[donjuan]

Oh and by the way...go back to the first message and you can see how (frankly, simply) it is calculated. The key aspect is...there is no zero on his 100 dot die. AND, that you need to use max 1/2 of the original bankroll to make one bet, such that you are guaranteed of having at least one more crack at capturing your 10% odd (thanks again demonstrating how to fin that 10% *s*) Hence, the 5,000 handle used.

ps YES DonJuanita, calculating the odds on a die is important.

All you need to know is that you get numbers 1-55 and there are 100 numbers, thus giving you a 55% chance of winning on a given roll. But thanks for the lols.

[MonkeyF0cker]

Oh and by the way...go back to the first message and you can see how (frankly, simply) it is calculated. The key aspect is...there is no zero on his 100 dot die. AND, that you need to use max 1/2 of the original bankroll to make one bet, such that you are guaranteed of having at least one more crack at capturing your 10% odd (thanks again demonstrating how to fin that 10% *s*) Hence, the 5,000 handle used.

ps YES DonJuanita, calculating the odds on a die is important.

pss So we're clear, I have no criticism of Kelly. Might even look into it. Don't confuse my return-heckling of your angry misunderstanding, with a criticism of a concept which is old and well-used. I just gather I'm hearing the Kelly logic from the wrong 3 people...

LMAO. Here's a test for you. Write the numbers 1-100 down. Now count the total numbers. Hopefully, by the time you get to number 88 or so, you'll figure out that it equals 100.

[MonkeyF0cker]

HINT: Start counting at the number 1.

[Blax0r]

Warwick44, the EV of the dice roll (50.5) is correct, I'll give you credit for that. However it's not relevant to the original problem.

Although you're getting crucified right now, we're actually doing you a seriously huge favor. Re-read donjuan's/bztips explanations and monkeyf0cker's EV calculation, while ignoring their *good-natured* heckling. If you don't agree with what they are saying, you should consider taking a step back from trading/sports betting and re-evaluate whatever you're doing.

bottom line:
EV (for a 1 dollar bet @ 1-1 odds) is .55*1 - .45*1 = .1
odds are 1-1

Kelly stake is .1/1 = .1 of your bankroll. This is the optimal amount to bet per dice roll (read the kelly paper for justification).

[Pancho sanza]

Give it up warlock, lol.

[mjespoz]

Wow!

Just came back to have a look at this thread....
Warwick44, thanks. I laughed so hard reading your posts that I actually pissed my pants!
Please do yourself a favor and read the Kelly paper. Or ask someone with a maths background to explain it to you. Then you might realize how silly you sound.

Cheers,
mjespoz

[JohnGalt2341]

I have decided to run the test myself with a 20 sided Die(I don't have a 100 sided Die). 1 to 11 will represent 1 to 55(Wins). And 12 to 20 will represent 56 to 100(Losses). Obviously only 10 rolls isn't going to tell us much. I just want to sort of see how the different percentages fair against each other even if it is only 10 rolls(plays). To make it more interesting I will allow anyone that wants to... to "wager" a certain percentage on every roll. For me, I am going to bet 3% of my bankroll on every roll. Nobody can use 3%. I will allow only whole number percentages and once a number is taken it can't be used again. Everyone will start off with 10K. Pick your percentage of your starting bankroll(10K) to bet on every roll and the person with the most amount of "money" at the end of 10 Rolls will get 25 betpoints. I know it's not much... but hey... it's a free chance at 25 betpoints and there will probably only be like 3 people playing. By the way... if 3% Wins nobody will receive any points. I will make the 10 Rolls on May 1st. And likely post my results on the same day. Pick your winning percentage now! Remember, once a person uses a percentage... it can't be picked again! So for all of you that are in love with Kelly... 10% can be only taken once. Good luck!

[tomcowley]

I reserve 0%

[JohnGalt2341]

I reserve 0%

Thanks Tom. You are locked in at exactly 10K.

[Scooter]

JohnGalt2341 - I question the quality of the literature which interests you.

[Let me take a wild guess - birther?].

[mjespoz]

JohnGalt,

Since I have absolutely nothing to lose and 25 betpoints to gain - i'll take full Kelly at 10%.

Cheers,
mjespoz

[donjuan]

Where is BTC to tell us 59-100 outperformed 1-58 for the past 500 rolls and that we should wager on that subset at even money going forward?

[Blax0r]

I'll take half of the kelly - 5%.

[MonkeyF0cker]

I reserve 0%

This is the correct answer.

[u21c3f6]

I would wager a flat $2,000 per roll.

For this specific problem, while Kelly is optimal, IMO, Kelly is better used for wagers that can be repeated many times. In this case where you probably will only have one 10 roll shot, I would wager $2,000 per roll. In this short run, Kelly will only perform better if you roll less than 5 winners. The flat wager will outperform Kelly if you roll at least 5 winners with the one exception of if the first 5 rolls are losers. In the long run of repeating this many times, the Kelly bettor will wind up with the most total money but for this one-shot deal the flat wager will beat Kelly almost 3-1.

Joe.

[MonkeyF0cker]

If this were a contest where there was risk, I would probably optimize the most likely outcome which is 6 successful rolls out of 10 and wager 20% on each which would yield $12,230.59.

0 - $1,073.74
1 - $1,610.61
2 - $2,415.92
3 - $3,623.88
4 - $5,435.82
5 - $8,153.73
6 - $12,230.59
7 - $18,345.89
8 - $27,518.83
9 - $41,278.24
10 - $61,917.36

[statnerds]

You know what amazes me, besides pretty lights.

That the majority of posters on SBR will never realize that hitting 55% over hundreds of wagers is world class. Doesn't exactly fit with your hypothetical and 10 events, but thought I'd share what popped in my head.

What size would a 100 sided die be?

[Blax0r]

If this were a contest where there was risk, I would probably optimize the most likely outcome which is 6 successful rolls out of 10 and wager 20% on each which would yield $12,230.59.

0 - $1,073.74
1 - $1,610.61
2 - $2,415.92
3 - $3,623.88
4 - $5,435.82
5 - $8,153.73
6 - $12,230.59
7 - $18,345.89
8 - $27,518.83
9 - $41,278.24
10 - $61,917.36

Isn't 5 successful rolls the most likely? (~24.6%)

[MonkeyF0cker]

Wins Probability
0 0.000340506
1 0.004161744
2 0.022889589
3 0.074603106
4 0.159567755
5 0.234032708
6 0.238366647
7 0.166478293
8 0.076302551
9 0.02072415
10 0.002532952

[Blax0r]

how'd you get those numbers? I'm surprised to see that pr(0 sucesses) doesn't equal pr(10 sucesses).

i got these:
0 0.0009765625
1 0.009765625
2 0.0439453125
3 0.1171875
4 0.205078125
5 0.24609375
6 0.205078125
7 0.1171875
8 0.0439453125
9 0.009765625
10 0.0009765625

my bad; assumed a coin flip for some reason.

i got the same values.

[JohnGalt2341]

I would wager a flat $2,000 per roll. For this specific problem, while Kelly is optimal, IMO, Kelly is better used for wagers that can be repeated many times. In this case where you probably will only have one 10 roll shot, I would wager $2,000 per roll. In this short run, Kelly will only perform better if you roll less than 5 winners. The flat wager will outperform Kelly if you roll at least 5 winners with the one exception of if the first 5 rolls are losers. In the long run of repeating this many times, the Kelly bettor will wind up with the most total money but for this one-shot deal the flat wager will beat Kelly almost 3-1. Joe.

Hmmm... interesting. I'm not sure if I agree with you or not but because you did bother to write an explanation I will throw you in the mix at $2000 a wager. We'll see how it fairs against Kelly.

[JohnGalt2341]

If this were a contest where there was risk, I would probably optimize the most likely outcome which is 6 successful rolls out of 10 and wager 20% on each which would yield $12,230.59. 0 - $1,073.74 1 - $1,610.61 2 - $2,415.92 3 - $3,623.88 4 - $5,435.82 5 - $8,153.73 6 - $12,230.59 7 - $18,345.89 8 - $27,518.83 9 - $41,278.24 10 - $61,917.36

If you want in... I'll put you down for 20%. Let's see what happens.

[JohnGalt2341]

JohnGalt2341 - I question the quality of the literature which interests you. [Let me take a wild guess - birther?].

Let ME take a wild guess... you have never read Atlas Shrugged. If you question the quality of literature which interests me... please recommend something for me that you consider high quality. I will read anything! I often read stuff that is completely awful just to see what all the hype is about. A good example of this is the bible.

As far as being a "birther"... are you referring to that I question where Obama was born? If he was born on Mars and he was a good President it wouldn't bother me at all. However, if he was(is) a shitty President and he was born in the heartland of the USA it would worry me that America wants a crappy President that doesn't believe in Freedom and the Free Market. I don't give a rats ass where he was born to answer your question. I'm a Libertarian by the way... I despise Democrats and Republicans equally. If you truly believed in Freedom... you would be a Libertarian too.

[JohnGalt2341]

You know what amazes me, besides pretty lights. That the majority of posters on SBR will never realize that hitting 55% over hundreds of wagers is world class. Doesn't exactly fit with your hypothetical and 10 events, but thought I'd share what popped in my head. What size would a 100 sided die be?

I agree with you completely which is why I choose 55%. Mostly because I truly believe that is attainable if you are REALLY good. Also, I'm not sure how large a 100 Sided Die is although I am sure that they exist. My experiment will work just fine with a 20 sided Die. 11 out of 20 equals 55%. Which is exactly the same as 55 out of 100.

[JohnGalt2341]

I have decided to run the test myself with a 20 sided Die(I don't have a 100 sided Die). 1 to 11 will represent 1 to 55(Wins). And 12 to 20 will represent 56 to 100(Losses). Obviously only 10 rolls isn't going to tell us much. I just want to sort of see how the different percentages fair against each other even if it is only 10 rolls(plays). To make it more interesting I will allow anyone that wants to... to "wager" a certain percentage on every roll. For me, I am going to bet 3% of my bankroll on every roll. Nobody can use 3%. I will allow only whole number percentages and once a number is taken it can't be used again. Everyone will start off with 10K. Pick your percentage of your starting bankroll(10K) to bet on every roll and the person with the most amount of "money" at the end of 10 Rolls will get 25 betpoints. I know it's not much... but hey... it's a free chance at 25 betpoints and there will probably only be like 3 people playing. By the way... if 3% Wins nobody will receive any points. I will make the 10 Rolls on May 1st. And likely post my results on the same day. Pick your winning percentage now! Remember, once a person uses a percentage... it can't be picked again! So for all of you that are in love with Kelly... 10% can be only taken once. Good luck!

OK The results are in! First, here are the Roll results:
1. 18 Loss
2. 8 Win
3. 2 Win
4. 14 Loss
5. 12 Loss
6. 5 Win
7. 6 Win
8. 20 Loss
9. 1 Win
10. 3 Win

Here is how everyone ended up... I only did the math once so if I made any mistakes please let me know.
1st place flat betting 2K per Roll is u21c3f6 who ended up with 14K
2nd is MonkeyF0cker who bet 20% per roll. He ended up with $12,230.58
3rd is mjespoz who used full kelly at 10%. He ended up with $11,623.22
4th is Blax0r who used half kelly at 5%. He ended up with $10,915.17
5th is JohnGalt2341 who used 3%. I ended up with $10,570.86
Last place is tomcowley who bet 0% per bet. He ended up with 10K

I'm very curious as to how things would have turned out had I rolled a Loser instead of a Winner on my last roll. I'm too lazy right now to figure out the results. Thanks for playing everyone! And congrats u21c3f6!

[u21c3f6]

I'm very curious as to how things would have turned out had I rolled a Loser instead of a Winner on my last roll. I'm too lazy right now to figure out the results. Thanks for playing everyone! And congrats u21c3f6!

Thank you.

Here are the results if the last roll was a loser:

1st place is a tie between tomcowley who bet 0% per bet and u21c3f6 who flat bet 2K per roll: $10,000.00.
3rd is JohnGalt2341 who used 3%: 9,955.08.
4th is Blax0r who used half kelly at 5%: 9,875.62.
5th is mjespoz who used full kelly at 10%: 9,509.90.
Last is MonkeyF0cker who bet 20% per roll: 8,153.73

This is actually an excellent experiment IMO to help someone better understand Kelly. Please note that in this experiment, regardless of the # of winners, full-Kelly would never be the victor even though it is mathematically optimal. Kelly is a compounding formula and requires a longer run to show its superiority. Those that only look at Kelly for a relatively small run will come to the incorrect conclusion that it is not optimal as evidenced by the many "heated" threads on the subject. Of course this is a much larger discussion which exists in many other threads so I won't bore everyone with it again.

Joe.

[JohnGalt2341]

I think I'm going to try 100 rolls with Full Kelly starting at 10K sometime within the next month. When I do so... I will post the results here. Like I mentioned earlier... the only thing that scares me about Full Kelly is losing 8 to 12 in a row.

[diondublin]

Let's say you were on a Game Show and you made it to the final round. In this round you have 10K to play with. The game is rolling a 100 Sided Die. If the Die lands on numbers 1 to 55 you Win. If it lands on 56 to 100 you Lose. Their is no juice in this game. It's all even money. You can bet as much or as little as you want per roll. You get 10 rolls total. After 10 rolls what ever money you have left you get to keep. What would be the optimum percentage of your bankroll to bet on each roll? Thanks in advance for any and all responses.

If your advantage is 10% then Kelly Criterion says to bet 10%.

However whilst this is mathematically top-EV, it is not necessarily sane in the real world. Depends how final busting would be for you, for one thing...

[MonkeyF0cker]

I think I'm going to try 100 rolls with Full Kelly starting at 10K sometime within the next month. When I do so... I will post the results here. Like I mentioned earlier... the only thing that scares me about Full Kelly is losing 8 to 12 in a row.

Here, I'll make it easier for you.

[JohnGalt2341]

Here, I'll make it easier for you.

Thanks Monkey!

[Jontheman]

Kelly says to bet 10% of your networth on this situation. Since the max play the 1st roll is 10k, one should bet 10k if they are worth more than 100k. If they win the 1st roll, the limit is now 20k. One should bet the whole 20k, if their networth is 200k or more. This will continue until you lose, or the max bet is more than 10% of your worth. At this point, you should bet 10% of your net worth.

Basically, the answer is to bet the max or 10% of your net worth, whichever is less for each roll.

Math arguments aside I'm surprised that nobody noticed that what this post implies: that you see every single penny of your net worth (presumably including such non-liquid and essential assets as your house) as being part of your gambling bankroll. Can I be the one to question whether that's a good idea and suggest that this is a fundamentally bigger error than any argument regarding bet strategy.

[JohnGalt2341]

Math arguments aside I'm surprised that nobody noticed that what this post implies: that you see every single penny of your net worth (presumably including such non-liquid and essential assets as your house) as being part of your gambling bankroll. Can I be the one to question whether that's a good idea and suggest that this is a fundamentally bigger error than any argument regarding bet strategy.

I agree.

I have another question about Kelly...

Here's the scenario... it's late November or mid April and there are literally 100's of different games to bet on on this particular day. You find 11 Plays that you are EXTREMELY confident about. Unfortunately most of these games are either on at exactly the same time or they are overlapping. If your Bankroll was 10K would Kelly recommend that you bet $909.09 on every single game?

[MonkeyF0cker]

I agree.

I have another question about Kelly...

Here's the scenario... it's late November or mid April and there are literally 100's of different games to bet on on this particular day. You find 11 Plays that you are EXTREMELY confident about. Unfortunately most of these games are either on at exactly the same time or they are overlapping. If your Bankroll was 10K would Kelly recommend that you bet $909.09 on every single game?

No. It would not.

These things have been hashed over many times before here. You would be best served by reading up on past threads related to Kelly. You should probably start by reading those which were created by Ganchrow.