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Holgininho
Joined: 01 Jan 2007
Posts: 468
Location: Essen
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 Posted: Fri Aug 24, 2007 4:49 pm Post subject: Blackjack: Probability of losing that much... |
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Actually I believe this post belongs partly in VRR, but I'm really interested in finding out how likely this is:
I've played 1995 hands of black jack at an online casino, the average bet size was $8.35. I've played with $10 bets most of the time and $5 bets some of the time. Most of the time I've played three hands at the same time against the dealer's hand (I don't know if this is important). I've wagered $16658 - and lost $896.
The game was Single Deck Black Jack. I've used basic strategy, and the house edge should be 0.26 %.
Now, how do I calculate how likely it is to lose that much money while playing? How likely is it if I assume I have made mistakes that result in a higher house edge (say 2 %)?
Fortunately I received $800 of bonus money, so I didn't really lose much, but I think that was one of the most frustrating experiences in my life. 
Edit: beatingbonuses.com has a return/variance calculator. According to this my expected gain was $730 and my chance to make a gain was over 90 %. Naturally, I thought my chance of success was even higher. 
The only good thing about this is that it really helped me to understand how easily a downswing can happen - in poker there is always the chance that bad play is one of the reasons of your losses. In Blackjack this isn't the case - and still you can lose so much in the short term... |
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chrisjp
Mr. Lovable
Joined: 03 Jun 2004
Posts: 5014
Location: Round Rock, TX and Las Vegas
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| Posted: Fri Aug 24, 2007 8:34 pm Post subject: Re: Blackjack: Probability of losing that much... |
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| Holgininho wrote: | | Most of the time I've played three hands at the same time against the dealer's hand (I don't know if this is important). |
This dramatically increases variance because players at a table tend to win and lose together since the dealer's total is common to all 3 of your hands.
Chris |
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Holgininho
Joined: 01 Jan 2007
Posts: 468
Location: Essen
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| Posted: Sat Aug 25, 2007 4:57 am Post subject: Re: Blackjack: Probability of losing that much... |
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| chrisjp wrote: | | Holgininho wrote: | | Most of the time I've played three hands at the same time against the dealer's hand (I don't know if this is important). |
This dramatically increases variance because players at a table tend to win and lose together since the dealer's total is common to all 3 of your hands.
Chris |
I thought variance would be lower if I bet $5 on 3 hands against the dealer's hand than if I tripled the bet size and played only one hand (can this sentence be correct? It looks horrible...).
The numbers above were calculated for playing three hands.
The most frustrating thing about this whole bonus chase was that I lost $460 while wagering the last $2000. This isn't even within two standard deviations from my expected return (at least this is what the calculator tells me). |
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the_hawk
Chelsea FTW!
Joined: 13 Jul 2005
Posts: 4449
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| Posted: Sat Aug 25, 2007 6:52 am Post subject: Re: Blackjack: Probability of losing that much... |
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| Holgininho wrote: | | I thought variance would be lower if I bet $5 on 3 hands against the dealer's hand than if I tripled the bet size and played only one hand (can this sentence be correct? It looks horrible...). |
That is, of course, correct. You have to compare like with like. In ascending order of variance:
Single hands of bet size X < 3 hands at once of size X << single hands of size 3X.
Wizardofodds is your friend here. |
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the_hawk
Chelsea FTW!
Joined: 13 Jul 2005
Posts: 4449
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| Posted: Sat Aug 25, 2007 6:55 am Post subject: Re: Blackjack: Probability of losing that much... |
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| Holgininho wrote: | | The most frustrating thing about this whole bonus chase was that I lost $460 while wagering the last $2000. This isn't even within two standard deviations from my expected return (at least this is what the calculator tells me). |
It's a given of the casino bonus chaser (a fallacy, but psychologically a given nonetheless) that the last bit of wagering requirement to finish a bonus results in substantial loss. |
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chrisjp
Mr. Lovable
Joined: 03 Jun 2004
Posts: 5014
Location: Round Rock, TX and Las Vegas
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| Posted: Sat Aug 25, 2007 8:59 am Post subject: Re: Blackjack: Probability of losing that much... |
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| Holgininho wrote: | I thought variance would be lower if I bet $5 on 3 hands against the dealer's hand than if I tripled the bet size and played only one hand
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Absolutely true, sorry if I was confusing. It certainly would be lower to play 3 hands of $5 per hand than one of $15. But it would be better, although take a lot longer of course, to play $5 per hand. By better I mean the standard deviation would be lower. Hawk said it all. And Wizard of Odds does have a lot of great stuff in it. Appendix 4 in the Blackjack part addresses this topic..
Chris |
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Holgininho
Joined: 01 Jan 2007
Posts: 468
Location: Essen
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| Posted: Sun Aug 26, 2007 2:47 am Post subject: |
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| Thank you, I'll take another look at the Wizard of odds. I find the site layout quite confusing, so I sticked to the material at beatingbonuses, which doesn't go into much depth. |
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Bugsbunny
Wascally
Joined: 07 Apr 2004
Posts: 7723
Location: Drinking Carrot juice
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| Posted: Sun Aug 26, 2007 9:07 am Post subject: |
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| chrisjp wrote: | | Holgininho wrote: | | Most of the time I've played three hands at the same time against the dealer's hand (I don't know if this is important). |
This dramatically increases variance because players at a table tend to win and lose together since the dealer's total is common to all 3 of your hands.
Chris |
No, this doesn't increase variance. What it does do is increase your actual bet size, but reduce variance on that increased bet size (that's not exactly what happens, but it's close enough for an analogy).
In reality if you're counting you want to play 1 hand when the deck is bad and multiple hands when it's good. (and yes I realize that this is singl;e deck meaning that they shuffle after each hand, or at least I suspect they do).
The one thing that playing multiple hands will do is give you better information for playing adjustments, but you won't gain enough to offset the house edge.
I have to dig up the exact formulas - it's been a LONG time. But I think that co-variance runs at about .6.
Are you sure that you're playing the correct Basic Strategy for the rules in play? And are you sure you're playing it correctly?
(just checking).
The multiple hands, sometimes, complicate things a bit but let me see what I can come up with, like I said I have to dig up some formulas. By the way what are the EXACT rules in play? |
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Holgininho
Joined: 01 Jan 2007
Posts: 468
Location: Essen
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| Posted: Sun Aug 26, 2007 11:06 am Post subject: |
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I'm not exactly sure I'm playing correctly. I'm using a strategy table from beatingbonuses. Namely this one:
Link.
It doesn't account for playing multiple hands, and I can't do it on my own.
I played at Victor Chandler Casino, and the deck is indeed shuffled after each hand. The exact rules are:
- Dealer stands on soft 17
- Dealer doesn't peek for Blackjack
- Double on 9 - 11
- No double after split
- Only draw once to split aces
- No surrender
According to beatingbonuses.com this should result in a house edge of 0.26. I assume I can read the table correctly, but make a mistake here and there, mainly because I click too fast. |
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