Does anyone know how to interpret the data in Panama Rick's Lucky Lady sims regarding variance. He has a column labeled SD, but that does not seem to be the SD per hand (unless I am missing something). Basically, I am trying to get the variance so that I can compute the correct Kelly wager. Any help is appreciated.
Lucky Ladies Question for Panama Rick or Others
- Thread starter Coug Fan
- Start date
Adam N. Subtractum
Well-Known Member
Very good question...
You bring up a very valid question, in that determining the variance is, of course, a very important factor in sizing our wager for this side bet.
If you read further into Rick's post, he explains the SD figure that is used in the charts.
"...Yes. The EV in 2D for +7 is 1.67%, SD =0.1460 (I should have written SD as a percent). This means there is a 68% chance your actual advantage is between 1.67%-14.60% = -12.93% and 1.67%+14.60% = +16.27%."
You see here, he states that the SD figures he presents were not given in percent, but in raw form. Here, he also provides a simple explanation and example.
Now how can we use this information to determine the size of our wager on the sidebet?
We need to determine the variance, which is simply done, because we know that SD^2 = V (Standard Deviation squared equals Variance...for more info see my post entitled "Root Mean Squared Deviation of Blackjack"). So the SD figures in PR's charts must be converted to percentage (SD * 100), and then squared (SD%^2) to produce the Variance. We can now figure optimal bet size.
I could post a follow-up with an example or two, if necessary.
ANS
You bring up a very valid question, in that determining the variance is, of course, a very important factor in sizing our wager for this side bet.
If you read further into Rick's post, he explains the SD figure that is used in the charts.
"...Yes. The EV in 2D for +7 is 1.67%, SD =0.1460 (I should have written SD as a percent). This means there is a 68% chance your actual advantage is between 1.67%-14.60% = -12.93% and 1.67%+14.60% = +16.27%."
You see here, he states that the SD figures he presents were not given in percent, but in raw form. Here, he also provides a simple explanation and example.
Now how can we use this information to determine the size of our wager on the sidebet?
We need to determine the variance, which is simply done, because we know that SD^2 = V (Standard Deviation squared equals Variance...for more info see my post entitled "Root Mean Squared Deviation of Blackjack"). So the SD figures in PR's charts must be converted to percentage (SD * 100), and then squared (SD%^2) to produce the Variance. We can now figure optimal bet size.
I could post a follow-up with an example or two, if necessary.
ANS
Adam N. Subtractum
Well-Known Member
Lucky Ladies...??Exploitable sidebet??
Umm...maybe I'm missing something here. I *hope* somebody can correct me.
As I looked over Panama Rick's essay again, I wasn't so sure of my above answer, so decided to go ahead and calculate the variance the long way (see Wong's PBJ) to get a solid figure...but than, as I started looking over Rick's numbers a little closer (I hadn't taken the time to go over this essay in detail prior), I intuitively questioned the possible gains from this illeged "exploitable sidebet".
Just a quick tally of the frequencies of favorable situations reveals we only have an edge on the sidebet 1.23% of the time. Hmmm...so we won't actually be placing the bet that often at all, this in itself should show us that there won't be much to be gained.
But, since the expectation figures are quite impressive, it does warrant further research, so let's do some more calculations. Going through the charts and summing (adding) the f * E (frequency times expectation) for each TC given shows that our overall gain for placing the sidebet only in favorable situations is...(drum roll, please)...a WHOPPING .074172%!!!
Now a wonger would obviously see better gains, for more than one reason, but will it be enough to make it exploitable? Some preliminary numbers suggest it will improve the situation exponentially, I estimate the overall gain to be in the neighborhood of .4%...not quite remarkable, but a notable gain, no doubt (I'll try to confirm this number in a follow-up). It is important to note though, that a backcounter would only see a count of +2 <18% of the time with this game, and subsequently, would only make marginally more $$$ on an hourly basis than the play-all player, because the play-all player is effectively "wonging-out" of the sidebet as well, by not placing a wager. Now the backcounter would make more on an hourly basis because he would be off seeking out shoes with higher counts when the sidebet becomes disadvantageous, while the play-all guy is wasting time waiting. A noticable increase ($$$/hr) CAN obviously be be expected, but definitely not the increase of over 5 times that the .074% to .4% figures seem to suggest.
I'd appreciate any comments on my reasoning, and forgive me if I have made any mistakes.
ANS
Umm...maybe I'm missing something here. I *hope* somebody can correct me.
As I looked over Panama Rick's essay again, I wasn't so sure of my above answer, so decided to go ahead and calculate the variance the long way (see Wong's PBJ) to get a solid figure...but than, as I started looking over Rick's numbers a little closer (I hadn't taken the time to go over this essay in detail prior), I intuitively questioned the possible gains from this illeged "exploitable sidebet".
Just a quick tally of the frequencies of favorable situations reveals we only have an edge on the sidebet 1.23% of the time. Hmmm...so we won't actually be placing the bet that often at all, this in itself should show us that there won't be much to be gained.
But, since the expectation figures are quite impressive, it does warrant further research, so let's do some more calculations. Going through the charts and summing (adding) the f * E (frequency times expectation) for each TC given shows that our overall gain for placing the sidebet only in favorable situations is...(drum roll, please)...a WHOPPING .074172%!!!
Now a wonger would obviously see better gains, for more than one reason, but will it be enough to make it exploitable? Some preliminary numbers suggest it will improve the situation exponentially, I estimate the overall gain to be in the neighborhood of .4%...not quite remarkable, but a notable gain, no doubt (I'll try to confirm this number in a follow-up). It is important to note though, that a backcounter would only see a count of +2 <18% of the time with this game, and subsequently, would only make marginally more $$$ on an hourly basis than the play-all player, because the play-all player is effectively "wonging-out" of the sidebet as well, by not placing a wager. Now the backcounter would make more on an hourly basis because he would be off seeking out shoes with higher counts when the sidebet becomes disadvantageous, while the play-all guy is wasting time waiting. A noticable increase ($$$/hr) CAN obviously be be expected, but definitely not the increase of over 5 times that the .074% to .4% figures seem to suggest.
I'd appreciate any comments on my reasoning, and forgive me if I have made any mistakes.
ANS
Adam N. Subtractum
Well-Known Member
Lucky Ladies UNDRESSED...part I
After looking over PR's essay once again, I *think* I figured out what the SD figures he gives are for, not the actual Standard Deviation of the hand, but the SD of the hand's Expectation. In my opinion (I very well could be wrong), Standard Error would've been the more appropriate term.
While digging around for some more info on the topic I came across this post by Coug Fan, at bj21:
Panama Rick posted this on the free (beginner) page on 5/14/02 in response to my question on the same subject:
"The expected values for the various payouts are (6 decks):
Any 20 = 0.4007
Suited 20 (same suit) = 0.2078
Matched 20 (e.g. 2 jacks of spades) = 0.0928
2 Queens of hearts = 0.0371
2 Queens of hearts with a dealer blackjack = 0.0146
Total = 0.7529
House Edge = 24.71% "
There really is no point in knowing the individual expected value for each payout, because its not as if we can pick and choose which jackpot we want to go for like with some other wagers (ie. craps). Also, I believe PR's use of the combined Expectation of payouts to deduce the house edge to be flawed. According to my calculations:
_Dealt__Payout__Frequency (in %)____Odds____Expectation_
2QH&BJ__1001____0.00146406_____1 in 68,303__.0146552406
_2QH_____125____0.03091763______1 in 3,234__.0386470437
Suit&Rank_19_____0.49468216_______1 in 809___.0939896115
Suited 20___9_____2.57234726________1 in 39___.2315112537
_Any 20____4____10.07000000*_______1 in 10___.4280000000
All Other___-1____86.83058888_______1 in 1.15__-.8683058888
*figure is taken from Wong's PBJ Table D3 due to discrepencies between calculated frequencies of two Ten card hands, and simulation results (see PBJ pages 292-3 for more info). All other frequencies and ev's calculated using basic probability equations.
Now we know the total Expectation is the sum of the Expectations of each and every payout, so we add the right-hand column which totals -.0615027392, so we can deduce that the House Edge on the Lucky Ladies sidebet is -6.15%. In PR's hypo above, he fails to include the negative payouts of non-twenty hands, which alters the outcome drastically (also many of my numbers vary slightly, perhaps someone knows if he calculated these or simmed them?)
So to calculate our total Expectation if wagering only in advantageous situations, with perfect play (no Standard Error), we would sum the right-hand column EXCEPT for the last entry (All Other), which totals to .80680314961, an Expectation of +80.68%. Now remember, we would only see this advantage 1.23% of the time, so we could calculate an overall Expectation of 80.68% * 1.23% = +.992364% with perfect play. This obviously represents the upper limits for this sidebet, and shows us it is impossible to reach a 1% overall advantage.
Now, again let's see what can be gained in real-world play (w/ a high Standard Error). From Panama Rick's essay (TC = true count, ev = expected value, n = # of hands, f = frequency, SE = standard error):
__TC_______ev________n_________f_____SE__
__6.5_____0.50%___797,833____0.38%___13%
__7.0_____2.72%___578,783____0.25%___13%
__7.5_____4.91%___417,682____0.18%___13%
__8.0_____7.08%___313,499____0.13%___14%
__8.5_____9.27%___221,484____0.09%___14%
__9.0____11.57%___170,614____0.07%___15%
__9.5____13.93%___105,475____0.05%___15%
_10.0____16.24%____84,955____0.04%___15%
_10.5____18.73%____60,349____0.03%___16%
_11.0____21.26%____41,676____0.02%___16%
_11.5____23.71%____26,872____0.01%___17%
_12.0____26.24%____19,184____0.01%___17%
_12.5____28.61%____13,330____0.01%___17%
Again, by summing the products of the ev and frequency of each favorable TC (multiply each TC's ev & frequency, then add all together) we get the overall Expectation (or ev) for the sidebet when a wager is placed only when favorable, +.074172%.
As we stated before, this figure would be substantially higher when wonging, only partly due to more frequent higher counts, but more noticably because the ratio of advantageous situations to hands played would be significantly reduced by only playing in positive counts (because of less hands played). Now as noted before, the increase would not be proportional to the decrease in hands played because of other factors involved. This +.074% edge is not really a "fair" figure, since these days, anybody-who's-anybody is Wonging out (?Schlesingering?) by at least a TC of -5.
First we'll examine the case of Wonging out at a TC of -1. We can see from PR's chart that we will be playing 68.34% of the time with this methodology (4.5/6 pen). Now to determine the percentage of advantageous hands (still speaking of the sidebet), out of played hands, we must divide each TC's frequency by 68.34%. The product of this frequency, and its TC's ev, will be our overall Expectation.
continued...
ANS
After looking over PR's essay once again, I *think* I figured out what the SD figures he gives are for, not the actual Standard Deviation of the hand, but the SD of the hand's Expectation. In my opinion (I very well could be wrong), Standard Error would've been the more appropriate term.
While digging around for some more info on the topic I came across this post by Coug Fan, at bj21:
Panama Rick posted this on the free (beginner) page on 5/14/02 in response to my question on the same subject:
"The expected values for the various payouts are (6 decks):
Any 20 = 0.4007
Suited 20 (same suit) = 0.2078
Matched 20 (e.g. 2 jacks of spades) = 0.0928
2 Queens of hearts = 0.0371
2 Queens of hearts with a dealer blackjack = 0.0146
Total = 0.7529
House Edge = 24.71% "
There really is no point in knowing the individual expected value for each payout, because its not as if we can pick and choose which jackpot we want to go for like with some other wagers (ie. craps). Also, I believe PR's use of the combined Expectation of payouts to deduce the house edge to be flawed. According to my calculations:
_Dealt__Payout__Frequency (in %)____Odds____Expectation_
2QH&BJ__1001____0.00146406_____1 in 68,303__.0146552406
_2QH_____125____0.03091763______1 in 3,234__.0386470437
Suit&Rank_19_____0.49468216_______1 in 809___.0939896115
Suited 20___9_____2.57234726________1 in 39___.2315112537
_Any 20____4____10.07000000*_______1 in 10___.4280000000
All Other___-1____86.83058888_______1 in 1.15__-.8683058888
*figure is taken from Wong's PBJ Table D3 due to discrepencies between calculated frequencies of two Ten card hands, and simulation results (see PBJ pages 292-3 for more info). All other frequencies and ev's calculated using basic probability equations.
Now we know the total Expectation is the sum of the Expectations of each and every payout, so we add the right-hand column which totals -.0615027392, so we can deduce that the House Edge on the Lucky Ladies sidebet is -6.15%. In PR's hypo above, he fails to include the negative payouts of non-twenty hands, which alters the outcome drastically (also many of my numbers vary slightly, perhaps someone knows if he calculated these or simmed them?)
So to calculate our total Expectation if wagering only in advantageous situations, with perfect play (no Standard Error), we would sum the right-hand column EXCEPT for the last entry (All Other), which totals to .80680314961, an Expectation of +80.68%. Now remember, we would only see this advantage 1.23% of the time, so we could calculate an overall Expectation of 80.68% * 1.23% = +.992364% with perfect play. This obviously represents the upper limits for this sidebet, and shows us it is impossible to reach a 1% overall advantage.
Now, again let's see what can be gained in real-world play (w/ a high Standard Error). From Panama Rick's essay (TC = true count, ev = expected value, n = # of hands, f = frequency, SE = standard error):
__TC_______ev________n_________f_____SE__
__6.5_____0.50%___797,833____0.38%___13%
__7.0_____2.72%___578,783____0.25%___13%
__7.5_____4.91%___417,682____0.18%___13%
__8.0_____7.08%___313,499____0.13%___14%
__8.5_____9.27%___221,484____0.09%___14%
__9.0____11.57%___170,614____0.07%___15%
__9.5____13.93%___105,475____0.05%___15%
_10.0____16.24%____84,955____0.04%___15%
_10.5____18.73%____60,349____0.03%___16%
_11.0____21.26%____41,676____0.02%___16%
_11.5____23.71%____26,872____0.01%___17%
_12.0____26.24%____19,184____0.01%___17%
_12.5____28.61%____13,330____0.01%___17%
Again, by summing the products of the ev and frequency of each favorable TC (multiply each TC's ev & frequency, then add all together) we get the overall Expectation (or ev) for the sidebet when a wager is placed only when favorable, +.074172%.
As we stated before, this figure would be substantially higher when wonging, only partly due to more frequent higher counts, but more noticably because the ratio of advantageous situations to hands played would be significantly reduced by only playing in positive counts (because of less hands played). Now as noted before, the increase would not be proportional to the decrease in hands played because of other factors involved. This +.074% edge is not really a "fair" figure, since these days, anybody-who's-anybody is Wonging out (?Schlesingering?) by at least a TC of -5.
First we'll examine the case of Wonging out at a TC of -1. We can see from PR's chart that we will be playing 68.34% of the time with this methodology (4.5/6 pen). Now to determine the percentage of advantageous hands (still speaking of the sidebet), out of played hands, we must divide each TC's frequency by 68.34%. The product of this frequency, and its TC's ev, will be our overall Expectation.
continued...
ANS
Adam N Subtractum
New Member
Re: Lucky Ladies UNDRESSED...part I 1/2
continued...
So it's clear that we can substantially reduce the ratio of hands played to advantageous sidebets by Wonging out,which technically increases the Expectation, BUT this will not affect our hourly win rate WHATSOEVER. This is a clear example of the reason why conventional Wonging cannot increase gains to the degree that the ratio of hands played to advantageous sidebets would imply. But, there will be a gain as we stated previously, we just have to approximate to what degree.
Some side notes, the link below leads to a company pushing the sidebet, and gives some figures and lists the different payouts available (a good resource). The funny part is, the House Edge figures that they give suffer the same flaw as the figure given by Rick. You MUST sum the products of *all possible outcomes* and frequencies. I've really tried to convince myself that I am in err here (especially seeing PR's #'s are close to the vendors), but I just can't see it. The calculations were very tedious, but I always triple check, and any differences between mine & PR's #'s are slight, so I don't believe that to be a factor. A Google search supplied an old post by the Mayor stating a HE of around 11% to 17%, but the post wasn't that recent and I don't *think* it mentioned the payouts used. Perhaps he will comment on this.
In part II, we'll try to develop a "brute force" Wonging attack to capitalize on the potential gains. Also, I have a few ideas, including some *minor* base count modifications, and *very* simple sidecounts that might provide a notable improvement, even in the play-all case. After that, I'll post a final follow-up showing how to calculate the Variance and size wagers optimally for the sidebet. This is a very important factor...novices taking the hefty ev figures and running with them will no doubt drop them, trip, and land smack dab on their face if they are not adjusting for Variance. And I'm not talking about a V of 1.32...some initial figures suggest a Variance of around 20 (and if you think that's bad, I've been contemplating dividing by the ratio of the winning wager to a losing one, ala Thorp w/ roulette
.
ANS
ps: We can clearly see the presence of high Variance, high Standard Error, and low Correlation in the fact that we receive winning hands 13.2% of the time, yet only perceive an advantage 1.32% of the time! It seems fairly obvious we should try to better equip ourselves to attack this shoe.
continued...
So it's clear that we can substantially reduce the ratio of hands played to advantageous sidebets by Wonging out,which technically increases the Expectation, BUT this will not affect our hourly win rate WHATSOEVER. This is a clear example of the reason why conventional Wonging cannot increase gains to the degree that the ratio of hands played to advantageous sidebets would imply. But, there will be a gain as we stated previously, we just have to approximate to what degree.
Some side notes, the link below leads to a company pushing the sidebet, and gives some figures and lists the different payouts available (a good resource). The funny part is, the House Edge figures that they give suffer the same flaw as the figure given by Rick. You MUST sum the products of *all possible outcomes* and frequencies. I've really tried to convince myself that I am in err here (especially seeing PR's #'s are close to the vendors), but I just can't see it. The calculations were very tedious, but I always triple check, and any differences between mine & PR's #'s are slight, so I don't believe that to be a factor. A Google search supplied an old post by the Mayor stating a HE of around 11% to 17%, but the post wasn't that recent and I don't *think* it mentioned the payouts used. Perhaps he will comment on this.
In part II, we'll try to develop a "brute force" Wonging attack to capitalize on the potential gains. Also, I have a few ideas, including some *minor* base count modifications, and *very* simple sidecounts that might provide a notable improvement, even in the play-all case. After that, I'll post a final follow-up showing how to calculate the Variance and size wagers optimally for the sidebet. This is a very important factor...novices taking the hefty ev figures and running with them will no doubt drop them, trip, and land smack dab on their face if they are not adjusting for Variance. And I'm not talking about a V of 1.32...some initial figures suggest a Variance of around 20 (and if you think that's bad, I've been contemplating dividing by the ratio of the winning wager to a losing one, ala Thorp w/ roulette
.ANS
ps: We can clearly see the presence of high Variance, high Standard Error, and low Correlation in the fact that we receive winning hands 13.2% of the time, yet only perceive an advantage 1.32% of the time! It seems fairly obvious we should try to better equip ourselves to attack this shoe.
learning to count
Well-Known Member
Re: Lucky Ladies UNDRESSED...part I 1/2
This is definately an archive post. Excellent dicsussion on this side bet. Lucky ladies is by far the most ineteresting of the current trend of ploppy stocking stuffers that the evil "genuises" of the gaming world have bestowed upon the gambling public. I wait for your next cornacopia of BJ knowledge and what strategy you have devised to unlock the secrets of the ladies. Your math looks very good I have learned a lot. The two queens are devious but do come up frequently. I have experienced them personally once with a bet and several times near and far with out a wager. Excellent post.
This is definately an archive post. Excellent dicsussion on this side bet. Lucky ladies is by far the most ineteresting of the current trend of ploppy stocking stuffers that the evil "genuises" of the gaming world have bestowed upon the gambling public. I wait for your next cornacopia of BJ knowledge and what strategy you have devised to unlock the secrets of the ladies. Your math looks very good I have learned a lot. The two queens are devious but do come up frequently. I have experienced them personally once with a bet and several times near and far with out a wager. Excellent post.
Adam N. Subtractum
Well-Known Member
Thanks LTC...and some additional comments..
Thanks for your interest in my work on this matter LTC. I have gone over my figures once again, and I do believe them to be accurate.
As for your point about the Queens, I believe your observations correspond with the numbers, as 1 in 3,234 hands is effectively 1 in 32.34 hours (assuming 100/hr), which depending on how much action the sidebet receives, may in fact, seem to occur, and subsequently hit, quite frequently.
By keeping a simple sidecount of the Queens of Hearts (only 6 cards, assuming 6 decks), we can improve the Expectation of _this particular_ payout substantially, but of course only marginally improve on our overall Expectation for the sidebet.
Unfortunately, this seems like the only payout that can be somewhat exploited on a practical basis (assuming conventional methods). Of course you would have a better idea on the odds of the jackpot payout (2QH & DBJ) if your system includes an Ace sidecount (as well as our QH side), and of course you could get a better idea of the odds of the Suited, and Suited & Ranked payouts by employing a type of "selective sidecounting" (dubbed by Ted Forrester), but both cases are just not practical enough to deem feasable.
Some additional comments on the point I brought up about Wonging out, and its null effect on our hourly win rate (see part 1 1/2)...there are some points that must be clarified. Firstly, I was assuming Wonging out for bathroom breaks, phone calls, etc. NOT Wonging out, and seeking new shoes (like I should have. Obviously in that case we WOULD improve our hourly win rate, as we would be spending more time per hour in positive territory than one just taking bathroom breaks, etc. I am using on an approximation from my Wong In/Out studies to give us an idea what kind of improvement we can expect for both cases.
**Further Notes:
a. In order for the tables in "UNDRESSED Part I" to format properly, it may be necessary to minimize the menu to the left.
b. The link I provided in my last post didn't go through for some reason, I'll try to post it again in a follow-up.
ANS
Thanks for your interest in my work on this matter LTC. I have gone over my figures once again, and I do believe them to be accurate.
As for your point about the Queens, I believe your observations correspond with the numbers, as 1 in 3,234 hands is effectively 1 in 32.34 hours (assuming 100/hr), which depending on how much action the sidebet receives, may in fact, seem to occur, and subsequently hit, quite frequently.
By keeping a simple sidecount of the Queens of Hearts (only 6 cards, assuming 6 decks), we can improve the Expectation of _this particular_ payout substantially, but of course only marginally improve on our overall Expectation for the sidebet.
Unfortunately, this seems like the only payout that can be somewhat exploited on a practical basis (assuming conventional methods). Of course you would have a better idea on the odds of the jackpot payout (2QH & DBJ) if your system includes an Ace sidecount (as well as our QH side), and of course you could get a better idea of the odds of the Suited, and Suited & Ranked payouts by employing a type of "selective sidecounting" (dubbed by Ted Forrester), but both cases are just not practical enough to deem feasable.
Some additional comments on the point I brought up about Wonging out, and its null effect on our hourly win rate (see part 1 1/2)...there are some points that must be clarified. Firstly, I was assuming Wonging out for bathroom breaks, phone calls, etc. NOT Wonging out, and seeking new shoes (like I should have
. Obviously in that case we WOULD improve our hourly win rate, as we would be spending more time per hour in positive territory than one just taking bathroom breaks, etc. I am using on an approximation from my Wong In/Out studies to give us an idea what kind of improvement we can expect for both cases.**Further Notes:
a. In order for the tables in "UNDRESSED Part I" to format properly, it may be necessary to minimize the menu to the left.
b. The link I provided in my last post didn't go through for some reason, I'll try to post it again in a follow-up.
ANS
learning to count
Well-Known Member
Re: Thanks LTC...and some additional comments..
I would think that at a high TC that making the side bet would result in a positive result. I mean and I am only guessing (from the results of the indices I have used) and the results, that a hand of twenty is prevalent at times and can add extra EV. The actuall dealing of a twin QofH is a approx.3000 to one possibility. But add the other possibilities of twenty I think this is a good gamble(at a High TC). That is why when wonging in and experiencing climbing counts it may be a good side bet. And only if you bet the max Green chip.
I would think that at a high TC that making the side bet would result in a positive result. I mean and I am only guessing (from the results of the indices I have used) and the results, that a hand of twenty is prevalent at times and can add extra EV. The actuall dealing of a twin QofH is a approx.3000 to one possibility. But add the other possibilities of twenty I think this is a good gamble(at a High TC). That is why when wonging in and experiencing climbing counts it may be a good side bet. And only if you bet the max Green chip.
Adam N. Subtractum
Well-Known Member
re: LTC...
I think maybe you misunderstood me, re-read if you get a chance. By saying QH was the only payout that could be practically exploited (to a small degree), I was speaking of increasing our edge through additional means, ie. sidecounts, modifications, etc. ON TOP of our base count info. Obviously frequency of two card twenties, and subsequently the other payouts, is going to increase in higher counts, that is the reason the bet is exploitable in the first place.
ANS
I think maybe you misunderstood me, re-read if you get a chance. By saying QH was the only payout that could be practically exploited (to a small degree), I was speaking of increasing our edge through additional means, ie. sidecounts, modifications, etc. ON TOP of our base count info. Obviously frequency of two card twenties, and subsequently the other payouts, is going to increase in higher counts, that is the reason the bet is exploitable in the first place.
ANS
learning to count
Well-Known Member
Re: re: LTC...
No I agree with you 100%. I side track the QH"s. It is necessity. Your strike number will change depending on the weight of QH's light or heavy as the cards are laid out. Excellent article thanks. I am still basically math weak but I am learning. Also ace knowledge is good to have but I feel that being more apprised of the TC is more important.
No I agree with you 100%. I side track the QH"s. It is necessity. Your strike number will change depending on the weight of QH's light or heavy as the cards are laid out. Excellent article thanks. I am still basically math weak but I am learning. Also ace knowledge is good to have but I feel that being more apprised of the TC is more important.