I need help with the math

**Dean** · 05-31-2016, 03:12 PM

averages and percentages are rounded.

Dealer shows a 4, 5 or 6. Dealer has a 42% chance of busting. Player has a 12 with a 31% chance of busting or a 13 with a 38% chance of busting. Why is it considered the proper move to not take a card with a 12 or 13? Can someone show me the math?

Also how does one reconcile the odds of the dealers percentage to the players percentages of busting or winning? I am not sure how to do that.

Thanks.

RS · 05-31-2016, 03:26 PM

I don't know how to do the math, but consider this: hitting a 12 and catching an ace through 4 does not improve your hand. Only a 5-9 improves the hand.

**Norm** · 05-31-2016, 03:36 PM

If there are multiple players, you have no idea what chance the dealer has of busting. Most useless stat in BJ.

In any case, you have to play first. If you bust, you lose. It won't matter what the dealer does.

**Norm** · 05-31-2016, 05:13 PM

The point is that the dealer bust rate depends on the number of players because as the number of players increases, the likelihood that the dealer must hit increases. Which is to say that dealer bust rate, which is so very often used in voodoo systems, is a silly stat.

**ZenMaster_Flash** · 05-31-2016, 05:22 PM

Note that the dealer bust rate (28.5% overall) hardly changes with the composition of the remaining cards (True Count)

Neophytes and those saddled with snake-oil panacea systems never seem to realize this.

Nor do they understand that they will never find a "count" where they are favored to win an upcoming bet.

**Norm** · 05-31-2016, 05:37 PM

Suppose there is one player. If that player busts or gets a BJ, the dealer will not have a chance to bust. Suppose there are seven players. The dealer will nearly always have to play her hand because the odds of ALL players busting or getting a BJ are small. I really don't like the dealer bust rate stat as it depends on the number and strategy of players. In any case, you must look at all following plays. So many times I've seen "math" that assumed the player or dealer can only hit once.

**Bodarc** · 05-31-2016, 05:37 PM

Hi Dean

I don't know why this is in the disadvantage forum. There are some things you just take as fact. Basic strategy is one of them because it has been analyzed, simmed and beat to death by some of the greatest minds. You take the charts and memorize them.

Now, if you want to know how basic strategy is developed in about 15 minutes by the Wizard of Odds using Excel, go to this URL:

https://www.youtube.com/watch?v=jCF-Btu5ZCk

Hope this helps

**Norm** · 05-31-2016, 05:42 PM

It's a decent question that he posted in this forum. I'll move to the general forum.

**Three** · 05-31-2016, 07:34 PM

Originally Posted by Dean

Dealer shows a 4, 5 or 6. Dealer has a 42% chance of busting. Player has a 12 with a 31% chance of busting or a 13 with a 38% chance of busting. Why is it considered the proper move to not take a card with a 12 or 13?

Using you numbers:
If you hit:
1) You lose 31% of the time no matter what.
2) Of the 69% of the time you don't lose before the dealer plays you lose 58% of the time that the dealer then makes a hand for an additional 40.2% of the time.
3) Add the two and if you hit you lose 71.2% of the time and you will also push some made hands.
So you will win (100%-71.2%-the push percentage) or 28.8%-pushes
4) Taking out pushes the win versus loss percentage is (28.8%-pushes)/(100%-pushes)
5) The result of the faction in 4 is less than 28.8% if there is at least 1 push. How much less increases as pushes increase.

If you stand:
1) You lose the 58% of the time the dealer doesn't bust and win 42% of the time.
2) The win versus loss rate is 42% since there is no pushes.

Since 42% win is more than (28.8 or less)% win you stand.

**LoneWoLF** · 05-31-2016, 07:49 PM

Originally Posted by RollingStoned

I don't know how to do the math, but consider this: hitting a 12 and catching an ace through 4 does not improve your hand. Only a 5-9 improves the hand.

A vastly overlooked thing though is an A through 4 might not improve the hand, but you've just taken another small card that the dealer couldve used to make his hand.

**Three** · 05-31-2016, 07:50 PM

Originally Posted by Boz

No, he's not going to lose 58% of the time because it is now impossible for the player to bust (you already subtracted that) AND he's always taking a card.

Yep. My bad. The math needs more info for that part but that is the mathematical method. you would need to know the percentage you made a hand better than the dealers made hand.

**Three** · 05-31-2016, 07:59 PM

Well pushes aren't really that simple to deal with when figuring advantage. I mean if you are at a disadvantage the more pushes the better but at an advantage you want a high frequency of resolved bets in an ideal world. You can't include them without context and understand their effect. You can't eliminate them and understand the big picture.

**Tarzan** · 05-31-2016, 09:09 PM

I'm kind of agreeing with Norm on the idea of driving yourself crazy for a relatively meaningless statistic. When someone says, "But I want to understand the math of why you do this or that... so it all makes sense to me". The what is more important than the why. Knowing exactly what to do is more critical than knowing the why behind doing it. Sure, you can locate all the gory details of the why, heaping loads of data, go over it all to gain a thorough knowledge of it all and then you can say, "Whew, I feel better now", but the what part is unwavering throughout the process. It remains the same whether you know the math behind it or not. Follow the parameters for basic strategy, any applicable parameters of your method in terms of index play, etc. first and foremost. What you are supposed to do is what you are supposed to do regardless of the dealer bust rate when you have 12vs5 or whatever. This is why this is a relatively meaningless statistic and there are much more important mathematical aspects to examine if you are determined to learn the why of it all.