life is short

sagefr0g · Feb 7, 2009

k_c said:
It's very easy to figure the probability of any number of low cards in a row being dealt from a give shoe composition. If starting comp is full 6 deck shoe, prob of 1 low card in a row is 120/312. Prob of 2 low cards in a row is 120/312*119/311. Prob of 3 low cards in a row is 120/312*119/311*118/319.....etc.

Code:

Prob of 1,2,3,4,5,6,7,8,9,10 low cards (2-6, rank ignored) in a row being drawn from a full shoe: 1 .3846154 2 .147168 3 5.601877E-02 4 2.121099E-02 5 7.988555E-03 6 2.992456E-03 7 1.114836E-03 8 4.130377E-04 9 1.521718E-04 10 5.574611E-05 Prob of 10 low cards in a row = .00005574611 = 1/17938.47

The probability that some number of low cards in a row will be dealt at some point in a shoe given the shoe will be dealt to a pre-determined pen is a harder problem. It would be very easy to sim, though. Just shuffle up the cards and deal shoe after shoe and look at the cards up to the given pen, recording the number of times the criteria is met and keep track of the number of shoes dealt. You could record when 10 or more low cards in a row appeared or when exactly 10 cards in a row appeared or whatever.

there you go, thanks a lot k_c.

so i made an excel shuffler and got it to indicate when five low cards present in a row sort of thing. if zero show you get zero, if one appears you got a five low card in a row at some depth, sort of thing.

now all i gotta do is try and figure out a way for it to count how many shuffles it takes to ring up a five low cards in a row at some depth.

:whip:
probably i'll have to use a macro to get excel to keep track of numbers of shoes and the changing number or cards in a row presentations.

sagefr0g · Feb 9, 2009

k_c said:
It's very easy to figure the probability of any number of low cards in a row being dealt from a give shoe composition. If starting comp is full 6 deck shoe, prob of 1 low card in a row is 120/312. Prob of 2 low cards in a row is 120/312*119/311. Prob of 3 low cards in a row is 120/312*119/311*118/319.....etc.

Code:

Prob of 1,2,3,4,5,6,7,8,9,10 low cards (2-6, rank ignored) in a row being drawn from a full shoe: 1 .3846154 2 .147168 3 5.601877E-02 4 2.121099E-02 5 7.988555E-03 6 2.992456E-03 7 1.114836E-03 8 4.130377E-04 9 1.521718E-04 10 5.574611E-05 Prob of 10 low cards in a row = .00005574611 = 1/17938.47

.....

ok so, if from a fresh six deck pack ten low cards came out in a row, then the probability of say five high cards coming out after those ten low cards would be:
(120/302)*(119/301)*(118/300)*(117/299)*(116/298) or circa 0.00941 .
and as your figures above, the probability of five high cards coming out of a fresh pack would have been circa 0.00799 .
so the improvement favoring seeing five high cards come out after seeing ten low cards come out of a fresh pack would be 0.00941 - 0.00799 = 0.00142 . lol.

so, pretty much impractical worrying about it anyway as the odds of seeing a shuffle where the first ten cards out are low cards is 1 to 17,938 and for not much improvement in probability for seeing some high cards.

pretty much close to gambler's fallacy as far as that idea i guess.

:whip:

below is a screen shot of my shuffler where after shuffling what seemed like for ever, ten low cards in a row finally came out, then notice for all that the next five cards out only had one high card. oh well, at least the true count was one.

k_c · Feb 9, 2009

sagefr0g said:
ok so, if from a fresh six deck pack ten low cards came out in a row, then the probability of say five high cards coming out after those ten low cards would be:
(120/302)*(119/301)*(118/300)*(117/299)*(116/298) or circa 0.00941 .
and as your figures above, the probability of five high cards coming out of a fresh pack would have been circa 0.00799 .
so the improvement favoring seeing five high cards come out after seeing ten low cards come out of a fresh pack would be 0.00941 - 0.00799 = 0.00142 . lol.

so, pretty much impractical worrying about it anyway as the odds of seeing a shuffle where the first ten cards out are low cards is 1 to 17,938 and for not much improvement in probability for seeing some high cards.

pretty much close to gambler's fallacy as far as that idea i guess.:whip:

below is a screen shot of my shuffler where after shuffling what seemed like for ever, ten low cards in a row finally came out, then notice for all that the next five cards out only had one high card. oh well, at least the true count was one.

Here's something you can mess with. It records streaks of all durations for all HiLo groups (low, med, high) and longest streak without a card from a given group. On my sloooow computer (I think Excel tends to be slow as well) it takes 40 sec to go through 100,000 single deck shoes where 39 cards are dealt. You could input up to 9,999,999 shoes and could edit the code to input more if you want. Just run the listHiLoStreaks macro and input what you want.

sagefr0g · Feb 10, 2009

k_c said:
Here's something you can mess with. It records streaks of all durations for all HiLo groups (low, med, high) and longest streak without a card from a given group. On my sloooow computer (I think Excel tends to be slow as well) it takes 40 sec to go through 100,000 single deck shoes where 39 cards are dealt. You could input up to 9,999,999 shoes and could edit the code to input more if you want. Just run the listHiLoStreaks macro and input what you want.

ha, ha. wow k_c that's way cool! thank you very much.

sagefr0g · Feb 28, 2009

fuzzy betting

Quote:
Originally Posted by White Guy View Post
Does that mean you lose 33$ an hour if you double hard 12 and 15 if you stay?? Or???? WHat bet spread is that based on?? I am still trying to figure sims out.
Thanks

Kasi said:
No lol. Frog was just using a probability calculator. The -15 is a percentage indicating your expected value, "EV", when you are dealt a Ten,2 vs a dealer 6. So, if you bet $1 and stay, as you should of course, you expect to lose 15 cents.

The -33 is how much you'd expect to lose as a percentage of your original bet if you doubled.

Not a sim at all.

is this maybe part of the theory of fuzzy betting? i mean ok your flat betting some unit for however many rounds, playing perfect basic strategy and departures. you lose some amount over say 50 cents your expectaion, say $15 or what ever. then bet at a higher unit hoping on the chance the 'swing' of getting back where you 'should' be will sweep you back to even or better cause of your raised bets.

:whip:

sagefr0g · Mar 13, 2009

less than optimal stuff... or whatever

so here are some stats on going less than optimal on some game that a sim was set up for a 1-8 spread optimal as can be i guess.

for what it's worth, i got images for:

1-8 play all .....ror 17.43%
1-8 wongout half the time at zero and below ror 9.09% (if i did it right

:whip

1-6 play all ror 16.90%
1-6 wongout half the time at zero and below ror 5.24%
1-4 play all ror 30.79%
1-4 wongout half the time at zero and below ror 3.52% (seems crazily low)

maybe Kasi, if you see this does betting half a unit at zero and below tc in the spread sheet approximate wonging out half the time at zero and below as opposed to betting one unit at zero and below tc for play all?

:whip:

well anyway aslan look at the ROR's.

Kasi · Mar 15, 2009

sagefr0g said:
maybe Kasi, if you see this does betting half a unit at zero and below tc in the spread sheet approximate wonging out half the time at zero and below as opposed to betting one unit at zero and below tc for play all? :whip:

Don't know what you maybe mean by "wonging-out" but it seems to me when you switch to 0.5 unit and use 6 units as max above all you have done is made it a 1-12 spread with the same $roll and same $unit, say $10K with a $10 unit (effectively making the $10 unit a $5 unit and efectively making your total roll 2000 units.)

In other words, you could change it to 1-12 instead of 0.5 to 6 and change your $unit from $10 to $5 and get the same results.

It's still playing every hand isn't it? So you haven't really "wonged-out" of anything, have you? You're just really playing-all half the time with a 2000unit roll spreading 1-12 and half the time with a 1000 unit roll spreading 1-6.

As far as your post above that, I'm not familiar with the intricacies of "fuzzy betting"

I believe you to be the world's foremost expert on that subject. :grin: When's your book coming out?

I just change unit size sometimes when behind just based on voo-doo as you know. OK, also loosely based somewhat on probabilities of finishing x units ahead in the next y hands while flat-betting, as a start, lol. Since, the way I understand it, "fuzzy betting" is also loosely based on counting to some degree, if only based on the cards on the table and a feeling from a couple prior rounds or something, it probably should beat my non-counting black-magic voo-doo

Oh yeah, on the above, the 1-6 and 1-4 spreads may very well not be optimal keeping $unit and $roll the same. Even if the unit spreads actually are optimal, there's a good chance, like with 1-4, one would need more than 1000 units to keep the risk the same as it was with 1-8 spread.

I'd love to learn more about on sitting down at the top of a shoe and leaving at some point. How it would effect frequencies maybe of playiing -TC's and how it may effect unit size or spreads, how it differs from back-counting etc.

Did I say learn more, - I'm pretty much absolutely clueless on the subject lol.
But I think that was part of your point too.

sagefr0g · Mar 15, 2009

Kasi said:
...
I'd love to learn more about on sitting down at the top of a shoe and leaving at some point. How it would effect frequencies maybe of playiing -TC's and how it may effect unit size or spreads, how it differs from back-counting etc.

Did I say learn more, - I'm pretty much absolutely clueless on the subject lol.
But I think that was part of your point too.

yeah now that you got me thinking about it, it's hard to imagine how one would go about playing all half of the time and playing a wong out approach half of the time. i mean it's easy to say ok i'm gonna play all for say 100 hands. but it's not so easy to say ok i'm gonna play a wong out approach for 100 hands where you leave the table if the true count is zero or below. lol, first off the count starts at zero. so for practical purposes i guess you'd have to say start off a shoe and if the true count goes below some tc, say tc <=-1 then leave and go to another fresh shoe, sort of thing. but to complicate matters even more it's entirely possible one might play 100 hands and never see a negative tc and therefore never wong out for those 100 hands. wow, that would be sweet, lol.
so scratch that idea, lol.

:whip:

sagefr0g · Apr 9, 2009

more sub optimal questions

for a six deck s17 das 67% pen game with a six grand bankroll and a five dollar unit that say i want to bet a 1-8 spread on then the ramp depicted in the chart below gives me a 10.21% one hour trip ROR and a 17.43% long term ROR. this is about as optimal a ramp for that spread that a sim would come up with for rational betting.

ok now for the same game, bankroll and unit size the bottom chart depicts a 1-4 spread that i believe gives the best one hour trip ROR of 0.44% and best long term ROR of 30.79% . well the 30.79% ROR is needless to say crummy but the one hour trip ROR of 0.44% seems pretty sweet and comparing the two charts the lower total variance for the 1-4 spread is appealing.

so the question i have is how is it that one can have such low total variance and a nice low trip ROR for the lower spread but then the long term ROR shoots up so high?

:whip:

Sonny · Apr 9, 2009

sagefr0g said:
so the question i have is how is it that one can have such low total variance and a nice low trip ROR for the lower spread but then the long term ROR shoots up so high? :whip:

Your short-term variance is low because you are not putting much money at risk. You have a small max bet so it isn’t likely that you will lose much money over the course of an hour or so. The reason your long-term risk is so high is that you are playing with a smaller advantage. You are less likely to show a profit and the high variance could easily overpower what little profit you expect to get.

Think about the absolute extreme – a flat betting play-all card counter. His "session RoR" will be very low because he is never betting more than 1 unit, but his long-term RoR will be 100% because he does not have an advantage. Now imagine the opposite extreme – a card counter spreading from 1:50 with no cover. His short-term swings will be wild but his advantage will be large so his long-term risk will be lower.

-Sonny-

jack.jackson · Apr 9, 2009

Sage, you can see this first hand on CVCX, by watching your RoR, as you change your spreads. You'll notice that it starts to revert backwards, right at a 1-7 unit spread in either direction, with about a 10k roll.

sagefr0g · Apr 10, 2009

thank you for the critique guys.
so, ok i can see here that wonging is about the only way to pull off a lower spread and still keep the long term ROR in control and the variance lower.
like i think the two charts below show:

sagefr0g · Apr 12, 2009

ok one more question on this stuff.
so it's a s17das 67%pen game near full table sort of thing.
$6000 bankroll and $5 unit.
the images below show a play all one to four spread and
a one to four spread for never playing tc < -1 .

the question is what kind of lifetime and trip ROR could one expect if a circa fifty fifty mix of play all and never playing tc < -1 was performed?

i mean if you play all you have this lifetime ROR of 30.79% and if your never playing tc < -1 then your lifetime ROR is only 2.70% . so it looks like if you did a mix of the two ways of playing you'd end up some where between the higher risk of ruin and the lower risk of ruin. i wonder would cvdata be able to determine this sort of stuff?

Kasi · Apr 14, 2009

sagefr0g said:
for a six deck s17 das 67% pen game with a six grand bankroll and a five dollar unit that say i want to bet a 1-8 spread on then the ramp depicted in the chart below gives me a 10.21% one hour trip ROR and a 17.43% long term ROR. this is about as optimal a ramp for that spread that a sim would come up with for rational betting.

ok now for the same game, bankroll and unit size the bottom chart depicts a 1-4 spread that i believe gives the best one hour trip ROR of 0.44% and best long term ROR of 30.79% . well the 30.79% ROR is needless to say crummy but the one hour trip ROR of 0.44% seems pretty sweet and comparing the two charts the lower total variance for the 1-4 spread is appealing.

so the question i have is how is it that one can have such low total variance and a nice low trip ROR for the lower spread but then the long term ROR shoots up so high? :whip:

Well, this is just off the top lol, but, like Sonny said, if you have 1200 units in both cases, naturally, since, intuitively, the 1-4 spread will give rise to a smaller avg unit bet and a smaller avg unit SD/rd. Intuitively, when you think about it, you are betting relatively smaller amounts of money in + counts compared to - counts. (since you are always betting the same 1 unit in - counts lol).

If you want to make the 1-4 spread have the same risk as the 1-8 spreads you need to either keep the $5 unit but increase $roll, to say $8K or lower $unit from $5 to say $3.75. Either way you end up with say a 1600 unit roll and now your ROR is maybe close to the same in both cases.

Apparently, maybe you are using about a 60 unit roll (apparently $300) in both cases for 1 hour of play. If you want to have the same 10% ROR for 1 hour of play, you only need to take say 35 units for the 1-4 spread.

Your UNIT EV and UNIT SD will be the same for each and every spread no matter how many units you have. How could it be otherwise since your frequencies of TC's, advantages and variance associated with them won't change no matter how much you to choose to spread and when with whatever amount of money?

No matter what you do, in this case, spreading smaller, 1-4 vs 1-8, just means you are playing with a lower avg unit bet, a lower unit EV, a lower avg %age win rate and a lower SCORE. Even if you change to a 1600 unit roll, one way or the other, either with lower $unit with same $roll or same $unit with a larger $roll, won't change the fact your lower 1-4 spread is a worse way to bet the same game.

More units in roll will lower your risk but it won't change the game itself.

Think units, not dollars, maybe, lol.

Kasi · Apr 14, 2009

sagefr0g said:
ok one more question on this stuff.
so it's a s17das 67%pen game near full table sort of thing.
$6000 bankroll and $5 unit.
the images below show a play all one to four spread and
a one to four spread for never playing tc < -1 .

the question is what kind of lifetime and trip ROR could one expect if a circa fifty fifty mix of play all and never playing tc < -1 was performed?

i mean if you play all you have this lifetime ROR of 30.79% and if your never playing tc < -1 then your lifetime ROR is only 2.70% . so it looks like if you did a mix of the two ways of playing you'd end up some where between the higher risk of ruin and the lower risk of ruin. i wonder would cvdata be able to determine this sort of stuff?

I don't see why one can't play as many different ways as one chooses to, as often as one chooses to.

Even a "real AP" may play lots of different ways, either in the same game with different pens, or different games with different pen levels, or maybe even in same game, sometimes backcount or sometimes play-all. Or sometimes spread to multiple hands and sometimes not.

All that means, to me, in my ivory castle lol, he should attempt to match each to a different sim lol. Call me an idealist lol.

If he has a sim for each style/game/spread, knows (makes best guess) how many rounds he played that way, one can always combine total results over all the different stuff later.

As far as this "wonging-out" stuff you seem to have an example of, first of all, be careful since one is no longer playing or seeing every hand. Second of all, "wonging-out", to me, seems as if it would just have to change the frequencies of TC's. Assuming no mid-shoe entry in effect. Like, in your "wonging-out" example, I don't see how that differs from "back-counting" but entering, say, at -TC1. Since the frequency of TC-1 (or any) has changed.

In other words, if one could "back-count" and just sit there and play whenever one chose to, say never a hand at TC-2, sometimes he would see some some TC-2 hands but the count would recover to TC-1 and he would bet.

But if no mid-shoe entry is allowed, one would never recover half the time from TC-2 to TC-1 and still be able to bet??

I don't know but I think CVCX uses that "Departure Point" stuff for "wonging-out" but there is no need to if "back-counting".

And be careful of using my crap for either if one is not playing all hands lol.

Or at least maybe use my "back-counting" crap that, hopefiully, deals with only playing so many hands of so many seen.

Or, be smart, use Norm's stuff that I think can handle all that you ask about lol.

My latest guesses are CVDATA can't figure out an optimal spread but CVCX can. CVDATA can't do "wonging-out" (starting at the top of a shoe but leaving at some point) but CVCX takes its best shot at it.

In other words, if Captain Kirk only had CVDATA and had to figure out how fast to go for how long around the sun to return to his "time", he'd still be stuck here. But, fortunately, he had Spock (CVCX) to make a wild-ass guess.

And, as we all know, the rest is history - 40 years ago Kirk made it back to the 21st? century. All because Spock had, obviously, there is really no other logical explanation, CVCX to figure it out.

That's not voodoo, that's fact.

sagefr0g · Apr 14, 2009

Kasi said:
....

And be careful of using my crap for either if one is not playing all hands lol.

Or at least maybe use my "back-counting" crap that, hopefiully, deals with only playing so many hands of so many seen.

....

did you have some back counting stuff? i think i remember you had a sheet you were trying to use that allowed playing two hands.

:fish:

here's cvcx shots where i think they are agreeing with your sheets for play all and the no play tc<-1 as in the link below:
http://www.blackjackinfo.com/bb/showpost.php?p=129191&postcount=33
erhh, uhmm, i changed the custom bet in the play all image to two units instead of three like cvcx wanted it to be.

maybe the problem comes in where the question of how many hands are played and seen sort of thing as far as ev/hr?
well anyway, the image on bottom right shows more sheet detail for the not playing below a true count of minus one stuff. seems to agree with the sim, no? looks like just average bet is off?

Kasi · Apr 15, 2009

sagefr0g said:
did you have some back counting stuff? i think i remember you had a sheet you were trying to use that allowed playing two hands. :fish:

here's cvcx shots where i think they are agreeing with your sheets for play all and the no play tc<-1 as in the link below:
http://www.blackjackinfo.com/bb/showpost.php?p=129191&postcount=33
erhh, uhmm, i changed the custom bet in the play all image to two units instead of three like cvcx wanted it to be.
maybe the problem comes in where the question of how many hands are played and seen sort of thing as far as ev/hr?
well anyway, the image on bottom right shows more sheet detail for the not playing below a true count of minus one stuff. seems to agree with the sim, no? looks like just average bet is off?

Well I have "back-counting" stuff that agrees with the Tables in Don's book.
But there, the frequencies are the same regardless of whether one "plays all hands" or only hands at, say, +TC2 or more, "back-counting". Therefore he is only playing, say, 20% of all hands dealt. So I based stuff on that in my back-counting sheets.

Now, it seems, Norm's stuff, even when "back-counting", normalizes the frequencies and expresses the frequencies relative to all hands actually played. In other words, even when "back-counting", the frequencies add to 100%.

Somewhere, a while back, I think it was Prince Dragon, posted a sim where the "back-counting" block was checked and right after it said like 75%. I think it was for a TC-1 scenario. The frequencies added to 100% but I then knew he was only playing 75% of all hands dealt.

So, in my crap, if the frequencies add to 100%, it assumes you are playing "all-hands".

So, as you surmise, it all comes down to whether, in a "back-counting" case, one wants to express stuff per "physical round" actually played or just go with every hour assumes 100 rounds. I know winning the most per hour is maximizing the use of one's roll but, for some reason, blame it on the internet, I just like to know what to expect per round and don't really care that much about "hourly" stuff in that if I played 60 hands in an hour or 100 hands in an hour, it was always ultimately simpler for me to just know how many hands I played. Divide by hours invested later if I wanted to lol.

Like a back-counter has an avg bet of 4 units/rd, but only plays 25% of all hands dealt. 100 rounds later he has bet 100 units. Is his avg bet 1 unit or 4 lol kind of thing.

But, ultimately, as far as this "play off the top of every shoe but leave at some -count" just isn't really "back-counting" to me anyway. I mean if you could jump in and out of a shoe whenever you wanted, you'd never play that way in the first place?

If it is a NME game and one must play from the top of a shoe, well, that's where maybe I feel I don't understand it all to a degree I would ever feel comfortable playing that way anyway.

I guess in a way, it also comes down to understanding exactly what a sim's results is actually telling you.

You know, if I played at all lmao.

Aren't most low limit tables, say $5-$100, allowing MSE anyway? I mean, if so, as painful as it might be to implement, why not back-count? With $6K maybe you could have a $25 unit and a lowish ROR and a niceish EV.

I can usually work backwards to figure out what's assumed for the way I like to figure it out - how else do you think I knew you'd suddenly switch to some hourly assumption of 60/hds/hr instead of 100 without telling me lmao.

Thanks for reminding me of that spreading to more than 1 hand stuff because some nice guy took the time to point out to me what a piece of crap some sheet I recently posted actually was lol. And I appreciate that.
That's what I get for getting fancy lol.

I'll send you all his tables with every spread if you want lol. Just something to look at lol. They're useless anyway for leaving at -counts since "<0" is all lumped together and averaged out.

sagefr0g · Apr 15, 2009

Kasi said:
Well I have "back-counting" stuff that agrees with the Tables in Don's book.
But there, the frequencies are the same regardless of whether one "plays all hands" or only hands at, say, +TC2 or more, "back-counting". Therefore he is only playing, say, 20% of all hands dealt. So I based stuff on that in my back-counting sheets.

Now, it seems, Norm's stuff, even when "back-counting", normalizes the frequencies and expresses the frequencies relative to all hands actually played. In other words, even when "back-counting", the frequencies add to 100%.

Somewhere, a while back, I think it was Prince Dragon, posted a sim where the "back-counting" block was checked and right after it said like 75%. I think it was for a TC-1 scenario. The frequencies added to 100% but I then knew he was only playing 75% of all hands dealt.

So, in my crap, if the frequencies add to 100%, it assumes you are playing "all-hands".

So, as you surmise, it all comes down to whether, in a "back-counting" case, one wants to express stuff per "physical round" actually played or just go with every hour assumes 100 rounds. I know winning the most per hour is maximizing the use of one's roll but, for some reason, blame it on the internet, I just like to know what to expect per round and don't really care that much about "hourly" stuff in that if I played 60 hands in an hour or 100 hands in an hour, it was always ultimately simpler for me to just know how many hands I played. Divide by hours invested later if I wanted to lol.

Like a back-counter has an avg bet of 4 units/rd, but only plays 25% of all hands dealt. 100 rounds later he has bet 100 units. Is his avg bet 1 unit or 4 lol kind of thing.

But, ultimately, as far as this "play off the top of every shoe but leave at some -count" just isn't really "back-counting" to me anyway. I mean if you could jump in and out of a shoe whenever you wanted, you'd never play that way in the first place? If it is a NME game and one must play from the top of a shoe, well, that's where maybe I feel I don't understand it all to a degree I would ever feel comfortable playing that way anyway.

I guess in a way, it also comes down to understanding exactly what a sim's results is actually telling you.

You know, if I played at all lmao.

Aren't most low limit tables, say $5-$100, allowing MSE anyway? I mean, if so, as painful as it might be to implement, why not back-count? With $6K maybe you could have a $25 unit and a lowish ROR and a niceish EV.

I can usually work backwards to figure out what's assumed for the way I like to figure it out - how else do you think I knew you'd suddenly switch to some hourly assumption of 60/hds/hr instead of 100 without telling me lmao.

Thanks for reminding me of that spreading to more than 1 hand stuff because some nice guy took the time to point out to me what a piece of crap some sheet I recently posted actually was lol. And I appreciate that.
That's what I get for getting fancy lol.

I'll send you all his tables with every spread if you want lol. Just something to look at lol. They're useless anyway for leaving at -counts since "<0" is all lumped together and averaged out.

don't worry, lmao, i finally got it through my thick head that the frequencies are going to be different if you play all as opposed to never playing if the tc reaches some number. don't ask me why i was missing that lol.
i guess that fact just seems strange to me. i mean it would seem that whether somebody is watching what ever way the tc frequency is what it is. so i guess the thing is depending on how someone watches can make for what they are gonna see.

well, i guess i'm confused but maybe that's good, cause maybe if i think about this i might just learn something.

i would like to see those tables.

edit: i dunno, like i guess maybe the way apparently the tc frequencies change according to wonging is kind of like how it's can be dependent on how you determine your tc according to deck estimation, how your resolve the tc, full deck, quarter deck, ect. and then how you round, truncate or floor, sort of thing.

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