BR Collapsed 50%, What To Do!?

[zengrifter]

Yeah, so long as it's not like 5 max bets total. Then the non-linearity of blackjack could come into play.

OK, how about 5xKelly betting and my BR is 2000u. Am I still 50% likely to double as to tap? zg

 

[sagefr0g]

OK, so we're in agreement that grossly overbetting will NOT result in greater than 50% RoR IF the target is simply to double the bank?

This is counter-intuitive (no pun intended) because I can think of another example -

What if I have 1000u and I bet 4xKelly - can my RoR be only 50% if my target is to double my bank?
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Thats where it falls apart for me. zg

don't know if this will help any......
note: game is DD s17 set at twice kelly but look at custom bets they have been doubled....

 

[zengrifter]

don't know if this will help any......
note: game is DD s17 set at twice kelly but look at custom bets they have been doubled....

You mean it says MORE than 50% RoR before doubling!!?? What da fuaaa? zg

 

[sagefr0g]

You mean it says MORE than 50% RoR before doubling!!?? What da fuaaa? zg

look again the double kelly ROR is 38% found for optimal betting
then when those bets are doubled the ROR is 62% found in the custom bets when the optimal bets are doubled.

 

[Sonny]

look again the double kelly ROR is 38% found for optimal betting
then when those bets are doubled the ROR is 62% found in the custom bets when the optimal bets are doubled.

So the 2xKelly ROR is 38% (66-max bet BR) and the 4xKelly ROR is 62% (33-max bet bankroll). This seems to match what moo321 was saying:

"I'm ONLY talking about your risk of ruin versus chance of doubling the bank, and even with 100 units it's probably less than 50%. But, if we're talking lifetime risk of ruin, then certainly it can be higher than 50%."

It looks like we've found our answer: Betting more than 3xKelly will give you over a 50% ROR before doubling your BR.

-Sonny-

 

[zengrifter]

Betting more than 3xKelly will give you over a 50% ROR before doubling your BR.

OH NO, SAY IT AINT SO!! zg

Ps - betting 1-5 2D w/100u is about 5-Kelly.

Pss - Moo, defend your claim!

 

[Automatic Monkey]

So the 2xKelly ROR is 38% (66-max bet BR) and the 4xKelly ROR is 62% (33-max bet bankroll). This seems to match what moo321 was saying:

"I'm ONLY talking about your risk of ruin versus chance of doubling the bank, and even with 100 units it's probably less than 50%. But, if we're talking lifetime risk of ruin, then certainly it can be higher than 50%."

It looks like we've found our answer: Betting more than 3xKelly will give you over a 50% ROR before doubling your BR.

-Sonny-

Hold the phone, those are absolute risks of ruin, where a bankroll goes to either zero or infinity. In some of those ruined bankrolls, the player is going to double it first and then go to zero.

What we need to calculate is how likely a player is to double the BR and then stop playing, compared to how likely he is to lose his bankroll and stop playing. The RoR calculator in CVData should be able to calculate that.

 

[Sonny]

Hold the phone, those are absolute risks of ruin, where a bankroll goes to either zero or infinity.

Then why wasn't the 2xKelly ROR 100%?

What we need to calculate is how likely a player is to double the BR and then stop playing, compared to how likely he is to lose his bankroll and stop playing. The RoR calculator in CVData should be able to calculate that.

You can use the online ROR calculators:

http://www.qfit.com/blackjack-calculator-c4.htm

Even with a 1-unit bankroll the ROR never goes beyond 50%. Intuitively, that seems wrong to me. If you bet your entire BR on a single hand, you have a 53% chance of going broke, hence a 53% ROR and a 47% chance of doubling it.

-Sonny-

 

[bluewhale]

Then why wasn't the 2xKelly ROR 100%?
-Sonny-

how is it possible to have a 100% ror when you're playing with an advantage??? i can see the ror being really high if you do 2x kelly, but i still don't see how its possible for it to be exactly 100%

 

[Sonny]

how is it possible to have a 100% ror when you're playing with an advantage??? i can see the ror being really high if you do 2x kelly, but i still don't see how its possible for it to be exactly 100%

There are a few examples earlier in this thread (around page 2 or 3 I think?). If you are always betting too much money, you will eventually hit a losing streak that takes it all away.

-Sonny-

 

[sagefr0g]

how is it possible to have a 100% ror when you're playing with an advantage??? i can see the ror being really high if you do 2x kelly, but i still don't see how its possible for it to be exactly 100%

well as you can see betting 2 x kelly gives you a high ROR. even while playing with an advantage. but kelly betting not only involves raising ones bets as ones bankroll increases but lowering ones bets as the bankroll decreases.
so imagine always betting over 2 x kelly when your bankroll decreases. the situation could present where you are living with that higher ROR as your bankroll decreases, eventually to the point where your bankroll is too low to play any more.

 

[Automatic Monkey]

Here is a RoR sim I did using a backcounting game with a 1-8 spread, late surrender and the player plays all positive EV hands and never plays a negative EV hand. IBA%= 1.933%, SD= 5.32/hand

100 units:
Risk of ruin= 58.12%
Likelihood of doubling BR= 63.16%

50 units:
Risk of ruin= 76.23%
Likelihood of doubling BR= 56.70%

20 units:
Risk of ruin= 89.71%
Likelihood of doubling BR= 52.69%

At an 89 unit bankroll the risk of ruin and of doubling are equal, at 61.7%.

Wait! That adds up to 123.4%, how can that be? The reason is that doubling and losing are not mutually exclusive, and at least 23.4% of the time the player will first double his BR and then proceed to lose it all.

But it can't work in the opposite order; once a player loses his BR he can't continue and double it. Being a player will always do one or the other, it is safe to say that if a player ever doubled his bankroll he didn't lose it first. So the right answer for this problem is:

100 units:
Doubled before losing= 63.16%
Lost before doubling = 36.84%

50 units:
Doubled before losing= 56.70%
Lost before doubling = 43.30%

20 units:
Doubled before losing= 52.69%
Lost before doubling = 47.31%

And so on down to a value approaching 50%. But being the spread is 8 and the SD is 5.32 units per hand, these numbers can't be relied on for bankrolls less than the greater of those two numbers. Or even more than that, since we're playing a DAS game and except at very high counts you do not have an advantage if you don't have enough left to double and split.

But according to this sim Moo has it right.

 

[zengrifter]

Lets go the other way - 2000u 6xKelly 1-5 spread 2D double vs. bust. zg

 

[k_c]

Your illustration with the royal is a good one because it demonstrates the effect of variance on bankroll and ruin, but it is easier than you think to have a larger than 50% RoR.

Suppose you have a biased coin that comes up heads 51% of the time. You have an advantage on every flip (assuming you bet heads) but if you are betting 10% of your BR, the chances are quite high that you will lose it all. I'm getting something around 80% RoR without doing much math.

I don't think this is correct. Let's say you had a 1% advantage on a biased coin flip and you flat bet 1 unit.

Bank   Goal    % of initial bank bet     RoR
  1      2     100                       .495
  2      4      50                       .490001
  5     10      20                       .47502
 10     20      10                       .450164
 50    100       2                       .268935
100    200       1                       .119196

I don't know what the RoR would be if you forced a bet of 10% of bankroll regardless of bankroll size, but I don't think it would be above .450164.

k_c

 

[moo321]

KC, part of the problem is that, at very few bets, your risk of ruin will rise above 50%. This is because you don't win 51% of your hands at 1% edge. You win like 43%, but you win more units on some hands (blackjacks, splits and doubles). Blackjack isn't quite a coin flip, although compared to something like video poker it is close.

 

[k_c]

KC, part of the problem is that, at very few bets, your risk of ruin will rise above 50%. This is because you don't win 51% of your hands at 1% edge. You win like 43%, but you win more units on some hands (blackjacks, splits and doubles). Blackjack isn't quite a coin flip, although compared to something like video poker it is close.

Granted that a flat bet at a fixed EV doesn't apply directly to blackjack, but AM seemed to be saying that even a biased coin flip with a fixed positive EV could lead to a RoR of 80%. I disagree with that.

In Theory of Blackjack, Griffin describes a way to approximate RoR for blackjack using the fixed EV method I used. As I recall what is needed is data such as p1 % of the time player bets b1 units at an EV of x1, p2 % of the time player bets b2 units at an EV of x2, and so on. p1+p2+....+pn should add up to 1. I don't understand the statisical theory behind the method, but I could use it.

k_c

 

[EasyRhino]

Back to the initial conundrum of the topic.

Conventional wisdom when taking a 50% bankroll haircut would be to drop betting level by 50% to keep the risk of ruin constant. The big downside, of course, is that average win rate is going to drop, and clawing back up to the original bankroll is going to be a long shitty grind.

But it's magnified here, since the bankroll was very overbet (assuming it's non-replenishable). So if you cut your overall betting level so it's, say, 1/4 or 1/8 of what it was originally, the grind is going to (relatively) be huge. Even though it might be the smart thing to do, it's going to suck.

I could see three options:

1) If your bankroll is truly replenishable, keep bombing away at the existing betting level. But, to be honest, with such high risk of ruin, this is more like high-stakes wild-ass gambling than advantage play.

2) Drop the bets, grind it out, bend over, and power through.

3) Quit.

Quitting might be a valid option if a) the bankroll is non-replenishable, and b) the decreased betting level is not "worth it" by whatever measure you measure this stuff with.

 

[Kasi]

Conventional wisdom when taking a 50% bankroll haircut would be to drop betting level by 50% to keep the risk of ruin constant.

Well, I don't think so, I think lol. At least compared to original risk.

If Kelly, chances of doubling roll before halving it=2 of 3.

Halving ur bank is square root of original risk.

So, the ultimate risk of losing ur original bankroll is about 1 in 20 if u halve ur stakes after losing half ur original roll.

Not the 1 in 3 u started with.


But, as u say, with the halved bankroll and half-bet, ur ROR is the same as it originally was, except u'll have to double ur money twice now to get back to where u originally would have been doubling ur original roll.

I think