First of all, I did a little research and found that the numbers I used above were overall probabilities, not probabilities for the first hand only. More accurate numbers are:
Win = 43%
Loss = 49%
Tie = 8%
As more hands are played from the shoe these numbers will approach my initial 43/48/9 estimates, but the numbers above pertain only to the first hand of the shoe.
tedloc said:
If you do this 11 times, sometimes you will tie. You can't consider this a loss after all is said and done.
That’s exactly my point. You can’t consider it a loss because the player did not lose any money, but you can’t consider it a win because the player did not win any money either. That is why we ignore the pushes and only use the actual wins and losses. The question only asks about wins and losses so pushes are meaningless.
tedloc said:
With a .05% house edge and the odds being 101 to 100 that means the house will win 101 and not win 100.
In this case, the house edge does not dictate the odds because the results are skewed by doubles, splits, surrenders, and 3:2 blackjacks. The odds of 101:100 will give the house a 50.25% chance of winning the first hand, which is not accurate. The house will win more hands than that but the house edge is decreased because we are winning more than 1 unit on many of the hands we win while often only losing 1 unit (or half of a unit in some cases) on the hands we lose. That is why you can’t use the house edge directly to calculate the odds in this case.
tedloc said:
I think the question is, "What are the chances, the house wins the hand on a fresh deck".
There is about a 54% chance that the house will win the first hand, which gives odds of 1.17:1 (excluding ties) or 1.12:1 (including ties). Simulation results using CVCX support this.
If we reword the question a few times you can see that including pushes will give us much different results:
“What are the changes that the house will
win or push on the first hand?”
49% + 8% = 57% = 1.33:1
“What are the chances that the player will
win or push on the first hand?”
43% + 8% = 51% = 1.04:1
As Ken said, blackjack is a messy game mathematically. Hopefully some of the mess I've made will clear things up.
-Sonny-