Probability of going broke with fixed odds
September 20th, 2013 at 12:55:31 AM
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So I'm gonna turn this into a few questions.
First the set up: There is a game where I know my opponent will win 62% of the time, but I can set the bet for each side. I have $4,000.
What bet amount for each side would make it a break-even game?
If I do make it in my favor (perhaps 10% of the bet), what should the bet size be so there is a 1% chance I will go broke? .5%? .005%?
This has been stumping me for over a month. If someone can help that would be incredible
First the set up: There is a game where I know my opponent will win 62% of the time, but I can set the bet for each side. I have $4,000.
What bet amount for each side would make it a break-even game?
If I do make it in my favor (perhaps 10% of the bet), what should the bet size be so there is a 1% chance I will go broke? .5%? .005%?
This has been stumping me for over a month. If someone can help that would be incredible
September 20th, 2013 at 1:52:48 AM
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for you to make a 1 unit betQuote: UnattendedBagFirst the set up:
There is a game where I know my opponent will win 62% of the time,
but I can set the bet for each side.
I have $4,000.
What bet amount for each side would make it a break-even game?
just q/p (.62/.38) = 1.631578947 = your win
so go to 1.7 to 1 for 2.6% edge (or 17 to 10)
you can calculate the HE from there?
if not just ask
as for your RoR...
for me now sleep time
this will get you started
Nice questions
winsome johnny (not Win some johnny)
September 20th, 2013 at 2:59:13 AM
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Quote: 7crapsfor you to make a 1 unit bet
just q/p (.62/.38) = 1.631578947 = your win
so go to 1.7 to 1 for 2.6% edge (or 17 to 10)
you can calculate the HE from there?
if not just ask
as for your RoR...
for me now sleep time
this will get you started
Nice questions
What does HE stand for? I'm not sure how to calculate rate of return either..
So i guess that only leaves the question on what size of bet would be most appropriate to minimize chance of bankruptcy
Bedtime for me too, thanks for the help!
I guess to expand also, at what amount of bankroll do I decrease the bet amount? increase?
September 22nd, 2013 at 12:46:15 AM
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Is there anyone else that can help out?
September 22nd, 2013 at 1:22:22 AM
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I can only help a little bit: your RoR is your Risk of Ruin, not your rate of return. He's saying what's the chance of you going broke on your bet with a 4000 bankroll (not knowing yet the size of your bet, but bottoming out on a run of bad variance) before you realize your hoped-for gains. I don't know how to calculate that or the others with any reliability, but I'm sure someone who does will happen along.
If the House lost every hand, they wouldn't deal the game.
September 22nd, 2013 at 3:51:35 AM
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search google for calculators, they are out there, I found the below quickly but don't know how good it is. I think you should do the heavy lifting of finding a proper calculator.
http://www.qfit.com/CVRoRC.htm
http://www.qfit.com/CVRoRC.htm
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
September 22nd, 2013 at 7:40:44 AM
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Quote: UnattendedBagWhat does HE and RoR stand for?
So I guess that means I can't calculate it or don't know how...
House edge (you can call it just edge) and Risk of Ruin
my 2nd tryQuote: UnattendedBagFirst the set up: There is a game where I know my opponent will win 62% of the time,
but I can set the bet for each side. I have $4,000.
What bet amount for each side would make it a break-even game?
there are many.
The ratio would need to stay at 62/38 for you.
So to be equal (0% edge) you could bet 38 the opponent bets 62
(many others as long as the ratio stays the same)
for the edge to be equal:
just use the EV(expected value formula for simple bet)
Pwin*$won = Ploss*$loss
so when $loss=1 (1 unit)
$won=Ploss/Pwin (q/p)
q=1-p
===========================
To calculate your edge and EV use:
Pwin*$won - Ploss*$loss = EV
(.38*$62 - .62*$38 = 0)
(House) edge is just EV/$Bet = 0/$38
============================
just use the EV(expected value formula for simple bet)
Pwin*$won = Ploss*$loss
so when $loss=1 (1 unit)
$won=Ploss/Pwin (q/p)
q=1-p
===========================
To calculate your edge and EV use:
Pwin*$won - Ploss*$loss = EV
(.38*$62 - .62*$38 = 0)
(House) edge is just EV/$Bet = 0/$38
============================
Quote: UnattendedBagIf I do make it in my favor (perhaps 10% of the bet), what should the bet size be so there is a 1% chance I will go broke? .5%? .005%?
You need to work with ev and sd (expected value and standard deviation)
another formula or two those can be found here:
https://wizardofvegas.com/forum/questions-and-answers/math/14785-suppose-you-could-beat-the-casinos-how-many-buyins-would-you-need-for-95-confidence/
RoR
r = e^[(-2ev x B)/(s.d.)^2]
Excel: =EXP((-2*ev*bankroll)/(st_dev^2))
r = e^[(-2ev x B)/(s.d.)^2]
Excel: =EXP((-2*ev*bankroll)/(st_dev^2))
Being that there are many such bet combos, here are a few you can start to work with
I just use a spreadsheet like Excel. makes it very easy to change values and create a table of data.
2.6% edge (your 10 wins 17 or the same ratio)
Risk of Ruin %
60 pays 102: 13.2866628546%
50 pays 85: 8.8735846790%
40 pays 68: 4.8431048637%
30 pays 51: 1.7653540981% (ev: 0.78 sd: 39.3)
20 pays 34: 0.2345566472%
10 pays 17: 0.0005501682% (ev: 0.26 sd: 13.1)
6.4% edge (your 10 wins 18) as your edge goes up,
your chance (Risk of Ruin) goes down
60 down to 10 bets
0.9854327874%
0.3911581736%
0.0978228952%
0.0097107778%
0.0000956932%
0.0000000001%
for the sd value (standard deviation) just use
(x+1) * square root of (p*(1-p))
where x = the x to 1 payoff
1.7 or 1.8 in my examples above
this concept for many is difficult until you work with it
or you can also use this formula:
=((p)*(win)^2 + (1-p)*(loss)^2 - (ev of the $bet)^2)^0.5
or easier to see
=SQRT((p)*(win)^2 + (1-p)*(loss)^2 - (ev of the $bet)^2)
(x+1) * square root of (p*(1-p))
where x = the x to 1 payoff
1.7 or 1.8 in my examples above
this concept for many is difficult until you work with it
or you can also use this formula:
=((p)*(win)^2 + (1-p)*(loss)^2 - (ev of the $bet)^2)^0.5
or easier to see
=SQRT((p)*(win)^2 + (1-p)*(loss)^2 - (ev of the $bet)^2)
many wait to double the bankroll first, but that is up to you.Quote: UnattendedBagSo i guess that only leaves the question on what size of bet would be most appropriate to minimize chance of bankruptcy
I guess to expand also, at what amount of bankroll do I decrease the bet amount? increase?
You can change the bets and re-calculate any time you want.
The RoR formulas assume your bets stay the same or
at least the bets made (for the average) are equally made.
That brings up Kelly betting for when you do have the edge.
https://wizardofodds.com/gambling/kelly-criterion/
The percentage of the bankroll for the next bet is edge/odds payoff
(where the odds payoff is x to 1.
for example .026/1.7 for the 2.6% edge above = 1.52941% of the current bankroll)
(where the odds payoff is x to 1.
for example .026/1.7 for the 2.6% edge above = 1.52941% of the current bankroll)
But for many Kelly betting has too much variance and extreme bankroll fluctuations
and in up to maybe 5,000 such bets, flat betting can do just as good or better.
Depends of the values you deal with.
Hope this helps more than hurts
see if my math was done correctly
added:
Now, just playing with an edge and a proper bankroll for RoR still does not
guarantee that after N bets made you will be showing some sort of a profit.
You still need N to get large fast just like a casino with many bets made.
This is where most all APs (advantage players) trip up IMO.
Even the math guys stay quiet on this point.
IMO, They do not want to scare anyone by telling the WHOLE truth.
They just say in the long run you will win and the vast majority thinks about
100 bets or so gets them into $$$
never to look back.
This is so far from the truth.
The 2.6% and 6.4% edge example I showed.
Here are some stats still showing a net LOSS after N rounds
500 bets
34%
14.5% about 1 in 7
1000 bets
27%
7% about 1 in 14
5000 bets
7.9% <<< this can drive an AP to stop playing, and many do just that
.04%
Trick is to always get these good edges that many would kill for
Good Luck
guarantee that after N bets made you will be showing some sort of a profit.
You still need N to get large fast just like a casino with many bets made.
This is where most all APs (advantage players) trip up IMO.
Even the math guys stay quiet on this point.
IMO, They do not want to scare anyone by telling the WHOLE truth.
They just say in the long run you will win and the vast majority thinks about
100 bets or so gets them into $$$
never to look back.
This is so far from the truth.
The 2.6% and 6.4% edge example I showed.
Here are some stats still showing a net LOSS after N rounds
500 bets
34%
14.5% about 1 in 7
1000 bets
27%
7% about 1 in 14
5000 bets
7.9% <<< this can drive an AP to stop playing, and many do just that
.04%
Trick is to always get these good edges that many would kill for
Good Luck
winsome johnny (not Win some johnny)
September 24th, 2013 at 12:56:14 AM
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Thank you 7craps, this was very helpful. I appreciate your math expertise
