Best blackjack bonuses

mstauff
mstauff
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September 8th, 2018 at 7:38:38 AM permalink
In the long run, mathematically, probabilities always prevail. However, no one can sit down and play a million hands of blackjack. Therefore, how much do probabilities based on millions of hands make a difference when you are playing a few hundred hands in a session? I have been playing blackjack in Las Vegas on an occasional basis for 35 years. What I have seen is that on a session by session basis, blackjack seems to be a very streaky game with lots of bad runs and good runs intermixed. Based on what appears to be a streak intensive game, is there a way to calculate the probability of being up at some point in a session that is X period of time long where X is an hour, two hours, etc?
billryan
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September 8th, 2018 at 7:52:07 AM permalink
Life is one long session. In a single short session, almost anything can happen. Play often enough, and you will experience It.
The older I get, the better I recall things that never happened
mustangsally
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September 8th, 2018 at 8:35:27 AM permalink
Quote: mstauff

is there a way to calculate the probability of being up at some point in a session that is X period of time long where X is an hour, two hours, etc?

yes.
discussed B4 here
but being up after X number of rounds played.

https://forumserver.twoplustwo.com/25/probability/blackjack-odds-winning-session-after-x-amount-hands-1466708/
part data from that thread
values are % - except round
roundwin push loss
142.4238888.48164749.094465
237.63551226.67590335.688585
342.32349611.48763846.188866
443.23985613.51645443.24369
544.0143649.7637346.221906
644.9391349.21447945.846387
745.22787.95835546.813845
845.7618037.26567446.972523
945.9757926.65491947.369289
1046.2752526.1487447.576008
1146.4459245.76186447.792212
1246.6282925.41289447.958814
1346.7593455.13707648.103579
1446.8816874.88889948.229414
1546.9809624.68178348.337255
1647.0694034.4966448.433957
1747.1453864.33577448.51884
1847.2126524.19151448.595834
1947.2720574.06285248.665091
2047.3250583.94640448.728538
2147.3726073.8407248.786673
2247.4154883.74403148.840481
2347.4543883.65515848.890454
2447.4898183.57302748.937155
2547.5222453.49678448.980971
2647.5520273.42571449.022259
2747.5794833.35921249.061305
2847.6048743.29677349.098353
2947.6284243.23796449.133612
3047.6503233.1824249.167257
3147.6707353.12982449.199441
3247.6898033.07990349.230294
3347.707653.0324249.25993
3447.7243822.98716849.28845
3547.7400952.94396549.31594
3647.7548722.9026549.342478
3747.7687862.86308149.368133
3847.7819022.82513249.392966
3947.7942812.78868849.417031
4047.8059742.75364949.440377
4147.8170292.71992149.46305
4247.8274892.68742149.48509
4347.8373922.65607549.506533
4447.8467742.62581449.527412
4547.8556672.59657349.54776
4647.8641012.56829649.567603
4747.8721022.54093149.586967
4847.8796962.51442649.605878
4947.8869062.48873849.624356
5047.8937522.46382649.642422
5147.9002552.43964949.660096
5247.9064322.41617249.677396
5347.9123012.39336249.694337
5447.9178762.37118849.710936
5547.9231742.34961949.727207
5647.9282072.32862949.743164
5747.9329892.30819249.758819
5847.937532.28828549.774185
5947.9418432.26888549.789272
6047.9459392.24996949.804092
6147.9498262.23151949.818655
6247.9535142.21351549.832971
6347.9570122.19594149.847047
6447.9603282.17877949.860893
6547.963472.16201349.874517
6647.9664462.14562749.887927
6747.9692612.12960949.90113
6847.9719242.11394449.914132
6947.974442.09861949.926941
7047.9768142.08362349.939563
7147.9790532.06894449.952003
7247.9811622.05457149.964267
7347.9831462.04049249.976362
7447.985012.02669949.988291
7547.9867572.01318250.000061
7647.9883941.99993150.011675
7747.9899221.9869450.023138
7847.9913481.97419750.034455
7947.9926741.96169650.04563
8047.9939031.9494350.056667
8147.995041.93739150.067569
8247.9960881.92557250.07834
8347.9970491.91396650.088985
8447.9979271.90256850.099505
8547.9987251.8913750.109905
8647.9994441.88036950.120187
8748.0000891.86955650.130355
8848.000661.85892950.140411
8948.0011621.84847950.150359
9048.0015951.83820550.1602
9148.0019631.82809950.169938
9248.0022671.81815850.179575
9348.0025091.80837850.189113
9448.0026911.79875450.198555
9548.0028161.78928150.207903
9648.0028851.77995650.217159
9748.0028991.77077550.226326
9848.002861.76173650.235404
9948.0027711.75283250.244397
10048.0026311.74406450.253305


the rules of the game also can matter to how accurate one needs to be

some say anything can happen in one short session...

well I never got 10 Blackjacks in a row only playing 10 rounds!

Sally
Last edited by: mustangsally on Sep 8, 2018
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billryan
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September 8th, 2018 at 9:04:29 AM permalink
Quote: mustangsally

yes.
discussed B4 here
but being up after X number of rounds played.

https://forumserver.twoplustwo.com/25/probability/blackjack-odds-winning-session-after-x-amount-hands-1466708/
part data from that thread

roundwin push loss
142.4238888.48164749.094465
237.63551226.67590335.688585
342.32349611.48763846.188866
443.23985613.51645443.24369
544.0143649.7637346.221906
644.9391349.21447945.846387
745.22787.95835546.813845
845.7618037.26567446.972523
945.9757926.65491947.369289
1046.2752526.1487447.576008
1146.4459245.76186447.792212
1246.6282925.41289447.958814
1346.7593455.13707648.103579
1446.8816874.88889948.229414
1546.9809624.68178348.337255
1647.0694034.4966448.433957
1747.1453864.33577448.51884
1847.2126524.19151448.595834
1947.2720574.06285248.665091
2047.3250583.94640448.728538
2147.3726073.8407248.786673
2247.4154883.74403148.840481
2347.4543883.65515848.890454
2447.4898183.57302748.937155
2547.5222453.49678448.980971
2647.5520273.42571449.022259
2747.5794833.35921249.061305
2847.6048743.29677349.098353
2947.6284243.23796449.133612
3047.6503233.1824249.167257
3147.6707353.12982449.199441
3247.6898033.07990349.230294
3347.707653.0324249.25993
3447.7243822.98716849.28845
3547.7400952.94396549.31594
3647.7548722.9026549.342478
3747.7687862.86308149.368133
3847.7819022.82513249.392966
3947.7942812.78868849.417031
4047.8059742.75364949.440377
4147.8170292.71992149.46305
4247.8274892.68742149.48509
4347.8373922.65607549.506533
4447.8467742.62581449.527412
4547.8556672.59657349.54776
4647.8641012.56829649.567603
4747.8721022.54093149.586967
4847.8796962.51442649.605878
4947.8869062.48873849.624356
5047.8937522.46382649.642422
5147.9002552.43964949.660096
5247.9064322.41617249.677396
5347.9123012.39336249.694337
5447.9178762.37118849.710936
5547.9231742.34961949.727207
5647.9282072.32862949.743164
5747.9329892.30819249.758819
5847.937532.28828549.774185
5947.9418432.26888549.789272
6047.9459392.24996949.804092
6147.9498262.23151949.818655
6247.9535142.21351549.832971
6347.9570122.19594149.847047
6447.9603282.17877949.860893
6547.963472.16201349.874517
6647.9664462.14562749.887927
6747.9692612.12960949.90113
6847.9719242.11394449.914132
6947.974442.09861949.926941
7047.9768142.08362349.939563
7147.9790532.06894449.952003
7247.9811622.05457149.964267
7347.9831462.04049249.976362
7447.985012.02669949.988291
7547.9867572.01318250.000061
7647.9883941.99993150.011675
7747.9899221.9869450.023138
7847.9913481.97419750.034455
7947.9926741.96169650.04563
8047.9939031.9494350.056667
8147.995041.93739150.067569
8247.9960881.92557250.07834
8347.9970491.91396650.088985
8447.9979271.90256850.099505
8547.9987251.8913750.109905
8647.9994441.88036950.120187
8748.0000891.86955650.130355
8848.000661.85892950.140411
8948.0011621.84847950.150359
9048.0015951.83820550.1602
9148.0019631.82809950.169938
9248.0022671.81815850.179575
9348.0025091.80837850.189113
9448.0026911.79875450.198555
9548.0028161.78928150.207903
9648.0028851.77995650.217159
9748.0028991.77077550.226326
9848.002861.76173650.235404
9948.0027711.75283250.244397
10048.0026311.74406450.253305


the rules of the game also can matter to how accurate one needs to be

some say anything can happen in one short session...

well I never got 10 Blackjacks in a row only playing 10 rounds!

Sally



Then you obviously haven't played enough.
In your theoretical example, would you quit after the tenth hand?
The older I get, the better I recall things that never happened
mustangsally
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September 8th, 2018 at 9:07:27 AM permalink
Quote: billryan

In your theoretical example, would you quit after the tenth hand?

no way. play until the streak (of BJs) ends
Sally
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Ace2
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September 8th, 2018 at 1:41:47 PM permalink
Quote: mstauff

Based on what appears to be a streak intensive game, is there a way to calculate the probability of being up at some point in a session that is X period of time long where X is an hour, two hours, etc?

This is the inverse of a risk of ruin problem...instead of finding the probability of ever being down x units over a period of time you’re looking for the probability of ever being up. I’ve never seen a formula for this scenario (negative EV, fixed number of plays, payout isn’t 1:1). As far as I know you can only get the (approximate) number via simulation or Markov chain.
It’s all about making that GTA
mustangsally
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September 9th, 2018 at 8:20:15 AM permalink
Quote: Ace2

As far as I know you can only get the (approximate) number via simulation or Markov chain.

I used the Markov chain solution
I also used the Wizard probability distribution found in the link

trying to be up at least one unit in X rounds (can over-shoot the 1 unit win goal)

this is flat-betting and using basic strategy only
20,50 and 100 unit bankrolls

target gain at least 1 unit
BJ rounds↓units 20. gain 1units 50. gain 1units 100. gain 1
200.8070051..
400.8595123..
50.0.87331430.8733143
1000.90771780.90810480.9081048
2000.92825050.93304360.9330436
3000.93282740.94414340.9441437 

sim data from cvdata
Bankroll:100 units
Target: 101
Max Rounds: 100
Sessions: 24,004,510
Hit Target: 90.97%


ruin trying for at least 1 unit
BJ rounds↓units 20. ruin units 50. ruin units 100. ruin
204.37E-05..
400.004259194..
50.1.32E-101.50E-38
1000.035988799.42E-061.19E-19
2000.058999920.0011232315.15E-10
3000.064288410.00481573.73E-07

*****
for being up more than 1 unit
that requires a different calculation with the same R code
(It is messy right now and not a function. maybe later)

now,
from MY gambling experience and observations...

many casino gamblers think that almost 100% of the time they will be UP at least 1 unit
in any session
well,
ain't so

but feelin' good while gamblin' is good
Sally
Last edited by: mustangsally on Sep 9, 2018
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mstauff
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September 9th, 2018 at 11:06:39 PM permalink
I appreciate all the explanations related to my question about what percentage of sessions a player is ahead in at some point.

I am not good enough with statistics to understand most of the explanations. However, I am not sure the question can be answered. When a player plays short sessions (15 - 30 minutes), it doesn't seem to me that the mathematical calculations come into play. I guess if someone tracked a bunch of short sessions over 10 or 15 years, they might see that the end results match what would be expected from simulations or calculations. But in short sessions of 50 to 100 hands, I really believe it is a matter of playing good basic strategy and just enjoying the company of the people at the tables and having fun and hopefully getting a few good runs now and then as incentive to keep coming back.
OnceDear
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September 10th, 2018 at 1:04:25 AM permalink
Quote: mstauff

I appreciate all the explanations related to my question about what percentage of sessions a player is ahead in at some point.

I am not good enough with statistics to understand most of the explanations. However, I am not sure the question can be answered. When a player plays short sessions (15 - 30 minutes), it doesn't seem to me that the mathematical calculations come into play. I guess if someone tracked a bunch of short sessions over 10 or 15 years, they might see that the end results match what would be expected from simulations or calculations. But in short sessions of 50 to 100 hands, I really believe it is a matter of playing good basic strategy and just enjoying the company of the people at the tables and having fun and hopefully getting a few good runs now and then as incentive to keep coming back.

Short sessions do adhere to the probabilities, but they are the probabilities of small numbers of events, which as you observe are wildly different to long term expectations. You can expect volatile and amusing variations in your session bankroll. That's why most of us play... for the amusement and occasional adrenaline rush... that and the enjoyment of the company of dealers and fellow players.
Those who are motivated by financial profit, are really playing a different game and fall into the categories of wise card counters (and exploiters of other weaknesses) or foolish system players.
If you're enjoying the game, you're already winning.
Psalm 25:16 Turn to me and be gracious to me, for I am lonely and afflicted. Proverbs 18:2 A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
mstauff
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September 10th, 2018 at 5:17:32 AM permalink
I kind of like the chaos of the short run sessions. They are way less mentally taxing and I have found that playing short sessions does not have the bankroll demands of longer sessions.

You are right when you say, if you are enjoying the game, you're already winning. I do enjoy the game and the people I have met along the way as well as the just being in Las Vegas. I have grown particularly fond of downtown Vegas in the last five or ten years. I am always happy when I pick up a month or two long consulting gig in Las Vegas... That gives me time to enjoy the area at a more leisurely pace than a four-day getaway.
Tanko
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September 10th, 2018 at 5:57:56 AM permalink
Quote: mstauff

I guess if someone tracked a bunch of short sessions over 10 or 15 years, they might see that the end results match what would be expected from simulations or calculations. But in short sessions of 50 to 100 hands, I really believe it is a matter of playing good basic strategy ......



You might be better off with a win limit, instead of a time, or hands played limit.

This is a study on the effect of win and loss limits, using a slot machine simulation of 900 players up to 5,000 plays each.

A $100 loss limit resulted in only 7.3% of players winning, and a $76 average loss.

A $100 win limit resulted in 48.3% of players winning, and a $153 average loss.

No win or loss limits resulted in 17.6% of players winning, and a $251 average loss.

A one hour time limit resulted in 35% of players winning, and a $30 average loss.

“Nevertheless, our simulation shows that using win limits can help reduce the average player’s losses and improve the probability a person leaves the casino as a money winner.”
mustangsally
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September 10th, 2018 at 1:43:14 PM permalink
Quote: mstauff

However, I am not sure the question can be answered.

you mean this one
"Based on what appears to be a streak intensive game,
is there a way to calculate the probability of being up at some point in a session that is X period of time long where X is an hour, two hours, etc?"

I agree playing for HOURS is really meaningless
unless U know about how many actual rounds of play were completed.

Quote: mstauff

When a player plays short sessions (15 - 30 minutes), it doesn't seem to me that the mathematical calculations come into play.

well, I 4 1 disagree with you on that 100%

start with a 50 unit bankroll and play a MAX 50 rounds.
what Do you expect to be the probability of being ahead at some point?

the math is easy to do once one knows how (Markov chains)
and the results are even easier to understand.

just because a fair coin flip is a 50% chance to get Heads,
I just flipped 4 Tails in a row

same concept
the probability does not change

Sally
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September 11th, 2018 at 12:06:59 AM permalink
N0 is often the term for the number of hands you need to play to be mathematically guaranteed above 0... for "most" blackjack counters this number is around 70,000 hands. Results will vary pending game conditions (rules, penetration, etc) and the counters advantage (indexes, mistakes per hour, etc, etc).
Playing it correctly means you've already won.
mcallister3200
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September 11th, 2018 at 1:16:35 AM permalink
Deleted
Last edited by: mcallister3200 on Sep 11, 2018
mstauff
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September 22nd, 2018 at 7:11:46 AM permalink
From the week before I ask this question to now, I have played over 10,000 hands of blackjack in many many session playing basic strategy using the 4-8 deck dealer does not hit soft 17 card from Wizard of Odds Website. I tracked every session, every run (run being a streak of winning or losing hands), every bet, every double down, every blackjack, every split, and every result in a very detailed excel spreadsheet. Based on my play I analyzed the percentage of sessions I was ahead at some point using various stop loss values (Originally 7 and as low as four). Over time I refined my gameplay default actions (when to quit session after x wins hands and win runs or loss hands and loss run. I actually played at two different online casinos (Vegascrest and Las Vegas USA). My results were within 2 or 3 percent playing at either online casino.

I found that I was ahead at some point in a session between 75% and 80% of the time.

Over the course of play I finished between 61% and 65% of the sessions ahead, I pushed in between 7% and 8% of sessions, and I lost money in between 18% and 22% of the session. Initially, I was losing between 2.29 units and 3.31 units per session and winning between 1.52 and 1.56 units per session. As I have finetuned my gameplay, the win to lose ration has narrow to the point that it is =/- about 15%.

Playing sessions with a low loss limit definitely narrow the ration of average betting units won to betting units lost. However, a lower loss unit also limits the ability to recover from multiple consecutive losses at the start of a session. There is a fine line between the high and low loss limit in terms of the most advantages to gameplay. In the end, as I have refined gameplay, I find that I hit my loss limit very infrequently. I am typically walking away from a session with a small win and not hitting a specific win or loss limit.

Had I been playing $100 a hand blackjack, my average win per day over the last week would be about $1,000 a day. The only problem with my gameplay is that I need my spreadsheet open to help me make the correct play decision.

At this point, I find myself wondering if I have been extremely lucky, or I am getting expected results based on playing short runs and walking away from a session whenever I am ahead a few bets. Because the results were so similar between the two online casino sites, my inclination is to say that it isn't just luck. However, I have had very few long negative runs. That is not normal. So, my common sense tells me I am mostly on a very lucky run right now.

Comments and thoughts on my experience would be not only welcome, but, appreciated.
OnceDear
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BlackjackLover
September 22nd, 2018 at 7:40:20 AM permalink
Quote: mstauff

Comments and thoughts on my experience would be not only welcome, but, appreciated.

Trust me. It's just luck. Not even extraordinary luck.

This may help

Plug your numbers into this. Substitute your loss limt into 'Starting bankroll'

Probability of Success <= (Starting Bankroll)/(Starting Bankroll + Target Profit)

You'll see that Probability of modest success can be quite high, but at the cost of potentially massive losses from time to time.
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mstauff
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September 22nd, 2018 at 8:27:26 AM permalink
Actually, you just proved my point if I understand your formula correctly. If I start a session with a loss limit of four and my goal is to win two units, my probability of success would be 4/(4+2)=67%.

My approach is that if I can play four sessions a day at $100 a hand with a $400 loss limit, knowing that at some point in every run I have a 75% chance of being ahead, I can win $100 or $200 a day. Your formula says I have a 67% chance of doing that.
OnceDear
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September 22nd, 2018 at 8:48:12 AM permalink
Quote: mstauff

Actually, you just proved my point if I understand your formula correctly. If I start a session with a loss limit of four and my goal is to win two units, my probability of success would be 4/(4+2)=67%.

My approach is that if I can play four sessions a day at $100 a hand with a $400 loss limit, knowing that at some point in every run I have a 75% chance of being ahead, I can win $100 or $200 a day. Your formula says I have a 67% chance of doing that.

Look closer at my formula. It says '<=' not '='. It's only '=' where the house has no edge.
And 66.67% is not 75%

You mix and match your $100s and $200s and pluck 75% out of the air. Here I'll do the calcs for $200. You can do similar for $100 and you'll get the same 0 profit outcome.

So... Take $400 into a casino with the win target of $200 each day

Let's be kind and assume no house edge, but let's be a bit tight and use precise floating point maths.

Each day, P Success = 4/(4+2) = 66.66% recurring. When you succeed, you walk out with $200 profit. When you fail, you walk out with $400 loss.

Let's do it for 3 days. Over that set of sessions, we can easily deal with that 66.6666recurring by saying we succeed 2 days and fail one day ( on average )

Day 1 Succeed... Profit so far $200
Day 2 Succeed... Profit so far $200 + $200 = $400
Day 3 Fail... Profit so far $200 + $200 - $400 =$0


Of course, some sets of days you will win all 3 days and some sets of days you will win none or one. Over hundreds or thousands of sessions, you'll get close to the 2/3 proportion, so closer to 0 profit 0 loss overall.

BUT.
If house edge is 0.5%. that's 0.5% of every dollar you stake, on average... On average, you won't break even you'll tend to lose.

But, it would be fun. $:o) I actually play a bit like this for recreation.
Psalm 25:16 Turn to me and be gracious to me, for I am lonely and afflicted. Proverbs 18:2 A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
mstauff
mstauff
mstauff
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September 22nd, 2018 at 9:03:07 AM permalink
Okay... I am a little brain dead this morning. It is a zero sum gain with no house edge.

The 75% number I was referencing is that in my play of over 10,000 hands, in about 75% of my sessions, I was ahead at some point during the session. I did not win at the end of 75% of the sessions.

However, if I did quit whenever I was ahead, I would have won money in 75% of the sessions. That would have limited my winnings to one unit a session for most of winning sessions though. My assumption before I started this excersice was that I would have large enough losses in the sessions that I was never ahead that my losses in the losing sessions would exceed my winnings in the sessions I won.

By setting a low loss limit, I was trying to limit the large losses.
OnceDear
OnceDear
OnceDear
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September 22nd, 2018 at 9:46:35 AM permalink
Quote: mstauff

Okay... I am a little brain dead this morning. It is a zero sum gain with no house edge.

Correct. In a zero edge game, you will break even on average, regardless of how you wager or what stop losses and win goals you set. You CAN skew the proportion of sessions you win ( eg target profit=1% of bankroll easily achieved, but cost of failure being relatively massive)
Quote:

The 75% number I was referencing is that in my play of over 10,000 hands, in about 75% of my sessions, I was ahead at some point during the session. I did not win at the end of 75% of the sessions.

Your perception of being ahead 75% of the time is reasonable, but has not mathematically accounted for the massive losses that you may have had, and would have had eventually
Quote:

However, if I did quit whenever I was ahead, I would have won money in 75% of the sessions. That would have limited my winnings to one unit a session for most of winning sessions though. My assumption before I started this excersice was that I would have large enough losses in the sessions that I was never ahead that my losses in the losing sessions would exceed my winnings in the sessions I won.

By setting a low loss limit, I was trying to limit the large losses.

You can limit the frequency of large losses, but your trade off is that those losses must be potentially and proportionally much larger.
Psalm 25:16 Turn to me and be gracious to me, for I am lonely and afflicted. Proverbs 18:2 A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
billryan
billryan
billryan
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September 22nd, 2018 at 10:19:26 AM permalink
Why limit your bets to $100? $1,000 bets will get you rich ten times faster.
The older I get, the better I recall things that never happened
unJon
unJon
unJon
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September 22nd, 2018 at 10:38:16 AM permalink
Quote: billryan

Why limit your bets to $100? $1,000 bets will get you rich ten times faster.



Heat comes too quickly spreading $1k to $15k.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
mstauff
mstauff
mstauff
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September 22nd, 2018 at 4:37:49 PM permalink
Limiting bet to $1000 would assume I had a $1000 and enough bankroll to ride out the ups and downs of the game at that level. For my testing, all bets have been $1. I was going through this exercise to try to understand what the probability of being ahead at some point in a session based on a selected loss limit. At the time of starting this process, I had no idea how I would use that information. Once I determined that I was consistently ahead in about 75% of the sessions based on a loss limit of 7 units, I started to play around with how to take advantage of that. So, far, I have been successful. However, I cannot explain why. As I stated several posts ago, it is very possible that I am just lucky in the hands I am receiving right now and success will be temporary.
familyguy96
familyguy96
familyguy96
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September 22nd, 2018 at 7:42:53 PM permalink
Always bet table max.
ChumpChange
ChumpChange
ChumpChange
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September 23rd, 2018 at 4:38:05 AM permalink
You could buy-in for 20 units at a $10 table for $200, double your bet if you're $30 or more ahead, and call it a winning session if you double your buy-in. You'll lose a bit rolling over that single-bet/double-bet borderline, but if you're on you're way up with no way down, it shouldn't matter. Probably should win 6 sessions before you increase your buy-in by 50% over 4 sessions.
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