For all you math guys out there

[Clayman]

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]

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]

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]

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]

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]

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.