Chance of winning a hand

In a game of Blackjack, assuming you follow optimum strategy, what is the % chance of winning a hand?

I don't mean the EV.

Suppose you play 10,000 hands, following optimum strategy. For each hand you just mark down whether you win, lose or push, and ignore the amount of money. If you beat the dealer, it's 1 in the wins column. If you double down and win, it's still just 1 in the wins. Get Blackjack, and it's still 1 win. How many hands can you expect in each category?

Yes, I googled it. Every calculation I've seen shows the EV, which isn't what I want.

If it makes a significant difference, say 8 decks, dealer stands on soft 17, no surrender.

Googled "percentage hands win and loss in blackjack basic strategy" and it came back with the %'s...

Quote: RonMiel

In a game of Blackjack, assuming you follow optimum strategy, what is the % chance of winning a hand?

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Ron,
I believe the answer you seek is at
https://wizardofodds.com/ask-the-wizard/blackjack/probability/

Quote: wizardofodds.com

According to my blackjack appendix 4, the probability of an overall win in blackjack is 42.22%, a tie is 8.48%, and a loss is 49.10%. I'm going to assume you wish to ignore ties for purposes of the streak. In that case, the probability of a win, given a resolved bet, is 46.36%.

That was quoting from https://wizardofodds.com/games/blackjack/variance/ which I think was based on 6 decks. There won't be much difference for 8 decks or even infinite decks, maybe the second decimal place.

If you propose to use this knowledge in some progressive system, give it up now.

Quote: RonMiel

In a game of Blackjack, assuming you follow optimum strategy, what is the % chance of winning a hand?

I don't mean the EV.

Suppose you play 10,000 hands, following optimum strategy. For each hand you just mark down whether you win, lose or push, and ignore the amount of money. If you beat the dealer, it's 1 in the wins column. If you double down and win, it's still just 1 in the wins. Get Blackjack, and it's still 1 win. How many hands can you expect in each category?

Yes, I googled it. Every calculation I've seen shows the EV, which isn't what I want.

If it makes a significant difference, say 8 decks, dealer stands on soft 17, no surrender.

link to original post

Unanswerable question unless you tell us how to handle splits.

I have always found these charts to be useful.

And the summary: Around 42% chance of the player winning a hand, when following basic strategy.

Quote: OnceDear

Quote: RonMiel

In a game of Blackjack, assuming you follow optimum strategy, what is the % chance of winning a hand?

link to original post

Ron,
I believe the answer you seek is at
/ask-the-wizard/blackjack/probability/

That was quoting from /games/blackjack/variance/ which I think was based on 6 decks. There won't be much difference for 8 decks or even infinite decks, maybe the second decimal place.

If you propose to use this knowledge in some progressive system, give it up now.

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Thank you for this. No progressive system, I'm just involved in a discussion on another forum.

One question, does the table have an omission? Isn't a win of 2.5 possible, where you split aces, get blackjack on one, and win the other?

Quote: RonMiel

Thank you for this. No progressive system, I'm just involved in a discussion on another forum.

One question, does the table have an omission? Isn't a win of 2.5 possible, where you split aces, get blackjack on one, and win the other?

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Generally no. If you split aces and draw a ten or face, it counts as 21, not Blackjack.

That makes sense. It's been a while since I played, so I forgot that point.

Quote: RonMiel

One question, does the table have an omission? Isn't a win of 2.5 possible, where you split aces, get blackjack on one, and win the other?

link to original post

Quote:

For each hand you just mark down whether you win, lose or push, and ignore the amount of money. If you beat the dealer, it's 1 in the wins column. If you double down and win, it's still just 1 in the wins. Get Blackjack, and it's still 1 win.

A blackjack counts as 1 win. A 6:5 blackjack counts as 1 win. A winning 2 card 21 counts as 1 win.

Adjusting for a 3:2 payout to count as more than 1 win gets into EV; I believe the initial question specifically attempted to avoid that.

You can potentially win 8x your initial bet. You can usually split three times for up to 4 hands and if the casino allows double after splits, you can win 2x on each hand.

Quote: jackace

You can potentially win 8x your initial bet. You can usually split three times for up to 4 hands and if the casino allows double after splits, you can win 2x on each hand.
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I give answers in this article for 2 and 6 decks.
https://www.888casino.com/blog/blackjack-tips/blackjack-combinatorial-analysis-by-simulation