Is 50K hands enough to approach EV?

Is 50,000 hands enough to approach what theoretical EV should be or are we still more so at the mercy of variance?

What game?

Yeah. Completely game dependant.

Quote: yvgtgh

Is 50,000 hands enough to approach what theoretical EV should be or are we still more so at the mercy of variance?

Big time game dependent BECAUSE your Variance will change from game to game, changing your Standard Deviations. I'm going to assume blackjack because you posted this in the Blackjack sub forum.

In blackjack, 50k is not "the long run"... but from what calculations I've done, that is "about" the point you can guarantee within 3 standard deviations to be "Even or Up." Remember, this isn't 99% sure near your EV, but you'll be at LEAST even or up with 99% confidence. So 50k hands is more/less the 'break even guarantee' point, not the guaranteed up/EV I think you're looking for.

Really you can never 'expect' to be spot on to your EV. If you run a million hands with a 1% edge and a $100 average bet, then after a million hands your EV is $1,000,000... but your SD is like PLUS or MINUS $200k. So while you're GUARANTEED to make money at that point, you're still not guaranteed to hit your EV.

I am going to assume the OP is talking blackjack....not sure why...I guess because I am a blackjack guy. :/

I'll let the 'math guys' present some formulas and such, and will answer based on my own actual experience. That answer is NO.

I have experience 4 different 40,000 hand runs (which is just about 6 months for me) where I have been in the red (negative results) for those 40,000 hands. The first 3 of these, even though the 40,000 run was in the negative, my total years results (75,000 to 80,000 hands) did come reasonably close to expectation. So that lead me to believe the number you (and I) were looking for was somewhere between 40,000 and 80,000.

That changed for me last year as my results for the entire year, while positive where far below expectation. I even played a bit more than usual, closer to 85,000 rounds as I tried to 'catch up'. I ended up just about 33% of expectation for the year. So now, I am not really sure what a reasonable assumption of that number is. :/

There are some variable factors involved, like how good or bad the game rules and conditions are, how much your bet spread is. In my own case, I play very different bet spreads, ramps and top wagers for different games, based on casino tolerance levels rather than bankroll limitations, and this style of play is going to really wreak havoc with variance and swings. I accept that going in.

Quote: kewlj

What game?

Well this is the BlackJack forum, so Blackjack. xD

Quote: kewlj

I am going to assume the OP is talking blackjack....not sure why...I guess because I am a blackjack guy. :/

I'll let the 'math guys' present some formulas and such, and will answer based on my own actual experience. That answer is NO.

I have experience 4 different 40,000 hand runs (which is just about 6 months for me) where I have been in the red (negative results) for those 40,000 hands. The first 3 of these, even though the 40,000 run was in the negative, my total years results (75,000 to 80,000 hands) did come reasonably close to expectation. So that lead me to believe the number you (and I) were looking for was somewhere between 40,000 and 80,000.

That changed for me last year as my results for the entire year, while positive where far below expectation. I even played a bit more than usual, closer to 85,000 rounds as I tried to 'catch up'. I ended up just about 33% of expectation for the year. So now, I am not really sure what a reasonable assumption of that number is. :/

There are some variable factors involved, like how good or bad the game rules and conditions are, how much your bet spread is. In my own case, I play very different bet spreads, ramps and top wagers for different games, based on casino tolerance levels rather than bankroll limitations, and this style of play is going to really wreak havoc with variance and swings. I accept that going in.

Thank you. This was very helpful. Just out of curiousity, were the 3 40K runs where you ran negative about 50% of your 40K runs ... or were they the majority?

Quote: Romes

Big time game dependent BECAUSE your Variance will change from game to game, changing your Standard Deviations. I'm going to assume blackjack because you posted this in the Blackjack sub forum.

In blackjack, 50k is not "the long run"... but from what calculations I've done, that is "about" the point you can guarantee within 3 standard deviations to be "Even or Up." Remember, this isn't 99% sure near your EV, but you'll be at LEAST even or up with 99% confidence. So 50k hands is more/less the 'break even guarantee' point, not the guaranteed up/EV I think you're looking for.

Really you can never 'expect' to be spot on to your EV. If you run a million hands with a 1% edge and a $100 average bet, then after a million hands your EV is $1,000,000... but your SD is like PLUS or MINUS $200k. So while you're GUARANTEED to make money at that point, you're still not guaranteed to hit your EV.

Thank you :D

Quote: yvgtgh

Is 50,000 hands enough to approach what theoretical EV should be ... ?

No.

But don't feel bad. The other side of the table doesn't see enough hands to get to their expected edge, either.

Quote: DJTeddyBear

No.

But don't feel bad. The other side of the table doesn't see enough hands to get to their expected edge, either.

Maybe not against individual players.

Quote: kewlj

I have experience 4 different 40,000 hand runs (which is just about 6 months for me) where I have been in the red (negative results) for those 40,000 hands.

Math geeks have something to say if you google "Zero crossings in 1D random walk"
- How long are my winning/losing streaks (aka when will I hit my EV exactly)?
- Closed-form expression is roughly (n/6.28) ^.5 (NOTE: Some google posts did the math wrong).

Best posts I saw were:
(a) http://mathworld.wolfram.com/RandomWalk1-Dimensional.html
(b) http://www.pokerfied.com/poker/Heres_a_gambling_math_question_that_might_surprise_you_529075.html

In 1 yr of blackjack with 100,000 hands (flat-betting), 125 zero-crossings (streaks average 800 hands).

In a 10-yr blackjack career with 100,000 hands/yr (1,000,000 hands), 400 zero-crossings (streaks average 2,500 hands).

As you play longer, your average winning/losing streak will grow as square root of time played;
i.e. play 2x as long, average winning streak will grow by 40% (1.414).

This isn't what you are looking for. You need
(a) 1-D random walks which have variable sized steps according to your game & bet sizing
(b) At 95%/99%/? confidence level, what is my longest expected streak? (aka time I will be -EV or +EV)

There is a lot of literature on 1-D random walks, and someone might have already calculated what you are looking for... I was more interested in average losing/winning streaks, not 95-99% confidence brackets (e.g. in 10 years, with 99% confidence, longest losing streak will be 50,000 hands or less...)

----
P.S. Applied to VUX hands. I've played about 200,000-250,000 hands (extrapolating from 17 royals ... assuming avg 5-play), 145-148% avg return (back in the first 1-2 yrs of playing, no longer track this number), and the streaks go up/down around EV, usually 4-12 month cycles of being above EV or below EV.

I tend to be +/- $3,000-5,000 compared to EV, except for "big hits" (aka over $4,000) which shoot me way above EV.

I was below EV for most of my first 6 months VUX, until I hit $4,005 on 5-play $1 with one 2X. Dealt one Ace and got 2x Aces with kicker on the last hand in the upper-right corner. Then I was above EV for a long time.

Quote: mamat

Math geeks have something to say

Yikes! Enough said, IMO. :)

There is a difference between both mathematical formulas and computer generated simulations and real world play. In the real world there are many variables not accounted for in computer simulations. Different rules, conditions, table limits, bet spreads and ramps, number of players, cheating, errors, human emotions leading to even more errors that are not accounted for in computer simulations.

The "math geeks" and "computer sim guys" never seem to realize this or the fact that computer sims are only a tool and at best an estimation (guess) as to what real life results MIGHT look like.

Quote: kewlj

The "math geeks" and "computer sim guys" never seem to realize this or the fact that computer sims are only a tool and at best an estimation (guess) as to what real life results will look like.

Totally agree.

Figuring out my real-world error rate...in my first years of BJ was surprising. One error/hr is huge. Real-world will tend to skew towards losing streaks.

Aside from math theory, I track real-world performance. Only the top machine APs I've met are concerned with hourly rate. Most machine APs are not as sophisticated as the BJ set, and are more concerned with "can I win money". Word I hear is that the best machine APs from 10-20 yrs ago all left for other stuff because $500-2,000/hr was no longer available...and they are bored playing for $10-20-50-100/hr.

P.S. I added some info to my earlier post with real-world experience at VUX.
I track Actual & EV for each month of play.

Also, I track landed multipliers, so I can see if I'm losing because I'm
(a) not hitting multipliers
(b) video poker just dealing bad cards.

One reason for tracking (in the land of machine AP), is detecting gaffed games.
Another is comparing actual return with machine settings (if you know them) & estimating variance (bankroll required for different machine AP games)

Real-world playing efficiency is calculated in the BJ world (aka simple strategies vs. complicated strategies), but rarely used in machine AP world.

For machines,
(1) "player equity" in slots
(2) "cashable equity" = "player equity" - expected loss playing for bonus
(3) playing efficiency: with $100 EV in plays in the casino, how much do you cash on average?
- (a) plays you don't recognize
- (b) plays you pass up waiting for better situations
- (c) playing in non-optimal manner
- (d) playing sub-100% games while waiting
(4) benefits in addition to play (e.g. promotions, mailers, free tournaments, marketing "fishing for players")

Real-world, many machine APs have 10% or lower playing efficiencies.
With $1,000/day EV in a casino (expecting $200/day EV due to competition), they make $20-40/day.
I call them "low playing-efficiency APs".

I doubt my own "playing efficiency" is higher than 50-70%.
Too many plays I don't recognize yet (or know how to play) or are too scared to play.
With slots, you may not get into the long-term before the game disappears.

Some are "break-even APs". Without the benefits (aka FP), they play a "negative game".

Some people (similar to BJ players playing "basic strategy" on cruises getting kicked out from being unprofitable) know they play a "negative game" on slots, but they play for the mailers. They are willing to play sub-100% games (e.g. 97-99%) for benefits.

Quote: yvgtgh

Is 50,000 hands enough to approach what theoretical EV should be or are we still more so at the mercy of variance?

This was one of the biggest questions I had when I started down the AP path. It led me to develop and evolve a system of tracking and analyzing my play, all in pursuit of the proverbial "when have I reached the long term".

First, you must realize we are playing a game of probabilities, not absolutes. So keeping that in mind, we can use the concept of N0 to tell us the number of rounds needed for EV to accumulate and overcome one negative standard deviation. But even at this juncture we only have a 68% probability of not losing.

To me that remains to close to gambling and a higher level of probability was needed. Then to extrapolate from N0, we know that 4 X N0 indicates we should have a 95% probability of being ahead (2 standard deviations). Now we are getting somewhere.

So, N0 for 2 standard deviations would indicate, with 95% probability, the number of rounds for us to be ahead. Again, we have accumulated sufficient EV to overcome 2 negative standard deviations. As an alternative to the illusive long term, I have adopted this measure as my definition of the long term. Now I can measure my results against this and get some comfort to where I am in the journey.

N0 is a good example, without understanding the effect of variance and ev per round (value of game), N0 can give you a distorted view. I can reach N0 for 2SD by only wong in at TC+2 in shoe games in as little as 14,000 rounds. I can influence this up or down by changing my average bet. If I play the same game "play all" with a comparable bet ramp, N0 might go to 75,000. My point is to ask what is N0 without the corresponding information is dangerous to your decision making.

One should exercise caution when looking at the metrics, either projected or measured, of blackjack. They must be taken in context.

Hope this helps.