Toy Gaming (part 4)
Posted by Sauce123
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in continuous/unpolarized ranges, the caller's range is equal to 1 - alpha hands that can beat a bluff, as opposed to 1 - alpha hands total.
I probably did not fully understand the whole video, but this quote from the last minute caught my attention, as we had some discussion about that same subject (see : Aaaand one more GTO question :-) , discussion btw me and BigFizsh ).
So,
- when facing a continuous range, we must call with 1 - alpha hands that can beat a bluff
and
- when facing a polarized range, we must call with 1 - alpha hands total
Is that right ?
I fail to see the difference, because in the second case our indifference calling range always beat a bluff.
Could you clarify, please ?
The difference is that the distributions (continuous vs polarized) have different solutions. There's not a simple formula that applies across all range distributions.
Not too shabby.
want knightdabest
Thanks for mixing up the video selection.
Id say this is your best most "forefront" type video so far. Its a topic that still isn't discussed as much today. Not much room for questions though, pretty self explanatory so maybe that is a downside. BUT I STILL PREFER IT (and I only play HUNL).
I mean its cool or whatever to watch you play HU, but really there isn't much value at mistakes IMO bc the situations aren't that tough and the series/sessions aren't long enough to matter. I vote for theory videos OR like a 5-6 part HU series released 2x a week for a month.
Really enjoyed this, thanks. Can we loosely apply this to the earlier streets? Seems like on the flop for instance it gets fuzzier since ranges are less polar, and the betting range will usually be much stronger, so defending 1-alpha is probably incorrect on most boards? At the same time we have to defend a little "extra" since all his bluffing hands before the river will have equity? Hopefully part 5 coming soon.
I'd say that the main take away from the video which applies to earlier streets is that when determining your defending frequency that the pertinent question is what should be the EV of your opponents "bluffs" which requires you to imagine the EV of those bluffs as a check. Going slightly further, you can try to determine which of your opponents bluff(s) will be indifferent, or nearly indifferent, between betting and checking and then defending accordingly.
For example, on nearly all occasions all of your opponents hands will be +EV as a check because you'll also likely have a checking range, and therefore his weakest hands will get there some small percentage of the time. So if your opponents bets on the flop there's hardly ever a situation where you'll want to defend enough so that it wouldn't be +EV for him to bet his weakest hands. But just because it's +EV for him to bet any two cards doesn't mean he'll bet his entire range or all his bluffs because it'll still be HIGHER EV for your opponent to check.
On an iPhone so can't really explain more but I hope it makes sense and allows you to explore the concepts from the video on earlier streets.
Good point Sant.
I think there's one more step to the analysis. It's true that all hands (at least in most situations) have EV as a check. If that's the case, then to make someone indifferent between betting and checking OOP should defend less than 1-A, supposing that the EV of bluffs is 0 for IP when he bets. But the EV of bluffs for IP is (almost never) 0, so in practice we need to weigh the EV of betting against the EV of checking.
It does, nice post thanks.
very good video tricky concepts
Very nice video Ben!
I don't see why the expected value of betting 76 is 0.07. OOP is calling roughly 43%, so it seems to me that the EV of betting should be 0.57*1-0.43*1=0.14. But I have never used CREV, so I guess there is something I'm misunderstanding.
BTW, have you used PokerJuice? In this case, what are the differences between PJ and Omaha Ranger?
I was not willing to spend like $2000 on Omaha Ranger and was considering getting PJ. But this is €120/month, so it may end up being more expensive that Omaha Ranger.
76's EV is .07 in this model because of card removal effects.
thankss, right after watching this I wasn't sure if or how it'd be practically applicable, but I've since found myself thinking about it a fair amount while playing. keep it up!
you remind me someone walking on your red carpet ........................ oh yes ..Louis XIV ... le roi soleil
many ... unconsciously ... understand ... and desert the country
Great video, Sauce. I really appreciate you using visual examples to illustrate your points.
@ 24:03 you make a point to mention that it's not as simple as to using indifference to make IP bluffs gain 0 EV. Then, using your example, prove that IP can unilaterally improve EV by now checking all hands. I have a few questions that I was hoping you could clear up:
- In MOP, the concept of ex-showdown equity was used to negate any value at showdown for the purpose of analyzing value gained by post-flop betting (bluffing). As a result, lower threshold hands only value came from their ability to bluff.
The concept of indifference applied such that by calling (1-a) of hands in distribution that beat bluff the ex-showdown equity of bluffs reduces to zero, while the value gained on upper threshold hands adjusts to the point of equilibrium.
Now, in MOP it is mentioned that in practice most distributions are not weighted towards (50% value, 50% bluff). It may be the case that an average range may consist of (70% value, 30% bluff), so while you create an indifference point at bluffing threshold by calling (1-a), you increase expectation of game for IP given a range weighted towards value.
Unless I am mistaken, this is the reason why you can't simply call (1-a), and why in your model IP gains value by checking all hands. It is not, as you mention, b/c OOP is simply calling with (1-a) and not considering which bluffs gain EV(which doesn't seem all that relevant).
I am not an expert, and you are def more knowledgeable about GT and analytics of poker, but it bothered me a lil bit how you trivialized the concept of indifference and subtlety belittled other posters knowledge of GT by using a model we assume to be true and a concept that may not be all that relevant.
Lefthook,
I'm not sure exactly what you're argument is in the post, so I apologize in advance if I'm misinterpreting what you said.
"Now, in MOP it is mentioned that in practice most distributions are not
weighted towards (50% value, 50% bluff). It may be the case that an
average range may consist of (70% value, 30% bluff), so while you create
an indifference point at bluffing threshold by calling (1-a), you
increase expectation of game for IP given a range weighted towards
value."
^^If I'm understanding you correctly, you're making the point that for a one street game, the player with the perfectly polarized range can only bet alpha (of his value betting region) hands as a bluff (for example, if the betsize is pot, and the polarized player has the nuts half the time and a bluff half the time, he can bet a=.5, or .5(5)=.25 of his range as a bluff, which means he can bluff with half of his bluffing hands). Now, supposing the bettor has a 50% or more bluffs in his range, the optimal betsize is infinite, meaning he can bet roughly 1:1 bluff for every value bet- this will make the EV of his range ~ equal to the potsize. Remember that in no case the EV of either player exceed the potsize (with range), or else a clairvoyant opponent can unilaterally improve their EV by always folding. So, if the bettor has less than 50% bluffs, he can bet less than infinity and still insure that he cannot be called. In your example, where the bettor's distribution is 70% value and 30% bluff, we can solve for the minimum betsize the bettor must use to make the caller indifferent given the bettor bets all his bluffs, in this case .3=.7a, or .43, so .43=s/s+1 so s=.75, in which case if the bettor bets .75pot or more his expectation with range is equal to the full pot.
The crucial point is that what causes the caller to fold more than 1-A of the time is that IP's hands have value as a check.
In any case, just remember that a game is not at equlibrium if either player can unilaterally increase the EV of their range. I tried to make two points in this video. The first is that between two continuous distributions all hands have varying expectations for IP to check back, just because even weak hands like the 90th (worst) percentile still wins the pot 10 percent of the time, it follows that the caller must call less than 1-A or equilbrium won't be reached. A good rule of thumb for the amount below 1-A that the caller should call with is '1-A hands that can beat a bluff'. The second point I made is that real poker distributions more closely resemble 0-1 distributions than completely polarized distributions in most instances, especially before the river and often on the river as well. In reality real poker distributions fall in between the 0-1 and the polarized distributions because hands fall into hand classes creating discontinuities, and almost always the two players have different distributions creating asymmetrical ranges. The unique features of the two distributions in any real poker situation determine what the equilibrium will be, but the rule of thumb 'call 1-a hands that can beat a bluff' holds up well (although it might be hard to find out what a bluff is).
In future videos we'll look at how to solve actual range v range situations in various poker games, or we can look at software to solve it for us.
Thx for the response, Sauce.
I wasn't really arguing for/against anything, just a little confused about how you applied the concept of indifference.
My main point was that in MOP, ex-showdown equity was considered which implies a check is worth 0 EV. This was the baseline for decision making in terms of optimal play. Therefore, when facing a bet, if u call with (1-a) of hands that beat bluff (in one street game) then the game converges to its equilibrium value.
Later, this point is expanded on when distributions are considered. Calling with (1-a) isn't optimal if villain has range weighted towards value, as he b/e on bluffs but increases expectation with value and bets it with higher frequency.
In your video, you make this same point but use a different method and reasoning.
In summary, as I understand it, calling with (1-a) of hands that beat bluff is insufficient once the composition of villains distribution is considered (ex-showdown equity). You make this same point without considering ex-showdown equity and, as a result, have IP hands have +EV as a check.
Both ideas reach the same conclusion, but in practice, I was unsure which is better or more correct.
Sorry if this is all jumbled, and again, great video. Really appreciate it.
I think the point will be clearer if we just dispense with most of the terminology and remember that a game is at equilibrium if and only if neither player can unilaterally increase their EV. In a 0-1 game, applying the heuristic 'call 1-A hands' won't satisfy this prior condition, but in a polarized game it will.
Great video series Ben... very much enjoyed it. My favorite was probably #2 but they were all good (1 was a bit simple, but a good intro. for your series). Thanks for taking the time to put these together, as they are obviously more difficult to do than a video analyzing hands from a session. Props and appreciation!
Thanks Brian, I really appreciate it.
I plan on doing quite a few more of these, and as they go on they'll get more and more useful at the tables.
Just thought I'd share that I loved the video!
Wish I didn't wait so long to watch this whole series. My brain hurts quite a bit atm so will likely need to rewarch a few more times.
Thanks these videos are excellent and a good intro to CREV too. Good work, looking forward to the next part
Hi ben,vnice series!
I don't understand something in your answer to Lefthook:
"Now, supposing the bettor has a 50% or more bluffs in his range, the optimal betsize is infinite, meaning he can bet roughly 1:1 bluff for every value bet- this will make the EV of his range ~ equal to the potsize"
Let's say our range is 70%bluffs 30%value
You bet (size=infinite) 30% value 30% bluff(and win 1sizepot) but you have to check and loose 40% of your bluff right?And then EV of your range is only 0.6potsize,not 1
Let me know where is my mistake here
"In your example, where the bettor's distribution is 70% value and 30% bluff, we can solve for the minimum betsize the bettor must use to make the caller indifferent given the bettor bets all his bluffs, in this case .3=.7a, or .43, so .43=s/s+1 so s=.75, in which case if the bettor bets .75pot or more his expectation with range is equal to the full pot."
I understand that caller is indifferent to call or fold with S=0.75,but if S>0.75,the caller can't call profitably right?Is it 70%nuts 30%air or is it continuous distribution?
You say 0.75 is the minimum but isn't it the only one who can makes caller indifferent to call or fold (if better's range is polarised)?For exemple for 1sizepot caller will loose 0.3X2-0.7X1= -0.1.
If i'm correct it seems like upper a certain sized,facing a 50%+ valuenut range,
u just can't call profitably with your bluffcacths and can't prevent better to bet all his bluffs
I don't understand what means 1-alpha hands that can beat a bluff.
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