Risk of Ruin Calculation (Based on Conditions)

Hi guys,

I'm an amateur interested in recreational blackjack. Just like to find out the risk of ruin probability based on these conditions:

1. Dealer stands on S17
2. Double allowed after splits
3. Early surrender
4. Deploying basic strategy but not card counting (am a newbie after all)
5. Flat-betting
6. Goal of increasing bankroll from 40 to 50-60 betting units
7. No specified number of hands

Appreciate the feedback and apologies for the noob post!

Quote: chronotrigger1

Appreciate the feedback and apologies for the noob post!

No need to apologize, we answer questions here no matter what the level of expertise is.

My first thought on this is that Risk of Ruin Calculators and charts always have foot notes about the effect of your tipping the dealer and tipping the Tray Lizard for the drinks. So do NOT forget that a theoretical risk of ruin is never what a REAL WORLD risk of ruin is. Also, unless you are going to be a stick in the mud bore, you will be chatting with the dealer, the floor person, the other players at the table, the cocktail waitress, the wandering masseusse, etc. Don't think this will not have an effect on your play, it does.

The math types on thsi forum will supply you with figures and there are charts available here and at WOO, but always remember that the Real World will be different. It always is.

As a very rough approximation of the math.
All you have to do is remember 20, 30, 40. And 1, 2, 4.
Thats it.
Thats your answer.

So if you want to play 1 hour you divide your bankroll by 20 and bet that amount .. and you will have sufficient funds to give yourself a 90 percent chance of avoiding a risk of ruin based on sheer normal variance.

For 2 hours you divide by 30 and for 4 hours you divide by 40.

Are these figures mathematically precise. Hell NO. Are they easy to remember and relatively easy to apply... Hell yes.

So lets assume you got five hundred dollars to 'play' with. And you want to play for four hours and have a decent chance of avoiding risk of ruin by sheer variance. Since this is an approximation the actual math is probably near 12.00 dollars but what casino is ever going to let you bet 12.00 dollars? So you bet 10 or 15.
Adjust for giving the poor girl with the sore feet some tips and adjust for the dealer getting rewarded for his sore feet... and well... you get the idea.

good luck.

Hey chronotrigger, and welcome to the forums!

Definitely a good question to ask. One thing to note from the top is that even if you have a good game (which you appear to have) there is still a built in house edge that will give your bankroll negative expectation over time. Thus, you could win tonight, tomorrow night, etc, but in the "long run" you WILL LOSE money. So I understand your goal is to increase your bankroll, but do understand that while you could do it (since you have a small goal) the math of the game is against you. Also, even IF you were to increase it form 40 to 60 units, your bankroll does not "reset" and so it wouldn't be a replicatable feat to continuously increase it by small amounts. Whether you play in Florida or Las Vegas, or if you play in January 2017 or Febuary 2018, a hand of blackjack counts towards your bankroll. There is only one bankroll and the hands will continue to count towards it... Thus, eventually, you will lose money. I just want to make that perfectly clear. There is no problem with that if you're recreational and see it as a source of entertainment, but if you want to actually make money in blackjack you MUST learn how to track the edge of the game and how to bet more when you have the edge in your favor.

Next, here is the risk of ruin chart provided by the Wizard: https://wizardofodds.com/games/blackjack/appendix/12/

Notice that to determine your Risk of Ruin (RoR) you must consider a few variables... What is your current bankroll? How many hands do you plan to play? So let's say you plan to play a 2 hours per week for the next month for a total of 8 hours... Getting approximately 80 hands per hour (assuming your game is a continuous shuffler no hole card game). That is a total of 640 hands, and you have a bankroll of 40 units... So let's trail those on the page to find your RoR percentage. It looks like you're at around 20% as you're in between 600 and 700 hands.

Do note though, this chart is set up for the specified game with a house edge of .414%. However, for the amateur recreational player, this chart should be "accurate enough." However, if you wanted to do a little simple math you could calculate your RoR for any game =). If you're not interested, stop reading, but if you are, you should do the following:

Get the exact house edge of your game. Based off your rules I would need more information. How many decks are used in this game? How many hands can you split to? Is this game on a continuous shuffler? Does the dealer peak or not take a hole card? I'm going to assume you're on a continuous shuffler game outside of the US where the dealer does NOT take a hole card (more than likely right given your rules). Basically you need to use this page and simply select the correct inputs to the rules: https://wizardofodds.com/games/blackjack/calculator/

Since you don't have enough information, I'm going to assume the following:
- 6 decks (continuous shuffler)
- Dealer stands on soft 17.
- Double After Split (DAS) allowed
- Double Any Two Card (DA2)
- Resplit to 4 hands
- No Resplitting Aces (RSA)
- Player loses ONLY original bet vs dealer blackjack (this one is important to know).
- Blackjack pays 3/2

This brings your house edge to .40622%.

Note that these are not on that page, but extended rules...
- Early Surrender vs 10 is worth .24% for the player.
- Early Surrender vs A is worth .39% for the player.

Assuming you have Early Surrender vs 10 (most common) that would bring your House Edge down to: .16622%... an excellent game.

Now, for the math part... Another way to look at your RoR is to look at the well known formulas for Expected Value (EV) and your Standard Deviations (SD). EV is simply the value you expect to lose (or win if you're playing with an edge) after a number of hands. SD is the +/- number of confidence that you'll be at your EV. SD's are what create the bell curve around your EV on a math chart. It's like in an election when they say "Clinton is favored to win with 52% of the vote, plus or minus 1%." That plus or minus is to account for variance and/or error.

EV = (NumHands*AvgBet)*(HouseEdge)
SD = Sqrt(NumHands)*OriginalSD

Given what you've posted, let's pretend your unit is $10. Thus, you have a $400 bankroll and you will flat bet $10 (so your AvgBet will always be $10).

AvgBet = 10
HouseEdge = .16622%
OriginalSD = 1.15 * AvgBet = 1.15 * 10 = 11.5... 1.15 is a variance modifier that is well known and accepted for blackjack. No need to worry about where it came from for now, just accept this is how you do the calculation =).

Now you're all set to "check" where you'll be at after ANY NUMBER of hands...

EV(100 hands) = (100 * 10) * (-0.0016622) = -$1.67 ...This means after 100 hands of blackjack playing PERFECT basic strategy you could expect to lose $1.67.

SD(100 hands) = Sqrt(100) * 11.5 = $115... This means that with 85% confidence you will be at your EV of -$1.67 PLUS or MINUS $115. This makes sense because you will rarely hit your exact EV in 1 given night. You could have a lucky run and win $100, or an unlucky run and lose $100... This is called Variance. While overtime you WILL lose, on any 1 given night you could win or lose (same goes for card counters except they WILL WIN in the long run).

So now let's look at the example from above, with 640 hands (8 hours of play over the next month)...

EV(640 hands) = (640 * 10) * (-0.0016622) = -$10.64. So after 1 month, playing 2 hours per week, getting 80 hands per hour, you could expect to lose $10.64.

SD(640 hands) = Sqrt(640) * 11.5 = $290... So after 8 hours you EXPECT to lose $10.64 PLUS or MINUS $290.

So you see... You have a "chance" to be "lucky" from variance and be UP potentially around $300. It's a smaller chance, but you could still be up. What really opens peoples eyes is when you look at the LONG RUN. This will take a recreational player YEARS and YEARS to get to, but you will eventually get to it, and you will eventually lose this amount (playing PERFECT basic strategy and not accounting for tips). Let's say in your lifetime you play 1,000,000 hands of blackjack. Well, what could you expect?

EV(1,000,000 hands) = (1,000,000* 10) * (-0.0016622) = -$16,622
SD(1,000,000 hands) = Sqrt(1,000,000) * 11.5 = $11,500

So do you see now how after playing 1,000,000 hands you CAN'T WIN. You're expected to lose $16k PLUS or MINUS $11,500 for variance so the LUCKIEST you could get is to be -$16,000 + $11,500 = -$4,500... but don't forget if you get unlucky. The WORST you could do is -$16,000 - $11,500 = -$27,500!

Using these formulas you can check what your EV and SD is at ANY number of hands =). Sorry for the long post but I always like to encourage even recreational players to gather a deeper understanding of the game and the simple math behind it. It might sound confusing but all we did was addition, subtraction, multiplication, and a square root on a calculator =).

Thanks for the very well thought out answers, guys! To be honest, this is one of the rare forums that actually has a very conducive atmosphere for learning - sans the flaming and nonsense I've encountered in so many others. Awesome work from an awesome community keeps a forum like this going strong!

Will keep you guys updated on my progress :)

Glad you found the long winded response useful. Feel free to post any other questions. If you ever wanted to go past basic strategy... There's an A to Z guide for that ;-).