Bankroll Management and When to Walk Away

Hi everyone! Brand new to the community but have scoured the pages of WoV and WoO for years; love the content and helpful information from all.

I have a guest that plays blackjack at the casino where I work and have grown to establish a decent relationship with the person. When they play, they only play for so long as it takes them to win 6 betting units above their initial buy-in amount (i.e. cashing out at $650 with a $500 buy-in while betting $25 units), and then they walk. I've seen this person begin at $25 bets, and work their way up to $200 bets in the matter of a couple months.

My question is, what is the probability that this individual will lose their session (buy-in amount totally wiped out) before achieving a 6-unit profit? Assume that:

- the buy-in is always 20 betting units
- rules are: s17, ls, ds, 8 deck shoe
- player utilizes perfect basic strategy with no form of advantage play

Also, is there any point during the session where it would mathematically make more sense to walk away than to continue to attempt to achieve a 6-unit profit, or even reach even?

Thanks for any and all help on this question!

Do whatever is in your power to keep that person there. Eventually he will lose it all back.

The risk of ruin is close to 6 / (20 + 6) = 23.1%
The actual risk of ruin is much more complicated to calculate, because BJ has a small house edge and the outcome isn't always +- 1 unit. 23% is a good estimate.

Mathematically, it makes sense not to play at all. You need to specify a risk of ruin tolerance before we can answer the question of when to walk away

Quote: MeltTheFeltPA

I've seen this person begin at $25 bets, and work their way up to $200 bets in the matter of a couple months.

Are you saying that now they are buying in at $4000 (20 x $200) and betting $200 every hand?
Or are they varying their bet from $25 to $200 in one session?

The probability that this individual will lose their session is different for betting the same amount every hand (flat betting) than when the player varies their bet.

Yes, this person is currently coming to the table with a $4000 buy-in, flat betting at $200 per hand. From what I've seen (a couple dozen sessions), their initial bet is what they bet consistently every hand.

The guest plays around every other day from what I can tell in the ratings system. Some days they lose (sometimes the entire buy-in), most days they walk away up, most frequently 6 units ahead. As a host, I want to encourage their play, but not if it has a high likelihood of breaking them and causing them never to return.

If the RoR really is somewhere around 25%, I almost feel obligated to let this player know what they're up against.

Quote: dwheatley

Mathematically, it makes sense not to play at all. You need to specify a risk of ruin tolerance before we can answer the question of when to walk away

Let's say the player wants an RoR at ~10%. Can this even be achieved without advantage play (most notably, counting)?

That's not your job to inform him about risk of ruin. You should only talk to him about winning -- how much did you win today, oh you lost that's too bad you'll get them next time, etc. He won't go bust flat betting. If he goes on tilt and does, great, you got his entire bankroll. Move on to the next fish.

Quote: MeltTheFeltPA

Let's say the player wants an RoR at ~10%. Can this even be achieved without advantage play (most notably, counting)?

Just a bigger bankroll. If you want a 10% RoR at the outset to win 6 units on a coin flip, you need a 54 unit bankroll ~ 6 / (55 + 6 ) = 10%. A little more to play blackjack.

Once the client is down 7 units, so he has 13 units and is trying to win 6+7 = 13 to get to his target, he has a 50% RoR on a coin flip (less at BJ). This would be a good time to walk away, since he now has less chance of making his goal than getting wiped out. But, if he always walks at -7, then his bankroll is 7, not 20...

So you're concerned about your client over-betting his bankroll? You could politely suggest that he lower his bet so that he has a ~50 unit bankroll, maybe trying to explain the RoR principle. You want a 10% risk? You need the spread between target and bankroll to be 10x the target.

" If the RoR really is somewhere around 25%, I almost feel obligated to let this player know what they're up against. "

I can not think of a better way for a host to lose his customer. REALLY !!

As I said before, I'm not trying to snap this player in half and break them; I'm trying to keep them around for a while. The conversation would be carried out tactfully, not a blunt, "You know, you have a 1-in-4 chance of losing your session bankroll every time you come in here with the way you play."

I'm looking for a way for this guest to continue to come back for the forseeable future, which for me is much more desirable than someone that has a quick loss once a month and disappears shortly after.