Higher R.O.R. = Better Odds of Winning

[Midwestern]

My position was to very simply - as I stated in my OP - show that RoR and profit were two entirely separate concepts and, more importantly, that lowering RoR could not possibly increase profits. I think that the idea of gradually adding to one's bankroll with very low RoR is sometimes confused with being "better" or "more profitable". It certainly will preserve one's bankroll, and for many, that's the most important component of their money management strategy. If everyone sought absolute minimum RoR, many would either be playing very small limits or could not actually find games small enough to play.

i agree with the above

but the methods you used to prove your point in earlier posts were very unclear, which suggested that you were misinterpreting the relationship between ROR and expected profit.

 

[LovinItAll]

i agree with the above

but the methods you used to prove your point in earlier posts were very unclear, which suggested that you were misinterpreting the relationship between ROR and expected profit.

I tried to re-word the OP with an edit, and I mentioned that I didn't think I took the time to explain my position carefully at first. I appreciate it.

I think that people also get in their minds that while there might not be a general correlation between x and y, there are scenarios where two unrelated concepts can be drawn together, such as the initial post with the data as presented, not as variables, you know?

Anyway, I really never intended for this to go beyond a couple of posts, but as always, I thank the people that have taken the time to think about the problem and present their take on it.

Best ~ LIA

 

[christopher1]

the way i see it, if all else is equal, the larger your spread/average bet, the higher your risk of ruin will be. the higher your average bet, the more money you will make per hour. but if u go broke that lowers the number of hours you spend in the casino. if you drive 10 minutes to a local casino then maybe you dont mind losing your trip bankroll in a half hour sometimes, but if u drive or fly 4 hours each way, you might want to be pretty sure u will be there for a little while.

 

[tthree]

so much for all my fancy math

Hi Lia. Since I did the wizard study analysis something was bugging me. This usually means my subconscious brain spotted a mistake that my conscious brain hadnt figured out yet. All math problems can be worked many ways finding your own mistake rarely happens unless you attack the problem a different way. I finally figured a more accurate way to work the problem(much simpler as well). The higher RoR is accurately found as the difference between the to times to hit the goal. That would give the length of time to increase the BR from $100 to $1000. The simple arithmetic produces 78.7 days not 91.125 days. I knew the difference looked way to small. My assumption of linearity was wrong producing erroneous results.

This shows a huge increase in win rate with higher RoR if you dont go bust. That is what balances everything to the average EV. The higher your RoR the higher your win rate and bust rate. Maybe that will help your friend understand. The average of those 2 gives you your EV. Maybe average isnt the best word but I think you get the point,

 

[blackriver]

whatever is being posted reminds me of discussions ive had or seen others have in the past where we both agree on some simple axiom but then not on the conclusion. then they go around trying to get people to say yes your axiom is right and then they go "see, i told you my conclusion was right" which could be done by either person in the debate. usually this is the person who is wrong and is trying to reframe the debate as if it has been about something more trival to begin with. Did your friend really think 1% of 5,000,000 was bigger than 1% of 10,000,000? if so, then you are terrible at communicating

also im pretty sure you can ask always frame the question so that either side of the discussion will be obviously correct. maybe this is why people assumed the heart of this debate was more than whats bigger 50,000 or 100,000

You are correct.

All other things being equal, reducing your risk will ALWAYS lower your expectation. Where in the world did you ever find someone who didn't understand THIS simple proposition?

i think this is also at the heart of what everyone was thinking this was and maybe is about. if you are betting larger than your kelly bet then you would INCREASE your long term expectation by LOWERING your bet. if you are coinflipping with someone paying you $2 to their $1 for any ammount you should bet your kelly which i think is 1/3rd of your bankroll (maybe it was half, i dont remember right now). If yould could only do this flip once and all you wanted to do was maximize your expectation on THIS bet then you would bet 100% of you bankroll. if you can make this bet 10000 times then you maximize your expectation on the series by betting kelly. if you bet more than kelly then you will actually LOWER your expectation over this series

 

[tthree]

Risk versus ruin lets make it apples compared to apples

You are correct.

All other things being equal, reducing your risk will ALWAYS lower your expectation. Where in the world did you ever find someone who didn't understand THIS simple proposition?

If you were playing with a very high risk of ruin resizing your bet as you go your eventual expectation would be you would be broke. I dont see how you could call this raising your expectation.

If you dont understand this consider where you have 90% advantage. You follow the high risk plan to the extreme and decide to bet your whole bankroll on every bet. Your return would be huge until you went broke. The overall expectation for this strategy is 100% of the time you will go broke.

I am not sure if the people who argue a higher expectation consider the cumulative affect on the average of the times a strategy will go broke that go broke. The more the minimum bet size allows you to size down the higher you can risk with a lower chance it will make you go broke.

The initial example didnt take time into consideration. She equated sessions of vastly different amounts of time as though they were equal. To make it a fair comparison she needed to break each example into numbers of hands to reach an equal target amount. That is complicated so we will only equalize the goal instead. Risking 2 units to win 10 (her math gave $250 expectation for 1 unit risked to win 5 so this would be twice that which is $500) compared to 1 unit to win 10 (her math $500). According to her math they would have the same expectation but one would have a much lower RoR while the other would require a bigger investment of time. The obvious winner would only require a larger buy in.

 

[LovinItAll]

If you were playing with a very high risk of ruin resizing your bet as you go your eventual expectation would be you would be broke. I dont see how you could call this raising your expectation.

If you dont understand this consider where you have 90% advantage. You follow the high risk plan to the extreme and decide to bet your whole bankroll on every bet. Your return would be huge until you went broke. The overall expectation for this strategy is 100% of the time you will go broke.

I am not sure if the people who argue a higher expectation consider the cumulative affect on the average of the times a strategy will go broke that go broke. The more the minimum bet size allows you to size down the higher you can risk with a lower chance it will make you go broke.

The initial example didnt take time into consideration. She equated sessions of vastly different amounts of time as though they were equal. To make it a fair comparison she needed to break each example into numbers of hands to reach an equal target amount. That is complicated so we will only equalize the goal instead. Risking 2 units to win 10 (her math gave $250 expectation for 1 unit risked to win 5 so this would be twice that which is $500) compared to 1 unit to win 10 (her math $500). According to her math they would have the same expectation but one would have a much lower RoR while the other would require a bigger investment of time. The obvious winner would only require a larger buy in.

Yikes....

First, I've said I worded the title of the thread poorly, so can we please push that aside? I still stand by my original statement and calculations, which are correct unless/until one starts plugging in variables that are not germaine to my specific analysis, which is simply this:

- A person that wagers more money in a game with a positive expectation will, over the long run, make more money than another person who plays the same amount of time but wagers less over the same time span.

As in my first example, a person with an unlimited bankroll who sits down once per day with $500 and doesn't leave until they have either doubled up or gone broke will make more money than the person that either leaves after winning $250 or after going broke. Neither person has any additional advantage from an EV perspective, but one is simply wagering more money in a +EV game over the long run. Since the betting units are $50 (or 10 units), it isn't likely (though it isn't impossible), that either person will be playing a very long session (3 hours would be a long session, imo. 12 hours would be a very long session).

As I've clarified (and it is indisputable), this was a question of volume, not EV. Yes, the RoR is higher for the 'double or go broke' player. My error was in my title, as obviously a higher RoR doesn't increase a player's EV. All things being equal, though, a higher RoR with the given parameters will net the higher volume player more dollars in the long run.

As for my friend, his contention was that lowering RoR would increase profits given an unlimited bankroll (save the 'no RoR for unlimited bankroll' argument, as we were talking about session-specific numbers that were sustainable by us). Perhaps I just chose a poor way of communicating that RoR and profits are two separate concepts. Again, all results are based on the data I initially posted. I understand that various scenarios can be devised that make 'session', 'bankroll', et. al. insignificant or more significant.

Take care ~ L.I.A.

 

[NightStalker]

Can't see whole math

(I knew I should have taken more time to present this problem. This isn't about a betting strategy that's intended to be implemented in 'real life'. It's a math problem that addresses the question, "Does a lower risk of ruin mean that one will make more money over an indefinite sample size." I said no. I think I'm right.)

Hey,

I was trying to explain to a friend who was asking me how to lower his session ROR [to make more money]. [I said] that lowering the ROR isn't necessarily the way to make the most money. He disagreed, saying that the lower the ROR, the more profit one would make. I tried to explain it like this:

(One unit = $50)

Over ten session with a +EV of 1%, here is the difference between a lower 'goal setting' ROR versus busting out:

Risk 10 Units To Win 10 Units
ROR = ~45%

Will reach goal 55% of the time: $2,750
Will go broke 45% of the time: $2,250

...for a net theoretical win over 10 sessions of $500

Risk 10 Units To Win 5 Units

Risk of Ruin = ~30%

Will reach goal of winning 5 units 70% of the time: $1,750
Will go broke 30% of the time: $1,500

...for a net theoretical win over 10 sessions of $250

So, the higher risk of ruin is the most profitable, [regardless of how long it may take].

My math is right, right? If not, where did I screw up?

Lowering RoR or increasing RoR- both will decrease the long-term EV. Optimal EV is Full Kelly which comes around 10-15%RoR(not sure). It is optimal betting strategy given your advantage and bankroll to maximize the bank growth(d(bank)/d(time))

 

[tthree]

making it simple

I guess what she was saying was if you gamble twice as long you will expect to win twice as much if you have an advantage. If she would have said that to begin with I think her friend would have agreed.

 

[LovinItAll]

Lowering RoR or increasing RoR- both will decrease the long-term EV. Optimal EV is Full Kelly which comes around 10-15%RoR(not sure). It is optimal betting strategy given your advantage and bankroll to maximize the bank growth(d(bank)/d(time))

I don't think that's right.

First, please consider that we're not talking about Blackjack, just a game that has a +EV that never changes. Given that the EV never changes, any betting strategy will not increase or decrease the EV (because it never changes).

The RoR certainly changes based on the wager amounts per 'game' (hand, lopsided coin - whatever).

Utilizing Kelly's criterion, given an adequate bankroll and minimum bets that fall within the 'Kelly' range, reduces RoR to less than 1% (theoretically 0%). Modified Kelly strategies have different RoR's, of course.

Best ~ L.I.A.

 

[LovinItAll]

I guess what she was saying was if you gamble twice as long you will expect to win twice as much if you have an advantage. If she would have said that to begin with I think her friend would have agreed.

Give me a little credit - I did say that, or more specifically:

"Look, dumbass, if you bet more and have the same advantage, you'll net more dollars over the long run."

My friend was convinced that lowering RoR impacted net winning dollars, or put another way, that lowering RoR increased a player's EV, or chance of winning given an unlimited bankroll. That my friend didn't understand that may be a reflection on my choice of friends, but doesn't change the math.