For all you math guys out there

Bruno712

Banned User
Joined
Mar 15, 2004
Location
Boston, MA
Excellent observation GM

GrandMaster said:
I have a question. What happened if you busted?

I only play private games and some if not most of the games were played at casinos that flip their hole card after each hand regardless of whether or not the player busts. Now you have me curious as to how many I busted out on. I emailed Kyle to add this to his analysis. He replied that he already had.

DOHC,

In order to conserve time (mine), please read all the posts.
 

GrandMaster

Dormant account
Joined
Jan 21, 2004
Location
UK
Bruno712 said:
I only play private games and some if not most of the games were played at casinos that flip their hole card after each hand regardless of whether or not the player busts. Now you have me curious as to how many I busted out on. I emailed Kyle to add this to his analysis. He replied that he already had.

Still the problem remains. If the dealer has less than 17 with the hole card, then you don't know what would have happened if he had finished the hand. The nice thing about the 30% probability of dealer high hands I mentioned is that it depends only on the number of decks and whether the dealer hits or stands on soft 17, not on the player's strategy, but this 30% is calculated over all hands. I think the proportion dealer high hands when the player does not bust would be slightly lower, but even if I am wrong the difference would not be big enough to explain the 96% you observed.
 

Clayman

Dormant account
Joined
Mar 12, 2004
Location
Pennsylvania, USA
GrandMaster said:
What happened if you busted? Unless you are playing at a multi-player table, in most software versions the dealer won't play out his hand if you bust, so you won't know what would have happened. How were these hands recorded? If the dealer doesn't always play out his hand, counting dealer 20's, 21's and BJ's is probably not the best thing,

When we use that 30% number, are we not assuming that those are probabilities of dealer final-hand totals, totals that are only counted when the player does not bust or has a tied BJ? It would seem as if dealer totals are inapplicable when a player busts or has a winning BJ since the dealer does not play out his hand.

I guess it occurred to me I've never seen a dealer final-hand table that had any totals of <17 listed.

On the other side of the coin, we wouldn't count player hand-totals as final-hand totals when the dealer has untied BJ's, would we?

In other words, in 100,000 dealer upcards we wouldn't really expect 30,000 dealer final-totals of BJ, 20 or 21, assuming we could see both dealer cards, would we?

Probably confusing myself after too much 19th hole.
 

fortyoz

Dormant account
Joined
Apr 30, 2004
Location
Moravia, Costa Rica
Regarding the starting post in this thread, I do not think it is that unlikely.

I live in Costa Rica and play regularly, this happened about three times, I played at 3-4 different casinos, up about $4,000 for the day, go to this one casino were I know I lose but for some reason just want to get them, go in.. they place the 4 decks in front of me, all the cards are there.

Shuffle up and go, there is no dealer hold card so my play "affects" that, but they pull great hands out of crappy ones all the time and I lose all my winnings and then some. I know they aren't cheating, and if you lose at statistical blackjack data, streaks like that are quite common, and i've seen them a lot.

What I find helps in those situations is to have a good bank roll available, I can go down $7,000 and be sure that i'll get it back, as long as I have a few grand in the pocket, but when you spend it all and have to get up and walk away to a loss like that, blows.

I play sort of progressive and the only time I get hurt is not backing down on the losses, i'm good at going up real high after winning, but do the same after losing a few and it goes quickly.

I also have a question, when I play in PlayTech casinos I notice blackjacks come sequentially, could just be something weird but when i'm playing i'll double my bet after getting a BJ and 70% of the time another one comes next, weird :)
 

Clayman

Dormant account
Joined
Mar 12, 2004
Location
Pennsylvania, USA
fortyoz said:
when i'm playing i'll double my bet after getting a BJ and 70% of the time another one comes next :)

Don't try this at home, kids. It's very difficult to do, unless your an expert.

Fortyoz - suggest table max bet after every BJ so you can retire sooner. :)
 

GrandMaster

Dormant account
Joined
Jan 21, 2004
Location
UK
Clayman said:
When we use that 30% number, are we not assuming that those are probabilities of dealer final-hand totals, totals that are only counted when the player does not bust or has a tied BJ? It would seem as if dealer totals are inapplicable when a player busts or has a winning BJ since the dealer does not play out his hand.

I guess it occurred to me I've never seen a dealer final-hand table that had any totals of <17 listed.

On the other side of the coin, we wouldn't count player hand-totals as final-hand totals when the dealer has untied BJ's, would we?

In other words, in 100,000 dealer upcards we wouldn't really expect 30,000 dealer final-totals of BJ, 20 or 21, assuming we could see both dealer cards, would we?

Probably confusing myself after too much 19th hole.

Let's get this thread back on track. Imagine that the dealer always plays out hand completely, like he does at Crypto multi-player tables, even if all the players have busted or have untied BJ. This means more than just showing the dealer's hole card, since the dealer may have had less than 17. Then the probability of a dealer high hand (20, 21 or BJ) is 30%. (This is remarkably accurate, for an 8 deck, S17 game the exact figure is 29.99985%.) When you are calculating the optimal strategy, you assume that the dealer always plays out his hand and you have to calculate the probabilities of all the possible outcomes.

Obviously, knowing the dealer's up card and the player's cards changes the probability, but averaging it over all possible dealer up cards and player's cards weighted with the appropriate probabilities is the same as if the dealer just played his hand from the top of the deck, without dealing any cards to the player, which provides an easy way of calculating it. Another great thing about this probability is that it is not affected by the player's strategy.
 

Bruno712

Banned User
Joined
Mar 15, 2004
Location
Boston, MA
I have one figure back

The percentage of dealer high hands (20, 21 and BJ), dealt and drawn, on all minimum and 2 x minimum bets was 30.96345%.

Still waiting for the player bust figures.
 

fast_eddie

Dormant account
Joined
Dec 14, 2003
Bruno712 said:
What are the chances of this occuring in a clean game of BJ?

Playing single hand BJ, (advertised at 6 decks I believe) playing approximately 100 hands while betting $25/$50 dollars, holding my own then maxing out to $400 and losing 9 straight hands. Not only losing, but losing to either a dealers BJ or a dealer 21. Then doing the same thing the next day and lsoing 6 to a BJ or 21. The next day 7 times (2 pushes) to a BJ or 21.


Chances are real good when the casino cheats......Play land based casinos only. Drop in a disc or play in fun mode only. The only way to beat um is to stop paying at their crappy casino.
 

Clayman

Dormant account
Joined
Mar 12, 2004
Location
Pennsylvania, USA
Bruno712 said:
The percentage of dealer high hands (20, 21 and BJ), dealt and drawn, on all minimum and 2 x minimum bets was 30.96345%.

So far, so good, I'd say. Keep us posted. (Do you know how many hands these are - just curious.)
 

GrandMaster

Dormant account
Joined
Jan 21, 2004
Location
UK
Bruno712 said:
The percentage of dealer high hands (20, 21 and BJ), dealt and drawn, on all minimum and 2 x minimum bets was 30.96345%.

Still waiting for the player bust figures.

This figure is much more reasonable, but the problem is that I don't know what the actual probability is and I cannot calculate it easily. If you give me the number of hands involved then I could test how likely it is that the probability of dealer high hands is the same for small bets and for the table max.

What I would really like to see is the number of hands played at each betting level, the number of units won/lost, and the number of hands won, tied and lost, because I could test these numbers easily.
 
Top