Going broke

With a trip bankroll of $1000 and flat betting $25 playing basic strategy, what is the number of hands before going broke - average.

Flat betting $25 per hand with a $1000 trip roll and stopping when ahead 2 units, what is the odds of going broke. Or ... on average how many trips would it take to go broke. Consider this like if you were at a microgaming casino and put the blackjack game on autoplay with a goal of 2 units.

Thanks,
Zenu

Well if you have a trip roll of $25 and you are betting $25 the first thing you should know is you have a significant disadvantage (on top of the penalty you incur for no doubt employing ploppy basic strategy) as you will not be able to double or split. I don't have any hard numbers but -3% sounds about right.

Quote: Zenu

With a trip bankroll of $25 and a bankroll of 1,000 playing basic strategy what is the number of hands before going broke - average.

Flat betting $25 per hand with a $1000 trip roll and stopping when ahead 2 units, what is the odds of going broke. Or ... on average how many trips would it take to go broke. Consider this like if you were at a microgaming casino and put the blackjack game on autoplay with a goal of 2 units.

Thanks,
Zenu

Pretty easy, go here:

http://www.beatingbonuses.com/simulator2.htm

Choose MicroGaming Vegas Strip Blackjack, or whichever one you're playing.

Your bankroll is 40 units and you want to stop win at 42 units.

Bonus-0
Deposit-40
Wagering Requirements-0
Bet Size-1
Target Bankroll-42
Simulations-(I'm doing 20,000)

Checkmark, "Always to Target"

Chance of Gain: 93.85%
Chance of Bust: 6.15%

Average Return: -0.31 units

Trying again and:

Chance of Gain: 94.04%
Chance of Bust: 5.96%

Average Return: -0.22 units

Those 20,000 dudes ran well the second time around.

BlackjackGuy,

I'm such an idiot. Thanks for pointing that out. I fixed it.

Sorry, forgot the first question.

The probability of busting out seems to be close to 50% pretty consistently around 2,425 hands...trial and error. Same simulator, obviously not shooting for the target of 42 units on that one.

It says the House Edge is 0.35% for that Blackjack game, so if you have:

(25 * 2425 * .0035) = 212.1875 is the expected loss, which is almost 8.5 units. The rest is just variance, once you're tapped, you're tapped.

That was really quick. Thanks so much. Sending the wife on a trip armed with basic strategy. I wanted to know what I was up against.

You're welcome, couple disclaimers:

1.) I use those simulators, but do not specifically vouch for them as they are not on this site.

2.) The simulator assumed a REALLY good Blackjack game. 0.35% HE is very good. I don't know if your wife will be playing that good a game.

3.) I want to say the simulator assumes OPTIMAL strategy as opposed to basic.

In other words, her average number of hands is probably slightly lower and probability of busting slightly-moderately greater.

I would have guessed around 1900 hands for a 50% risk of ruin assuming HE 35 bps, bankroll 40 units.

Quote: Ace2

I would have guessed around 1900 hands for a 50% risk of ruin assuming HE 35 bps, bankroll 40 units.

You know what? I think you're right. Because I wanted a finite number of hands I used, "Wagering Requirements," but that would take splits/doubles into account, as well.

Quote: Ace2

I would have guessed around 1900 hands for a 50% risk of ruin assuming HE 35 bps, bankroll 40 units.

one can look here too for something close:
https://wizardofodds.com/games/blackjack/appendix/12/

and using Blackjack Attack Survival criterion formula in Excel
'1900 hands for a X% risk of ruin assuming Z HE, bankroll 40 units'
.35% HE
Risk of ruin: 47.046%
.7% HE
Risk of ruin: 51.679%
1% HE
Risk of ruin: 55.663%

.7% HE BJ game
Probability to double the starting 40 unit bankroll flat betting
about 40% (not bad)

60% chance to turn $1000 into $1500

sounds fun
hope she has lots of it!
Sally

Thanks to all.

Could you help me with the acronyms?

What is HE. What is bps?

Quote: Zenu

What is HE. What is bps?

HE = house edge
different game rules changes the house edge.

How long would $1,000 last at an "average" .5% HE blackjack game, always flat betting $25? Well, we have to make a couple other assumptions... Assuming an "average" pace game of 80 hands per hour (60 being slow, and 100 being faster for shoe games), let's find out...

Expected Loss (EL) = (NumHands*AvgBet)*(HouseEdge)

Eventually you'll lose your $1,000 as expected... so:
-1,000 = (X*25)*(-.005) ...solve for X.

X*25 = -1,000 / -.005

X*25 = 200,000

X = 200,000/25 = 8000

So with all things considered "average" you'll lose $1,000 in expected value (EV) at 8,000 hands. On average then, I'd imagine your 50% mark (others are referring to) to be around 4,000 hands? This doesn't take the variance of the game in to consideration though. You could lose your $1,000 bankroll much sooner or later. The simulations others have provided are going to more accurately get that number of hands, I just wanted to do some raw number fun and hopefully give another perspective for others reading this thread about how to use other calculations (normally EV) to solve for other questions. Typically someone else is like, what's my -EV if I play X game for Y hours and you have to solve for "EL" above, not X...

Quote: Romes

How long would $1,000 last at an "average" .5% HE blackjack game, always flat betting $25? Well, we have to make a couple other assumptions... Assuming an "average" pace game of 80 hands per hour (60 being slow, and 100 being faster for shoe games), let's find out...

Expected Loss (EL) = (NumHands*AvgBet)*(HouseEdge)

Eventually you'll lose your $1,000 as expected... so:
-1,000 = (X*25)*(-.005) ...solve for X.

X*25 = -1,000 / -.005

X*25 = 200,000

X = 200,000/25 = 8000

So with all things considered "average" you'll lose $1,000 in expected value (EV) at 8,000 hands. On average then, I'd imagine your 50% mark (others are referring to) to be around 4,000 hands? This doesn't take the variance of the game in to consideration though. You could lose your $1,000 bankroll much sooner or later. The simulations others have provided are going to more accurately get that number of hands, I just wanted to do some raw number fun and hopefully give another perspective for others reading this thread about how to use other calculations (normally EV) to solve for other questions. Typically someone else is like, what's my -EV if I play X game for Y hours and you have to solve for "EL" above, not X...

An easier way to do this is take bankroll divided by house edge divided by bet amount. This works for any game, not just blackjack.

$1,000/0.5%/$25 = 8,000

However, the risk of ruin depends on the volatility of the game. Blackjack is very low, jacks or better VP is higher, super aces VP is higher than that, and slot machines are the highest.

Surprised no one has mentioned this....

For a novice, mistakes in basic strategy will probably drain the bankroll faster than the HE.
Once I was playing with a guy who was in Vegas for his daughter's wedding (cheaper to throw a wedding in Vegas).
Even though I only offered friendly advice on 1 or 2 hands an hour, after a few hours he commented that he wasn't losing his money quite so quickly.

Just one mistake an hour can be a 2 bet swing (-2.5% at 80 hph - hands per hour). WAAAY higher than HE.
And how many times do we see novices who make less than 1 error per hour?

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My estimate would be 4-8 hrs to lose 40 bets, but sometimes 100+ hrs.
Quite rare to lose 20 bets in an hour.
The "average" is less useful than the "median" or "20% worst case".

I don't usually play basic strategy, but with counting and a 5:1 press with $25 average bet, I would be +/- $250 most of the time for 1 hr of play.
So 16 hrs would be +/- $1,000 most of the time (ignoring any edge I had on the game).

Quote: mamat

Surprised no one has mentioned this....

For a novice, mistakes in basic strategy will probably drain the bankroll faster than the HE...

Just one mistake an hour can be a 2 bet swing (-2.5% at 80 hph - hands per hour). WAAAY higher than HE.
And how many times do we see novices who make less than 1 error per hour?...

This is a really, really phenomenal point mamat. I think everyone here (including myself) just assumes everyone is playing basic strategy perfectly, when in reality most amateur and medium experienced counters don't even know ALL of the differences in basic strategies pending game rules (H17/S17... 6D/2D... etc).

I've met very few people in my time counting that knew basic strategy 110% (i.e. knew it perfectly for the game we were playing, and for a game with slightly different rules).

I think one would have to not only know basic strategy but to actually play it despite drinks, chatter, arrival of attractive girls at the table, conversation with the dealer, floor. Even with all that there will always be lapses. No one plays perfectly all the time. Dealers make mistakes, players make mistakes. And after a few hours, fatigue and the effect of the booze may start having a subtle effect the player doesn't even notice.

Variance is most important. Lose your first five hands and its going to be different than winning your first five hands.

Quote: Romes

I think everyone here (including myself) just assumes everyone is playing basic strategy perfectly, when in reality most amateur and medium experienced counters don't even know ALL of the differences in basic strategies pending game rules (H17/S17... 6D/2D... etc).

I've met very few people in my time counting that knew basic strategy 110% (i.e. knew it perfectly for the game we were playing, and for a game with slightly different rules).

For almost everyone, 6:5 vs. 3:2 makes little difference. Their playing errors (-2% to -5% or worse) swamp the HE/EV.

(1) Easiest way for beginners to last longer is to play at a full table with lots of talking and slow play. 40-60 hph helps the money last longer.

(2) Second is get & use a plastic strategy card for $0.99-1.99 for the game you are playing (or any other BJ game). Some don't realize it's ok to put a strategy card on the table. After I put a strategy card on the table, I sometimes see 3-4 people at the table do the same thing. :-)

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Experienced counters tend to make errors with very small -EV. (e.g. DAS or No DAS). If you are +/- 1-2 on using an index, it's very little -EV and can be partial cover.

Novices make bigger errors on hands where they don't realize they should be checking their strategy card.
a) Splitting too much: 10s vs. 8-9-10, Splitting 5s. Not splitting 8s when it would put too much money on the table.
b) Splitting too little: Not realizing 2s, 3s, 4s, 6s can be split against small cards. Not splitting 8s
c) How to handle soft hards: e.g. not hitting A6 (some even stand on A2-A5). What to do with A7 and A8.
d) Not realizing they can double
e) Doubling too much: 10 vs 10, 12/13 vs 5, small pairs vs. 2/3
f) Not using insurance with a ton of face cards missing (which can be seen even if not using a count)
g) Hitting 12-16 against 2-6.
h) Doubling or splitting when they are too close to the end of their bankroll

Basic strategy is complicated for most people (even with a strategy card...you have know when to consult your card)
...and I know I don't remember all the 1D/2D/4D/6D, DAS/NoDAS, etc... variations.

However, blackjack experience means that I know where the tricky/marginal decisions lie...and I have a better idea when to consult a strategy card (or brute-force some easier computations in my head).

When I play, I often have a basic strategy card to consult (as part of my cover)...and ask the dealer for help/opinions on tougher decisions.

Some dealers maintain their own count (probably on a different system than mine)...and are helpful. Some are clueless. The worst are preferential shufflers. The best make errors in my favor (when plausibly deniable for the cameras and pits) and are helpful shufflers.

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...however, these days most people are looking for "sloppy" dealers, so their idea of a good dealer is different than mine.