Poker Video: No Limit Hold'Em by terp (Micro/Small Stakes)

Time Link to 00:07:24

I think this slide says so so much , content looks really obvious at first sight, but if you really focus on the content its really helpful. A shitload of players even through the high midstakes do, imo, NOT really get this concept!

thanks!

by the slide count, it might seem thin on raw amount of content, but i believe it's a very worthwhile discussion. nice to hear your thoughts

I thought this would be as good a place as any to pose this question.

I am only up to episode 4 so have 2 more and this may be dealt with in those 2.

What I'm struggling with is the ratio of value to bluffs being purely a ratio of raise size to pot size.

Lets consider the river (as its easier)

Out river bluffs have very close to 0% equity (usually they have more than 0% but its so unlikely that that they will induce a call from a lower hand that we can call it 0%) This part I am OK with.

Our value hands, however, rarely have 100% equity, unless we hold the nuts. Infact you could say that on average our Value hands are further away from 100% (on average) than our bluff hands are away from 0%.

So our bluff hands are close to 0% but our value bets are usually a fair distance form 100%.

This makes me wonder about value to bluff ratios.

If our total value range has little over say 50% equity should we halve the number of bluffs to compensate?

If our total value range had say 75% equity should we cut our number of bluffs by 1/4 to compensate?

Is the ratio of value to bluffs only a direct mirror of the ratio of raise size to pot size in the theoretical model where value always has 100% equity and bluffs 0% and since our value range is never close to 100% equity, are we not constantly overestimating the number of bluffs required to balance?

I hope I get my point across clearly, and look forward to hearing your response. In fact I am hoping I am wrong and your explanation as to why will help fill in a few pieces of the puzzle that I may be missing.

Best wishes

great question - it's this kind of stuff that calls upon calculus and can just make your head spin

a balanced range is indifferent to a call or fold. though i haven't done any math on your inquiry (but have thought a lot about it while making this series) i think any analysis would begin with that basic definition. when i started this series, though i had a lot of ideas, i wondered at times how i'd generate eight hours of presentation with math and examples...but questions like yours make it clear just how much there is to discuss.

i think i will take a look at this today and see if i can derive some kind of function...

I really enjoyed the vid, and I especially enjoyed the hand analysis discussion. As for the hand, I would let him keep bluffing, so I'd call the raise and x/c any river bet. After the hand I'd take a note.

Was doing some maths on a balance river bet and came across something i found weird.

Assume scenario: We bet the pot on the river. If we are balance, we wont care if villain call/fold because his expected value will be 0 either way.

Assuming our value range have 100% equity and our bluff range have 0% equity

Pot: 1
Bet: 1
Bluff: 1 Value: 2 (means we have 2 value hands to 1 bluff for balance)

Heros Equity: 66.67% (when called we win 2 times out of 3)

Villains EV when call: V.EV*MaxGain - H.EV*MaxLost
: 33.33% x (1+1) - 66.67% x 1
: 0 (Thus being balance)

Then i proceed to calculated the EV of my bet when called by villain:

H.EV = H.EV*MaxGain - V.EV*MaxLost
= 66.67% x (1+1) - 33.33% x 1
= 1 (Pot size bet)

And H.EV when villain fold is obviously the pot, 1. So regardless how many % villain fold we always have an expectation of 1 if we are balance? I find this rather weird, did i miscalculated something??

I tried solving for heroes value equity too. For Villain to have 0 ev when call, heroes total equity must be 66.67% for a PSB.

For example: when heroes value equity is 100%

Heroes Total Equity = H.V.Equity x %Value - (1-H.V.Equity) x %Bluff
=100% x 2/3 - 0% x 1/3 (2 Value to 1 bluff)
= 66.67%

So if heroes value equity is 75%

H.T.E = 75% x %V - 25% x (1-%V)
Solve for %V when H.T.E = 66.67%

66.67% = 100% x %V - 25%
%V = 66.67+25 = 91.67%

IF this is correct means we need around 92% value range or rather 11.5/1 value/bluff. Which seems rather weird as well cause it means we almost shld not be bluffing in this spot??

you are correct.

balance, by definition, means that our opponent cannot affect his expectation with his action. he can call. he can fold. he can call on sundays, tuesdays and fridays. always the same 0ev

i will look at your other scenario tomorrow but as you've suggested there is probably an error in it somewhere. thanks for the discussion

Time Link to 00:33:48

In the video it says we need to continue 80% of the time if we are getting 4:1. Isn't the actual frequency 20%?. If 80 is right, it kind of contradicts with the numbers in ep 2 where you say we need to continue 1/3 when getting 2:1.

Was doing some maths on a balance river bet and came across something i found weird.

Assume scenario: We bet the pot on the river. If we are balance, we wont care if villain call/fold because his expected value will be 0 either way.

Assuming our value range have 100% equity and our bluff range have 0% equity

Pot: 1
Bet: 1
Bluff: 1 Value: 2 (means we have 2 value hands to 1 bluff for balance)

Heros Equity: 66.67% (when called we win 2 times out of 3)

Villains EV when call: V.Equity*MaxGain - H.Equity*MaxLost
: 33.33% x (1+1) - 66.67% x 1
: 0 (Thus being balance)

Then i proceed to calculated the EV of my bet when called by villain:

H.EV = H.Equity*MaxGain - V.Equity*MaxLost
= 66.67% x (1+1) - 33.33% x 1
= 1 (Pot size bet)

And H.EV when villain fold is obviously the pot, 1. So regardless how many % villain fold we always have an expectation of 1 if we are balance? I find this rather weird, did i miscalculated something??

Notice i type it out wrongy, accidently use EV when i mean equity.

In the video it says we need to continue 80% of the time if we are getting 4:1. Isn't the actual frequency 20%?. If 80 is right, it kind of contradicts with the numbers in ep 2 where you say we need to continue 1/3 when getting 2:1.

hi great question and i am sorry i missed this earlier.

pre-river non-all-in spots create different math than river spots. hand equities are not finalized, stacks remain to be played, nobody is ensured a showdown, etc. remember that balance means indifference to our opponent's action - a balanced play offers our opponent no action better than another. we calculate this based on the odds we lay our opponent.

when we 3bet to pot, we're usually risking 1:2 and laying our opponent 2:1. in a normal pot bet spot, we lay ourselves 1:1 and lay 2:1, but raising pot requires us to wager double what is in the pot to win what is in the pot. thus, we get two fractions that appear to be 1/3 - our opponent, facing a pot bet, needs to 'win' 1/3 the time, and our range breaks even immediately if we get caught 1/3 of the time.

with the smallish raise in the AK hand our opponent laid himself better than 1:1 and laid us 4:1. that is, if this were a balanced river raise, he would have approximately 80% value and 20% bluffs. i'm having a hard time thinking how to paint this better than - nobody is really balanced here. i talked about it in the video: why raise the turn on a dry board with a value hand? why raise anything in position with these stacks? it just reeks of trying to force a specific action, which is the definition of unbalanced, since balance has no preference.

as far as how often we need to continue - this is where showdown v pre-showdown action is confusing. at showdown, a balanced range is indifferent to call/fold. pre-showdown, hand equities fluctuate enough that this is fairly tough to construct. recall how i talked about hands functioning as both bluffs and value in the same spot (small pocket pairs that 3bet).

at showdown, our opponent wouldn't care how often we called if he were balanced. pre-showdown, if our ranges were polarized to 'value' hands and zero equity bluffs, we would likely prefer a fold, since our value hands could only get worse and our zero equity bluffs could not improve - thus on the whole our range gets worse and worse. we 'balance' this by having bluffs with equity to compensate for the damage our value hands suffer on some runouts - we basically look to protect our range on various runouts: either our value hands are still strong or our semibluffs have become stronger. in essence, we're trying to be able to represent something on all/most runouts.

i think in the video i probably talked a bit too much about how often we should worry about calling here to avoid being exploited. avoiding exploitation should be your goal when your opponent is slightly unbalanced (toward exploiting you in a way which you cannot predict - if you knew how your opponent would exploit you, he wouldn't be able to do it!). in reality, i think this opponent is heavily unbalanced here to the point that protecting ourselves from exploitation is the wrong approach to this spot. instead, we should look to own him. we would do this by basically never folding a value hand and jamming all of our airballs.

is this unbalanced? of course. as i've said throughout this series, balance is a starting point we'd like to draw in the sand so we can calculate how unbalanced we can be!

hi terp,

~33min

u say that hero needs to continue 80% of the time due to pot odds he is getting (4 to 1) im not sure i get this, i would think that hero needs to continue 56% of the time due to CO odds he is getting on a bluff, so CO is risking 390 to win 490 so he need us to fold at least ~44% right ? or i just misunderstand what being balanced means in thie spot

hi terp,

~33min

u say that hero needs to continue 80% of the time due to pot odds he is getting (4 to 1) im not sure i get this, i would think that hero needs to continue 56% of the time due to CO odds he is getting on a bluff, so CO is risking 390 to win 490 so he need us to fold at least ~44% right ? or i just misunderstand what being balanced means in thie spot

Balance is not about folding equity I think, but about estimating how balanced/unbalanced Villian is and figuring a line to exploit this, by being unbalanced yourself.