Poker Video: Misc/Other by sthief09 (Micro/Small Stakes)

Great work Sthief09, alot of usefull info in there. But did you include exploitable, or did I just miss that?

Btw I would really love to see you do this using HH's.

Thanks for the video Josh! Looking forward to the upcoming episodes.

Great work Sthief09, alot of usefull info in there. But did you include exploitable, or did I just miss that?

Btw I would really love to see you do this using HH's.

The exploitable strategy was the original one at the beginning, when we determined it was optimal to bet A,K,Q,3,2, ie 40% bluff/60% value against the static range of calling A,K,Q,J,T.

Villain CAN exploit that by bluffcatching all cards 5 up through A. That led the the ppt explaining that we can either not adjust (villain is bad or unobservant), we can try to adjust as he adjusts (start value betting more and bluffing less when he starts bluffcatching), or we can make that slight tweak (bluffing the 3 only 50% of the time) to make us unexploitable, ie villain cannot adjust his range profitably.

The HHs will come soon. I just felt it was important to lay out the foundation this way, but no more one-card poker games for the time being.

Really amazing work! I enjoyed the two episodes so far and got really attached to doing this excel stuff.
(being a business analyst I am quite familiar with the functions but never used it for poker math stuff)

I have a question concerning the question from episode 1. Which is the best card hero should bluff with.
In the 2nd episode you said that this would be the 3. In my calculation hero should be indifferent between bluffing with the 2 and/or the 3 because the EV of the bluff is 1.67$ anyhow.

If we look to the EV difference between a bet and a check the bet with the 2 is even bigger than with the 3 because EV(CH) of 2 = 0 whereas EV(CH) of 3 is 0,83.

Have I missed something?!

Hi, interesting video to learn to do operations with excel / open office
find it difficult to use in game (maybe it's just my limited brain who has problem with abstraction)
i would take more "real NLHE " cases i, further episode( mayeb bases on HH/ players profil, hud stats, read...)
good idea to give tools at the end to use better excel/ open office
aniway thanks for your great job (do not take it as a bad reply, i m in an hurry to watch ep3 :=)
have a nice day,see u

edit i agree with 08-15 am i think it's better to bluff 2 because we gain 1.67 to bet instead of checking and only 0.83 with 3 so we make a better move to bet 2 than 3
are we wrong?

can u tell me what did u do around 7.06 time, when your CHECK word is getting changed to "Check". I have problems with this random word changes and still didn't figure it out what to do?

Excellent videos so far, looking forward to the rest. Do you do any work on multistreet games or games with the same scenarios but with holdem hand strengths? Do you think working with these toy one card games is sufficient to improving our holdem game?

Really amazing work! I enjoyed the two episodes so far and got really attached to doing this excel stuff.
(being a business analyst I am quite familiar with the functions but never used it for poker math stuff)

I have a question concerning the question from episode 1. Which is the best card hero should bluff with.
In the 2nd episode you said that this would be the 3. In my calculation hero should be indifferent between bluffing with the 2 and/or the 3 because the EV of the bluff is 1.67$ anyhow.

If we look to the EV difference between a bet and a check the bet with the 2 is even bigger than with the 3 because EV(CH) of 2 = 0 whereas EV(CH) of 3 is 0,83.

Have I missed something?!

Glad you're enjoying so far. Excel is so widely used and I'm hoping to teach some good applications to those of you who already know how to use it.

My wording here was a bit ambiguous. You're hearing it as "what card should we feel most strongly about bluffing?" but what I meant was "of the cards that we should bluff, which has the highest rank?"

can u tell me what did u do around 7.06 time, when your CHECK word is getting changed to "Check". I have problems with this random word changes and still didn't figure it out what to do?

I think I just decided I wanted it all capitalized so I wrote over it. Formatting generally doesn't much matter, but since I want people following along I'll definitely try to be more consistent and explain any changes in the future.

Excellent videos so far, looking forward to the rest. Do you do any work on multistreet games or games with the same scenarios but with holdem hand strengths? Do you think working with these toy one card games is sufficient to improving our holdem game?

Fear not. We'll start with this in episode #3.

I had 2 reasons for these one-card exercises:
- most importantly, ease everyone into creating OpenOffice Calc and/or EV tables for a very simple game so people didn't get caught up in the poker nuances of a hand.
- basically build out a skeleton for one-street situations. We'll be going into some river situations and we'll be able to apply what we've learned to look into real hold'em examples.

I think I just decided I wanted it all capitalized so I wrote over it. Formatting generally doesn't much matter, but since I want people following along I'll definitely try to be more consistent and explain any changes in the future.

Actually, you deleted the lower case version of 'Check' (because OOC has an annoying habit of converting entries to be equal to existing cells) thus enabling you to enter 'CHECK' in upper case and have it accepted. BTW, great series so far.

Hey Josh, I think you'll find that your 13-card river-bet game has a Nash Equilibrium in which both players play an optimal non-exploitable strategy. Your uncertainty as to whether playing the Psychology strategy (Option 2) goes on forever or stops at some point amounts to asking whether the Nash Equilibrium is stable (in which case it stops asymptotically) or unstable (in which case it goes on forever). My guess is that for this game it is stable so the players should converge on the optimal non-exploitable strategy. Of course, if they were that good both of them will have started at that strategy...

Good stuff with the spreadsheet tips. Being familiar with both Excel and OOC myself, I was already using locked cells and putting formulae in your tables with what card the Hero has as a variable. Working out the formulae with MIN and MAX functions was a little tricky, but is guaranteed to produce fewer errors than the hand entered values which you have been demonstrating. I understand however the need to keep things simple for the video - we are learning Poker and not spreadsheets after all!

My main request for the rest of the series is to use the results to demonstrate how to exploit typical weaknesses in opponents and to put numbers on it. Something beyond "they call too much so I should value bet more" and "they fold too much so I should bluff more". The mathematics of barreling multiple streets and what the optimal frequencies are for doing that and defending against it would also be interesting - I think that may show up something about polarized v balanced ranges but I'd like to see it in hard numbers.

In response to the F4 issue:

In Tools - Customize - Keyboard tab, you can reassign the F4 key to "relative/Absolute". First find the "Relative/Absolute" function under the Insert category, then find F4 in the Shortcut key list, press Delete to remove the currently assignedfunction and press Modify to assign the new function to F4

Shift+F4 may also work

In response to the F4 issue:

In Tools - Customize - Keyboard tab, you can reassign the F4 key to "relative/Absolute". First find the "Relative/Absolute" function under the Insert category, then find F4 in the Shortcut key list, press Delete to remove the currently assignedfunction and press Modify to assign the new function to F4

Shift+F4 may also work

F4 worked! thank you! that drove me nuts.

F4 worked! thank you! that drove me nuts.

The student becomes the teacher. Haha. I couldn't help that one. Glad I could give a little something back. Awesome stuff so far.

Hey Josh, I think you'll find that your 13-card river-bet game has a Nash Equilibrium in which both players play an optimal non-exploitable strategy. Your uncertainty as to whether playing the Psychology strategy (Option 2) goes on forever or stops at some point amounts to asking whether the Nash Equilibrium is stable (in which case it stops asymptotically) or unstable (in which case it goes on forever). My guess is that for this game it is stable so the players should converge on the optimal non-exploitable strategy. Of course, if they were that good both of them will have started at that strategy...

My intuition tells me that there does not exist a stable Nash Equilibrium for this game. But this is probably driven by the fact that I do not directly see what the strategies would be in this equilibrium and hence assuming that they are fairly complex so that you won't end up with such a strategy by simply maximizing EV.
Could you add any motivation to your guess of why it would be stable? Just out of curiosity, you don't have to feel obliged to actually answer ;-).

Josh, very interesting series btw!

Hey Josh, I think you'll find that your 13-card river-bet game has a Nash Equilibrium in which both players play an optimal non-exploitable strategy. Your uncertainty as to whether playing the Psychology strategy (Option 2) goes on forever or stops at some point amounts to asking whether the Nash Equilibrium is stable (in which case it stops asymptotically) or unstable (in which case it goes on forever). My guess is that for this game it is stable so the players should converge on the optimal non-exploitable strategy. Of course, if they were that good both of them will have started at that strategy...

Good stuff with the spreadsheet tips. Being familiar with both Excel and OOC myself, I was already using locked cells and putting formulae in your tables with what card the Hero has as a variable. Working out the formulae with MIN and MAX functions was a little tricky, but is guaranteed to produce fewer errors than the hand entered values which you have been demonstrating. I understand however the need to keep things simple for the video - we are learning Poker and not spreadsheets after all!

My main request for the rest of the series is to use the results to demonstrate how to exploit typical weaknesses in opponents and to put numbers on it. Something beyond "they call too much so I should value bet more" and "they fold too much so I should bluff more". The mathematics of barreling multiple streets and what the optimal frequencies are for doing that and defending against it would also be interesting - I think that may show up something about polarized v balanced ranges but I'd like to see it in hard numbers.

I'm sorry I didn't respond to this sooner but honestly it took me reading it several times to fully digest. It's a very intriguing post. I need to start reading around about game theory. I'm sort of learning about it in reverse. I'm not getting any formal education about it, but by running the numbers I'm starting to understand the inner workings of it.

I couldn't resist myself, so I quickly wrote some lines of code to see what would happen if the psychology option goes on forever. Apparently, it quickly starts alternating between a polarized range and value betting. The specific range and average EV are a bit dependent on which strategy you follow when Betting and Checking is neutral. Villain always starts iterating between calling a 5 or higher on the one hand to bluff catch and only calling Q or higher on the other hand
If you want to see this visualized, check out this page.

I couldn't resist myself, so I quickly wrote some lines of code to see what would happen if the psychology option goes on forever. Apparently, it quickly starts alternating between a polarized range and value betting. The specific range and average EV are a bit dependent on which strategy you follow when Betting and Checking is neutral. Villain always starts iterating between calling a 5 or higher on the one hand to bluff catch and only calling Q or higher on the other hand
If you want to see this visualized, check out this page.

Wow how did you do this?

A nash equilibrium should look like this:
- Player 2 has to call exactly 50% of his range to make player 1 indifferent to bluffing. So player 2 calls 100% with A-9 and 50% with an 8.
- Now player 1 can profitably valuebet with A,K,Q and to balance this bluffs with a 2 100% and a 3 50% (the strategy you described in the video).

Neither player can increase his EV by changing his strategy without getting exploitable again. Is this correct or did I miss something?

Wow how did you do this?

Well, I basically did the same thing you did in the spreadsheet but then in Matlab. I automated it so that it calculates EV given a fold/call range for villain and constructs a new bet/check range for hero. I've also written a method that calculates a new range for villain given a range for hero, so I can iterate this as many times as I want. I could also post the matlab files if you want

A nash equilibrium should look like this:
- Player 2 has to call exactly 50% of his range to make player 1 indifferent to bluffing. So player 2 calls 100% with A-9 and 50% with an 8.
- Now player 1 can profitably valuebet with A,K,Q and to balance this bluffs with a 2 100% and a 3 50% (the strategy you described in the video).

Neither player can increase his EV by changing his strategy without getting exploitable again. Is this correct or did I miss something?

Mmm, I'm confused now. Why do you add the "without getting exploitable again". Player 2 strategy is exploitable. He calls with his top 50%, so player 1 can start only valuebetting (namely A,K,Q) and his EV will be higher than with the strategy you've given. Of course, this strategy can be exploited as well but that is why there is imo no simple nash equilibrium and the players keep iterating between value betting and playing a polarized range.

You are right, forget the "without getting exploitable again" part. But still, player 2's strategy is not exploitable. If player 1 stops bluffing, his EV will not go up because bluffing against player 2 has 0 EV. He has to bluff with his weakest hands though to prevent getting exploited himself.
Maybe you could try to run your code with my strategies as initial strategies. If I am right the strategies shouldn't change no matter how many iterations you do.

Ok, I added it to the page. But as indicated in my previous post, although Hero's range is unexploitable, he can exploit Villains range by start to only value bet A,K,Q. That is the difference between option 2 (the psychology option) and option 3 from Josh's video. In the simulations I did the same as in the video series: find the strategy with the highest EV. It is of course also possible to choose the strategy which is not unexploitable, i.e. find the strategy for which the EV is the highest assuming villain plays the optimal counter strategy. If I would do that than the strategies would indeed stay the same, but you don't need iterations for this because this strategy is independent of the current strategy of the other player. It might actually be interesting to compare the EV of that strategy with the average EV from option 2

Well I finally found my mistake. I thought player 2 is unexploitable if the EV of bluffing for player 1 is zero. But because checking has some EV, we need to find a calling range for player 2 where bluffing with a '3' has the same EV as checking. If this is the case player 1 can chose to bluff 50% with it and check 50% and play a balanced strategy.

- The calling range for player 2 looks like this: A,K,Q,J,T (100%) and 9 (50%).
- Now I calculated the optimal counter strategy for player 1: BET(2), NEUTRAL(3), CHECK(4,5,6,7,8,9,T,J), BET(Q,K,A)
- To be balanced he choses: bet A,K,Q,2 (100%) and 3 (50%).
- Calculating the EV for player 2 again: CALL(A,K,Q), NEUTRAL(J,T,9,8,7,6,5,4), FOLD(3,2)
- Player 2 is unable to improve his EV, because what only matters is calling with A,K,Q and folding 3,2 (he already does that)
- Neither player can improve his EV -> Nash equilibrium

yes, you are correct but given that player 2 plays CALL(A,K,Q), NEUTRAL(J,T,9,8,7,6,5,4), FOLD(3,2), player 1 (hero) can improve his EV by starting to valuebet again. Since villain calls down to a 4 50% of the time, there is no value in having a polarized range. So he will stop bluffing with the 2 (and the 3 50% of the time) and will only bet A-J and T 50% of the time.

I also checked it with the matlab code and it says the same. After this, the same pattern arises than with other starting ranges but again switching between value and polarized.

yes, you are correct but given that player 2 plays CALL(A,K,Q), NEUTRAL(J,T,9,8,7,6,5,4), FOLD(3,2), player 1 (hero) can improve his EV by starting to valuebet again. Since villain calls down to a 4 50% of the time, there is no value in having a polarized range. So he will stop bluffing with the 2 (and the 3 50% of the time) and will only bet A-J and T 50% of the time..

Wait, why do you say villain calls down to a 4 50% of the time? Villain/player2 uses the unexploitable strategy of calling A,K,Q,J,T (100%) and 9 (50%). NEUTRAL doesn't mean he calls 50% of the time. NEUTRAL means calling/folding has the same EV, so it doesn't matter what he does against the SPECIFIC strategy of player 1. But if he wants to be unexploitable, he must choose a specific strategy (always calling J,T and calling 9 half the time, folding the rest of the NEUTRAL hands). Of course player 2 could use other strategies against player 1 which have the same EV, but he choses the one which is balanced in order to keep himself from getting exploited.

You can test it yourself. Player 2 starts with the strategy above (calling A,K,Q,J,T (100%) and 9 (50%). Player 1 now wants to find a strategy which maximizes his EV against that strategy. The answer is: BET(A,K,Q,2), CHECK(J,T,9,8,7,6,5,4), NEUTRAL(3). Because it doesn't matter what he does with the '3', an infinity number of strategies exists. He now chooses the one that makes him unexploitable (betting the '3' half the time). Now player 2 cannot improve his EV against the new strategy of player 1 because he already plays perfectly against the strategy of player 1. The strategy CALL100%(A,K,Q), CALL50%(J,T,9,8,7,6,5,4), FOLD(3,2) would have the same EV as the one he started with but would make him exploitable (as you described in your post).

I don't know how to explain it better and English is not my first language. Maybe I made a mistake somewhere but I doubt it.

yes, of course. That was silly of me, just was confused by the neutral for a second. Sometimes it helps to think ;-). I thought at first as well that the strategy you've given would give a nash equilibrium but the outcome of the simulations confused me. I forgot that for villain I chose the call 50% if neutral which of course he doesn't have to.

Thanks for the explanation!

My intuition tells me that there does not exist a stable Nash Equilibrium for this game. But this is probably driven by the fact that I do not directly see what the strategies would be in this equilibrium and hence assuming that they are fairly complex so that you won't end up with such a strategy by simply maximizing EV.
Could you add any motivation to your guess of why it would be stable? Just out of curiosity, you don't have to feel obliged to actually answer ;-).

Interesting stuff between you (duvelman) and WrongName based on simulation and the actual poker strategies. I am probably stronger in Maths than at Poker, but further thought on the subject leaves me convinced that the Nash Equilibrium (which definitely exists) is either stable or neutral. The intuition comes from the linearity of all the terms involved. If the equilibrium is actually neutral, simulations will run into trouble because oscillations can be induced by the simulation which don't exist in theory (but do, of course, exist in reality because real players really are imperfect simulations of the theory). By the way the linearity of all the terms that I am talking about disappears in real Poker because the ranking of Hands is (non-linearly) altered from street to street.

Back at University I did some great simulations of simple predator-prey relationships which shows beautiful boom-bust cycles that are (mathematically) chaotic in nature. Reminds me of Poker a lot! Especially Tournament Poker :-(

Again great episode Josh, you are Excel mastah !

And regarding the quiz question from the ep.1 which was - what is the best/highest card we should bluff:

Card - EV(Bet) - EV(Check) - Best Play
2 - $1.67 - $0.00 - Bet
3 - $1.67 - $0.83 - Bet
4 - $1.67 - $1.67 - Neutral

So the highest card we should bluff with is 3, but I would choose 4. Why ? Again because of rake, our opponent will bluff catch us from time to time and then win less money, because more rake will be taken out of the pot, xaxaxa, you mad bro ?