EV Theoretical & Actual, SCORE

[matt21]

Firstly, sorry for posing quite a few questions lately!!

Now that that’s out of the way....I am having some problems understanding the links between several sources. It would be super if anyone could shed some lights on these things. Basically I do want to get to a point where i am confident as to my EV rates for various playing conditions. I actually thought I had already reached this point, but now i am doubting!!

EV according to the forum – “1-2 units per hour”
Looking at posts and discussions on this forum, most posters indicate that, over the long run, good card counters work on an expectation of making somewhere between 1 and 2 standard units per hour (focusing on pure counting and excluding advanced techniques, value of casino comps etc). Although many start off with a small BR, and are thus effectively overbetting, the consensus seems to be that ideally a counter should start with a 1,000-unit BR. Thus for someone with a $10,000 BR, the standard unit should be $10 and the EV is in the range of $10-$20 per hour.

SCORE Discussion in Schlesinger’s Blackjack Attack –
SCORE is discussed in Chapter 9 and assumes a $10,000 BR with ROR of 13.5% (i.e. full Kelly). SCORE is then measuring the $won/100 hands played/observed. This all makes sense to me. However, looking at the data tables for say Hi-Low 6D Play-all S17 DAS 1-12 spread, SCORE is 19.8 and 33.6 for 75% and 83% respectively. This is effectively 2-3 units per hour, quite an increase from the forum’s consensus. Additionally, the SCORE for back-counting 6D, for SD and for DD is often above 50!!

CVCX Online Viewer
Entering a BR of $10,000, with ROR of 13.5% for 6D Hi-Low S17 DAS 75%pen 1-12 spread, I get $20.21 as hourly rate. So this agrees with the SCORE in Schlesinger’s data table.

Questions
1. Does this mean that if we search around and actually find those 83% pen levels, then we should really expect to make 3 units per hour? That is obviously a very big difference!
2. And if we manage to play 200 hands per hour instead of 100, does that mean we can double the SCORE (I think the new figure becomes a c-SCORE?) – thus if i am playing the same pen75 conditions as above, then my EV becomes 39.6 (19.8x2) – i.e. nearly 4 units per hour? And if i am playing 83pen at 200 hands/hour then my EV should be 67.2 (33.6x2)?
3. Why are so many of the SCORE figures on Schlesinger’s data tables in the 30’s, 40’s, 50’s and higher (indicating 3, 4, 5 or more units per hour)? No one has ever claimed to make 3, 4, 5, 6 units per hour by counting alone? What am I not understanding here?

At 4 units per hour this is now twice as much the upper end of the range that people are saying they are experiencing as long-run results. Obviously i am going to significantly more motivated to play for a long-run EV of 4 units per hour rather than 1.5-2. I just can’t make sense of the apparent inconsistencies. Could someone help?

Many thanks in advance & happy counting,
Matt

 

[SleightOfHand]

SCORE Discussion in Schlesinger’s Blackjack Attack –
SCORE is discussed in Chapter 9 and assumes a $10,000 BR with ROR of 13.5% (i.e. full Kelly). SCORE is then measuring the $won/100 hands played/observed. This all makes sense to me. However, looking at the data tables for say Hi-Low 6D Play-all S17 DAS 1-12 spread, SCORE is 19.8 and 33.6 for 75% and 83% respectively. This is effectively 2-3 units per hour, quite an increase from the forum’s consensus. Additionally, the SCORE for back-counting 6D, for SD and for DD is often above 50!!

See #3

1. Does this mean that if we search around and actually find those 83% pen levels, then we should really expect to make 3 units per hour? That is obviously a very big difference!

Yes, penetration is one of the biggest factors in evaluating a beatable game. A game with S17 DAS ES is useless if its played from a CSM (well, there is an OTT player advantage, but it is uncountable)

2. And if we manage to play 200 hands per hour instead of 100, does that mean we can double the SCORE (I think the new figure becomes a c-SCORE?) – thus if i am playing the same pen75 conditions as above, then my EV becomes 39.6 (19.8x2) – i.e. nearly 4 units per hour? And if i am playing 83pen at 200 hands/hour then my EV should be 67.2 (33.6x2)?

You are semi correct in that your hourly rate will double but the SCORE stays the same.

3. Why are so many of the SCORE figures on Schlesinger’s data tables in the 30’s, 40’s, 50’s and higher (indicating 3, 4, 5 or more units per hour)? No one has ever claimed to make 3, 4, 5, 6 units per hour by counting alone? What am I not understanding here?

The SCORE is calculated using optimum betting. This means that the minimum bet may or may not be 1/1000th of the BR. It is all about betting appropriately based on advantage and standard deviation. Also, the SCORE of 4 units per hour (or whatever) is using a 13.5% RoR. Most people would not want such a high RoR and would therefore sacrifice WR for a safer game (.5%-5% typically)

At 4 units per hour this is now twice as much the upper end of the range that people are saying they are experiencing as long-run results. Obviously i am going to significantly more motivated to play for a long-run EV of 4 units per hour rather than 1.5-2. I just can’t make sense of the apparent inconsistencies. Could someone help?

See #3

 

[Kasi]

[ However, looking at the data tables for say Hi-Low 6D Play-all S17 DAS 1-12 spread, SCORE is 19.8 and 33.6 for 75% and 83% respectively. This is effectively 2-3 units per hour, quite an increase from the forum’s consensus.Matt

Well, it's because one's unit has changed in the second case from $10 in the first case to $15 in the second case. Why - becasue one needs only 667 units of roll to have a Kelly risk rather than 1000 units in the first case. In the first case you are making say 2 units or $20/100 played and in the second you are making 2.3 units per 100 played except now it's say $15*2.3=$35. If you played the second case with a $10 unit, you'd still be making 2.3 units per hundred played ($23) but now have 50% greater roll than kelly and therefore a much lower risk to your roll than accepting a kelly risk.

In effect by keeping the $10 unit in the better game, you have chosen to subject your roll to very different risks just because the pen has changed.

Look at the 1-16 spread at 83%, you are now making about 3.5 units per 100 played but now you are back to a $10 and basically making the same $35 per 100 played when you keep risk the same.

Questions
1. Does this mean that if we search around and actually find those 83% pen levels, then we should really expect to make 3 units per hour? That is obviously a very big difference!
2. And if we manage to play 200 hands per hour instead of 100, does that mean we can double the SCORE (I think the new figure becomes a c-SCORE?) – thus if i am playing the same pen75 conditions as above, then my EV becomes 39.6 (19.8x2) – i.e. nearly 4 units per hour? And if i am playing 83pen at 200 hands/hour then my EV should be 67.2 (33.6x2)?
3. Why are so many of the SCORE figures on Schlesinger’s data tables in the 30’s, 40’s, 50’s and higher (indicating 3, 4, 5 or more units per hour)? No one has ever claimed to make 3, 4, 5, 6 units per hour by counting alone? What am I not understanding here?

At 4 units per hour this is now twice as much the upper end of the range that people are saying they are experiencing as long-run results. Obviously i am going to significantly more motivated to play for a long-run EV of 4 units per hour rather than 1.5-2. I just can’t make sense of the apparent inconsistencies. Could someone help?

Many thanks in advance & happy counting,
Matt[/QUOTE]

With back-counting you might have a SCORE of 50 or more but it may only represent a half-unit per 100 hands seen.

Any unit spread will have it's own "units won per hand". That can't change no matter how many units are in your roll.

Cowardly Lion that I am lol, I'd prefer to have every hand I played subjected to the same risk of my choosing to my roll and let my EV fall where it may.
If I liked the Kelly risk in Case A with a $10 unit, I'd bet $15 in Case B to keep my risk the same. If I liked the risk in Case B with a $10 unit, I'd lower my $unit in Case A. If the table min was $10, then I couldn't play that game with that roll and have the risk I liked.

 

[matt21]

thanks for the quick replies.

sleightofhand, your responses all make sense. Very clear and very helpful. It makes sense that the reason why players get lower than SCORE is because they are accomodating a ROR less than full Kelly. Perfect.

Kasi how are you doing?

Well, it's because one's unit has changed in the second case from $10 in the first case to $15 in the second case. Why - becasue one needs only 667 units of roll to have a Kelly risk rather than 1000 units in the first case. In the first case you are making say 2 units or $20/100 played and in the second you are making 2.3 units per 100 played except now it's say $15*2.3=$35. If you played the second case with a $10 unit, you'd still be making 2.3 units per hundred played ($23) but now have 50% greater roll than kelly and therefore a much lower risk to your roll than accepting a kelly risk.

Ok so how do I calculate the number of units i require in my BR in order to obtain a risk equal to Kelly i.e. 13.5%? ... Actually I looked at CVD functionality for this - i can work it out. I just love the CVD software :grin:

This conversly means that if i use the same unit-size bankroll for the 75pen and 83pen games, then my ROR will be lower for the 83pen. Or i can reduce the bankroll size for the pen83 game, but keep my risk level the same. Correct?

 

[matt21]

The SCORE is calculated using optimum betting. This means that the minimum bet may or may not be 1/1000th of the BR. It is all about betting appropriately based on advantage and standard deviation. Also, the SCORE of 4 units per hour (or whatever) is using a 13.5% RoR. Most people would not want such a high RoR and would therefore sacrifice WR for a safer game (.5%-5% typically)

this begs the question. Playing full Kelly means that the player has 13.5% chance of going broke before doubling BR. In other words there is a 86.5% of chance of doubling first, and a 13.5% chance of going broke (ignoring re-sizing for a moment).

I guess it's a little like playing russian roulette. but surely some people must be willing to risk a 1 in 8 chance of going broke in exchange for doubling their theoretical hourly rate... and still having a 7 in 8 chance of doubling their bankroll.

Is it just the swings that players want to avoid?

 

[johndoe]

surely some people must be willing to risk a 1 in 8 chance of going broke in exchange for doubling their theoretical hourly rate... and still having a 7 in 8 chance of doubling their bankroll.

Is it just the swings that players want to avoid?

Lots of us with jobs don't have a "fixed" bankroll, so we can be a little more (or less) aggressive when we feel like it, and also have some discretion over what we consider our bankroll to be. For example, I don't have my BR sitting quietly in a safe somewhere, it's just a sort of arbitrarily chosen amount that I'm ok with losing with some given % odds.

 

[SleightOfHand]

Ok so how do I calculate the number of units i require in my BR in order to obtain a risk equal to Kelly i.e. 13.5%? ... Actually I looked at CVD functionality for this - i can work it out. I just love the CVD software :grin:

This conversly means that if i use the same unit-size bankroll for the 75pen and 83pen games, then my ROR will be lower for the 83pen. Or i can reduce the bankroll size for the pen83 game, but keep my risk level the same. Correct?

A simple way to calculate the Kelly bet is Bankroll*Advantage/Variance. The Actual Kelly bet is slightly different (I think you subtract win rate from variance or something) but the difference is negligible for blackjack.

As to your second question, you are correct. Assuming the same betting ramp/BR, the game with a higher SCORE will give you both a higher WR and lower RoR. You can also (as you mentioned) have a smaller bankroll to give you the same RoR.

 

[Kasi]

sleightofhand, your responses all make sense. Very clear and very helpful. It makes sense that the reason why players get lower than SCORE is because they are accomodating a ROR less than full Kelly. Perfect.
Ok so how do I calculate the number of units i require in my BR in order to obtain a risk equal to Kelly i.e. 13.5%? ... Actually I looked at CVD functionality for this - i can work it out. I just love the CVD software :grin:

This conversly means that if i use the same unit-size bankroll for the 75pen and 83pen games, then my ROR will be lower for the 83pen. Or i can reduce the bankroll size for the pen83 game, but keep my risk level the same. Correct?

Doing fine thanks, Matt. I'll be doing better if the Pens can pull it out tied in the third period vs the Caps at the moment lol.

To me SCORE, when capitalized, means, by definition, one with a $10K bank who bets optimally and is subject to a fixed betting schedule where the bet size will not change as bankroll fluctuates and who will play at a Kelly risk.

When this happens SCORE will equal win rate for one hour of play. With a Kelly risk, SCORE will also minmize hours to N0 and hours to double roll. I think in theory they would be the same at Kelly risk. So it's just a way of trying to compare which game is "better" than another.

I'd use a sim to determine an optimal betting ramp.

I think that's correct lol. At 83% one needs a 667 unit roll. At 75% one needs a 1000 unit roll to have the same kelly risk. You could have a roll of $66,700 with a $100 unit at 83% and have a much greater win rate than SCORE but your risk would still be the same since it's a 667 unit roll.

 

[Kasi]

this begs the question. Playing full Kelly means that the player has 13.5% chance of going broke before doubling BR. In other words there is a 86.5% of chance of doubling first, and a 13.5% chance of going broke (ignoring re-sizing for a moment).
Is it just the swings that players want to avoid?

Well, not quite. Kelly assumes playing "forever" kind of thing.

So, sometimes one would double roll and still lose it all later with some bad luck.

Doubling roll before losing it all, assuming one also plays "forever", is actually a little better than what you say. Maybe like 88% to 12%, if you see what I mean.

Well, it's the swings that I would want to avoid lol. Like chances of halving roll are, I think, are the square root of original risk. So, I think , a fixed-bet Kelly guy has around a 36% chance of halving roll at some point.

 

[Kasi]

A simple way to calculate the Kelly bet is Bankroll*Advantage/Variance.

Well that's the way if one assumes one can change one's bet with every bankroll fluctuation and never play a -EV hand. I don't think maybe it applies very well to practical BJ ramps.

But I can't claim to really understanding "Kelly" that well anyway lol.

 

[Kasi]

Lots of us with jobs don't have a "fixed" bankroll, so we can be a little more (or less) aggressive when we feel like it, and also have some discretion over what we consider our bankroll to be. For example, I don't have my BR sitting quietly in a safe somewhere, it's just a sort of arbitrarily chosen amount that I'm ok with losing with some given % odds.

Well, if one wants to imagine many different bankrolls while playing under changing conditions, don't even worry about being "more or less aggressive", just imagine enough roll to make all your plays equal in risk while playing that hand lol.

I'd recommend imagining very large rolls to keep your risk near zero and keep stress to a minimum lol.

But I know what you mean lol.

 

[rukus]

Well, if one wants to imagine many different bankrolls while playing under changing conditions, don't even worry about being "more or less aggressive", just imagine enough roll to make all your plays equal in risk while playing that hand lol.

I'd recommend imagining very large rolls to keep your risk near zero and keep stress to a minimum lol.

But I know what you mean lol.

:laugh::laugh: