Hi,

This is probably very easy, but I just don't know how to figure it out.

If I play 10 hands of blackjack at $1 a go, have a $10 roll and the house has a 3% edge, what is my risk of ruin?

what is my risk of ruin if I do this 20 days in a row and never replenish my bankroll? I guess that the same as asking: "whats my risk of ruin playing 200 hands with a $10 roll at a $1 stake"

Can you explain how to do it? I'd like to learn how to figure this out for myself.

Are their any useful calculators online to figure out RIO?

Help will be very much appreciated thanks.

Of course you do this because you have to, not because its a good idea since its a negative EV game right?

You have to define your objective here.

You will find out for example that if the number of hands to play is big (or the total $ amount i mean required to bet overall activity) it may not make sense to play 1$ at a time.

So give us the objective here and we can answer.

Are you trying to maximize the chance to survive 200 hands of BJ at 3% deficit or to maximize the chance to reach a certain target and stop playing?

This is an interesting problem to study depending on your objectives here.


The solution for the risk of ruin if you bet 1 unit at a time and you have p chance to win and 1-p=q chance to lose is;

((q/p)^a-(q/p)^z)/((q/p)^a-1) if you start at position z bet units and want to reach a and stop or 0 and bust.


Blackjack has standard deviation bigger than 1 i think near 1.14 per hand and its not exactly 1 bet unit in p vs q form but can be modeled by such +100% vs -100% game for a given edge and standard deviation by selecting the correct bet unit and probability of win per hand.
However here you are playing until bust or until you complete 200 hands without a clear target.

So just define a bit more what is going on here and what is the most important objective.

Thanks for your post, I haven't checked back here in a while (I'd kinda given up hope for a reply)

It was to do with an online casino offer, You had to wager £10 (£1 being the minimum stake allowed in a day) to get a free spin on a slot which a guaranteed a win of between 20p and £50 slot bonus (at the time of posting I didn't realise it was a "slot bonus", I thought it was just cash you were immediately allowed to withdraw so now that adds a whole new big variable! But I don't mind ignoring that for the movement just so I can get my head around the first question which I'm finding very tough to understand).

Now I'm struggling to remember why I asked the chances of lasting 20 days because it seems its an on going offer with no deadline but again for the purposes of me getting my head around the problem we could keep it at 20 days if you think thats that not a terrible idea.

If you wanted (and if its even possible for you to look at this gambling website from where you are) the promotion is offered by a site called bwin.com.

As a side I have been told online BJ in the uk usually the house only has a .5 - 2% edge with 1% being fairly standard. (my sources on this could be wrong I'm not 100% on that).

Thanks for your time

http://www.gamesblackjack.org/strategy/risk-of-ruin.php

The table here implies it's a little above 50% risk of ruin over 200 hands.