How to calculate being up 5 units after 15 hands

This is a simple premise I'm trying to calculate however the mathematics are getting increasingly.

My question is assuming flat betting of one unit, starting with a bankroll of 5 units total, and playing a total of 15 hands, what are the odds that at SOME point in those 15 hands I will be up 5 units. Thank you so much and if it isn't too much trouble please show your work as not just curious about the answer but also how you came to it. Thanks!

Quote: michael.rinaldi

This is a simple premise I'm trying to calculate however the mathematics are getting increasingly.

My question is assuming flat betting of one unit, starting with a bankroll of 5 units total, and playing a total of 15 hands, what are the odds that at SOME point in those 15 hands I will be up 5 units. Thank you so much and if it isn't too much trouble please show your work as not just curious about the answer but also how you came to it. Thanks!

What game?

Blackjack. Thanks!

Quote: michael.rinaldi

Blackjack. Thanks!

It will matter for the calculation, how many decks and what rules are in use. Tell us as much as you can about that.

Sure and again thank you so much for helping. I'm really looking forward to your answer.

6 decks
Splitting pairs up to four times
Resplitting Aces but you only get one card after splitting Aces
Doubling after splitting
Natural blackjack pays 2:1

Thanks again

Quote: michael.rinaldi

Sure and again thank you so much for helping. I'm really looking forward to your answer.

6 decks
Splitting pairs up to four times
Resplitting Aces but you only get one card after splitting Aces
Doubling after splitting
Natural blackjack pays 2:1

Thanks again

Does the dealer hit or stand on a soft 17?

On what hand totals can you double?

And please verify blackjack.pays 2:1? That's unusual. Or is this not a real-world game?

EDIT : I did some looking at risk of ruin, and I must direct you to what the Wizard says about calculating it here:

https://wizardofodds.com/games/blackjack/appendix/12/

I myself do not know how to do the calculation you want, but I do know that one would have to know the questions above in my last several posts to provide an accurate answer. I'm afraid you may not get an answer, or perhaps an answer without a formula, based on the difficulty of the problem.

Just spitballing, but within the parameters you set.
If you win your first bet, you need to win four more in a row to get up five units.
If you lose the first hand, you need to win six in a row be up five units.
The chances of you having a five or six hand winning streak in only fifteen hands are very low. Each push works against you as it reduces your opportunity.
I don't know how to calculate the odds, but basic knowledge says the odds are pretty low. You have less than a fifty percent chance of being up even one unit if flat betting. In order to be up five units at the end of fifteen, you can only lose a maximum of five of the hands. Every push lowers your chances as well. Blackjack and splits enter into the equation, but I will guesstimate the answer would be less than 20%, and probably much lower.
As already mentioned, most BJs pay either 3-2( the good ones) or 6-5( bad ones).
Not 2-1.

Good point about 2:1, yes, this is not a cash game I'm basing this on. It is a tournament environment where you are competing against all players at all tables. Having said that I'm thinking if one can double their bankroll that will put me in a good position to win. So, let me clarify the rules again as I got them wrong.

BJ pays 2:1
No double after splitting
Dealer hits soft 17
No insurance
Double on any two cards

I tweaked the information below to calculate the odds of winning at least 10 hands of 15.

http://

math.stackexchange

.com

/questions/800997/flip-a-coin-6-times-what-is-probability-of-at-least-4-heads?rq=1

I know I'm losing out on the specifics taking into account the aforementioned rules however I'm pretty sure the 2:1 blackjack makes the game a EV(+) game and if that's the case perhaps I don't need to differentiate the difference between "being up 5 units at SOME point" vs "being up 5 units at the end of 15 hands". Subtle difference between the two but that was where I was curious how one could figure it out.

Ohhh...and based on the website about my calculation was a 15% of ending up at least 5 units after 15 hands so you were right Billryan. Very nice.

Again, still curious how to tweak the formula to calculate "Up 5 units AT SOME point" vs "after 15 hands". Reason being once I'm up 5 units in the tournament I would simply sit on my lead. Thanks again everybody for the time/effort.
m

Most tournaments I have played in have a minimum bet each round. If you are abetting one unit, you won't be able to slow play.
If you went all in on the first hand and won, you'd have a better than 50% chance of finishing plus 5 or better. Offhand, that's a play I would simulate.

Quote: michael.rinaldi

Again, still curious how to tweak the formula to calculate "Up 5 units AT SOME point" vs "after 15 hands". Reason being once I'm up 5 units in the tournament I would simply sit on my lead. Thanks again everybody for the time/effort.
m

My rule of thumb will give you an approximate answer
https://wizardofvegas.com/member/oncedear/blog/#post1370
Basically need to know what bankroll you are putting at risk and what target profit you want to achieve before going bust.