Simple Math

But I am a simpleton. tried to figure out percentage for a player getting 21 on a hand of split ACES, one card each. Multiplied 50x49
and got 2450 possibilities, then 34x33 for possibilities without a 10 value. 54% seemed reasonable. Then I decided to do it for a value of 20 and got 15%. I will soon be over 100%. Help !!!

50 cards left, the next two cards drawn have to be ten. there are 16 tens left in the deck.

16/50 * 15/49 = 0.09795918367346938775510204081633

I get a little over 1 chance in 10

Considering your starting place is two aces (1 chance in 221), that's a pretty rare thing to pull off.

Hold on, 16 cards are 10's, 32 are not, I get two shots at getting at 10, which is a 2 to 1 shot . this can not be 10%.

Quote: Buzzard

Hold on, 16 cards are 10's, 32 are not, I get two shots at getting at 10, which is a 2 to 1 shot . this can not be 10%.

Did I read it wrong? I thought you wanted to know what the probability is of hitting both tens. You actually want to know what the probability is of getting a ten on at least one hand?

Sorry if I did not state it right. Yes a 10 value on either hand, Then a 9 on either hand. Sorry I misled you !

Quote: Buzzard

Sorry if I did not state it right. Yes a 10 value on either hand, Then a 9 on either hand. Sorry I misled you !

Okay, we'll go with that:

The chances of hitting at least one hand of 21 with spit aces is
what's left of the probability of drawing something other than a
ten on both cards.

50 cards left, 34 are not tens
1 - ((34/50) * (33/49)) = 0.54204081632653061224489795918367

Better than half, 54% I like those odds.
--------
The chances of hitting at least one hand of 20 with spit aces is
what's left of the probability of drawing something other than a
nine on both cards.

50 cards left, 46 are not nines
1 - ((46/50) * (45/49)) = 0.15510204081632653061224489795918
--------
But I think you meant 20 or better so..

The chances of hitting at least one hand of 20 or 21 with spit aces is
what's left of the probability of drawing something other than a
nine or ten on both cards.

50 cards left, 30 are not tens or nines
1 - ((30/50) * (29/49)) = 0.64489795918367346938775510204082

Nearly two thirds.

Here is my problem. 10 =54 % no problem. But if 9 equal 15%, the wouldn't 8, 7, 6, 6, 5, 3 ,3 equal 15% ???

Ooops light just came on I think. was taking that 15% too literal. Forgot can get a 9 with a 10 value also. 64% makes sense now. I was thinking 8,7,6,5,4,3.3 all had to be 15% also. I am a DUMMY !

Thanks.

Quote: Buzzard

Forgot can get a 9 with a 10 value also.

ding!

Quote: Buzzard

Thanks.

yw :)