

Now, the reason I chose to put the chart in %s as opposed to outs is because we don't know exactly what outs are good. Since our villain will have a range of hands, not all our outs are always going to be live, but some of the time we may also gain outs. For example, if a better FD is in his range, we lose our flush outs against his hand, but we gain pair outs. If we have a weak pair, then our 2-pr and trip outs might be good vs TP, but not against a set, etc. Since I mostly created this chart to be used for hand analysis and not in the heat of battle, I just assumed we'll be able to estimate our equity to a percent. Regardless, I think restricting our chart to odds is limiting.

If you really want to find out odds, then just use the 2/4 rule. If you have 6 outs, then multiply by 4 to get your SD equity (so this would correspond to 24%, which is close enough to 25%). If you somehow suspect we only get 1 card to make our out, then multiply by 2, but then this is no longer showdown equity, in which case it's more complicated than merely comparing our fold equity to showdown equity of a check.

A final note on the chart by AcesFullMoon, I don't see the value of the last 2 columns, (FE+Pot Equity)=50%. This is because our FE is weighted as percent of the current pot, but Pot Equity is weighted as (corrent pot + our bet + villain call). So for that reason, you can't simply add the two to get the overall equity, it just doesn't make any sense, it must be a weighted sum.