[Closed] A blogpost after a very long time :-) | Augustus' Blog

Good Luck ! Looking forward to see results

Hi there again, as I promised, I ran some simulations and I am going to post some basic results .. I simulated 50 000 players playing 100 000 hands each, basicly playing all in to see, how the variance can be and how will the overall results be distributed. As a mathematician, you would expect the results to be Normally distributed, as the Central limit theorem suggests.

Here is the distribution of the final profits of the players (they were going all-in with a 60% advantage for 1 unit (imagine 1$), which basically means all the players were playing equally well, with 60% average advantage in every hand.

The expected value for every player therefore is (just theroreticall, no rakes):
(60%*2$-40%*2$)*50000 = 20000$. The simulated results follow :

Basic overall statistics :

Expected value : 20 000
Average result: 20 000,5124
Standard deviation : 310,065
Median : 20 000
Minimum : 18 790
Maximum : 21 404

About the fit to the Normal distribution next time By the way, if you have any ideas of what results would be interesting for you to see, please write it in here or by message

Hmm am I mistaken, or is putting people All in 100 000 times wrong, since with SSS for example you will be involved in only 10% of the played hands, so the variance should be much greater (since there is a smaller sample). Also I think you should reduce the avg. advantage to something like 55% (maybe even less), because is not realistic that we'll have an advantage so big in average.

Another thing that is not calculated is the strenght of the hand recieved, which probably increases variance.

I really like your study and I will be impressed if you manage to add more parameters to this to get an accurate result. I'm looking forward to it :).

Originally posted by RahXephon1
Hmm am I mistaken, or is putting people All in 100 000 times wrong, since with SSS for example you will be involved in only 10% of the played hands, so the variance should be much greater (since there is a smaller sample). Also I think you should reduce the avg. advantage to something like 55% (maybe even less), because is not realistic that we'll have an advantage so big in average.

Another thing that is not calculated is the strenght of the hand recieved, which probably increases variance.

I really like your study and I will be impressed if you manage to add more parameters to this to get an accurate result. I'm looking forward to it :).

Thank you so much for the feedback
- Regarding the sample size -> You are absolutely right .. We need to have much bigger amount of played (dealt) hands to have 100 000 allin hands, so the "total sample size" is like 1.1m hands, I forgot to mention that and I will definitely use only 10 000 hands in the next simulations (they will run 10 times quicker at least ♠_grin: )
- Average advantage -> already done that, I have simulations with 50%, 52,5%, 55%, 57,5% and 60% .. When I will have time, I will run them for more percentages, like 50%,51%,52% and so on, as I am really interested how the variance is affected by changing our advantage

As for the future I will do at least this :
- Simulate every hand with different win % (generate it randomly as in reality it is, even though the results should be the same as putting the same % in every hand in a big sample sizes)
- Look on the whole run of all the players in details to determine the longest losing streaks and their distributions -> this could lead to interesting results regarding ideal bankroll management, like how many BIs you need to have 99% probability of not going broke and so on

Once again, thank you very much for your feedback , I will certainly include it in the simulations the next days And of course, if you have any more ideas please write them in

Hi there!
Just wanted to post, to let you know there are some ppl who find it really interesting and cool that you are running those simulations, so im looking for more

Im also pretty drunked but well..

What source of randomness do you use? Do you know how good it is?
Thanks.

This one seems interesting, I'll be reading regularly maybe I can learn something about these numbers

@ Meiffert
Hi, I use Mersenne Twister, which is considered very good pseudorandom number generator, even passed the DieHard tests .. Maybe even too good for simulations like these (it is also used in software like MatLab)

@ JuiceQuadre & KidPokersKid (nice nickname
Thank you guys, very nice to know that someone actually reads this

Hi guys, as there was a nice discussion about roulette (see here :
The best way to play roulette?) I would like to post some basic math and my notes about roulette (there is no advanced math to be found there )

What is the expected value on betting (considering standard 36 number roulette with one 0):
- Betting a colour (18/37 chance of winning double your stake): E=18/37*2=36/37
- Betting a number (win 36 times your stake): E=1/37*36=36/37
- Betting a column (win 3 times your stake): E=12/37*3=36/37
- Betting a combination (0,5$ on red + 0,5$ odd): E(result red + odd) = 0.5*4*(10/37)+0.5*2*((8+8)/37) = 36/37

Conclusion :
As you can see, betting red, black or any other "special" selection is exactly equal to betting each number in the group, which means, you can only get 36/37$ of every dollar bet, whatever combination you bet on

You are down 0.027$ everytime you bet a single dollar on roulette .. So the best way to play roulette is not to play (or play with play money as sydney69 suggests)

The "double each stake strategy" (aka Martingale betting)
- There is a strategy to bet 1$ on red .. if you win, OK, bet 1$ on red again, if you loose, double your stake to 2$ .. If you win, nice, you have 1$ profit, if you lose, bet 4$ (if you win you have 4-2-1=1$ profit again) and so on
This strategy of course works theoretically, but it is profitable under 2 assumptions:
1) unlimited bankroll
2) unlimited maximum stake in the casino
However these conditions are not met in reality, so this strategy cannot work in real life

A few interesting notes
- Do you know, what is the sum of all numbers on roulette ♠_evil: ?
- Did you know, that using double betting strategy, it does not matter what colour you bet on each try ? (it does not matter if you always bet on black or you bet on random color each time)
- Americans are probably more greedy, as you lose more on american roulette (0,05263$ on every dollar), as there are 2 zeros but you still only win 36 times your bet on a number

Originally posted by AugustusCaesar
- Do you know, what is the sum of all numbers on roulette ♠_evil: ?

Hehe, nice one. I was like "Why the hell is he asking such an easy high school question?" :-)

Where did you get that nick name from?
:f_confused:

Originally posted by TribunCaesar
Where did you get that nick name from?
:f_confused:

Hi I am just a maniac into Roman history and Augustus is my most favourite historic figure, pretty simple

I could have guessed that..... you didn't really get the point imo ^^

Originally posted by TribunCaesar
I could have guessed that..... you didn't really get the point imo ^^

Well I see that our nicknames are quite similar but I would guess that your Caesar is actually Gaius Julius Caesar (correct me if I am wrong

And if your point (I can only guess as you did not write it) is that I was inspired by your nickname creating my own or even copied it, that is not true, as I used it playing on bWin long before I even knew PokerStrategy.com (see here if you care about the proof, I just want to close this thing)

PS. I have a lot of respect for you and really enjoy watching your videos

Originally posted by AugustusCaesar

Originally posted by TribunCaesar
I could have guessed that..... you didn't really get the point imo ^^

Well I see that our nicknames are quite similar but I would guess that your Caesar is actually Gaius Julius Caesar (correct me if I am wrong

And if your point (I can only guess as you did not write it) is that I was inspired by your nickname creating my own or even copied it, that is not true, as I used it playing on bWin long before I even knew PokerStrategy.com (see here if you care about the proof, I just want to close this thing)

PS. I have a lot of respect for you and really enjoy watching your videos

Cmon i think Tribun was just kidding, that was the point ^^

obv I was just kidding because of the similarity of the nicks. And btw: I was inspired by Gaius Julius, yes, but he never was a Tribun ^^

Hi there,

These day I have kind of a lot work to do, so I do not have much time to concentrate and play poker and I got pretty bored by grinding NL SH, so I was thinking about trying something else. After watching some bahmrock's videos I decided to give PLO a try, of course on PLO10, as I am a total newbie to the game. I find it very interesting, funny, and sort of "mind challenging", as combining 4 cards with a 3 card flop is much funnier than combining 2 with 3. Surprising thing - I found PLO10 very profitable in comparison with NLHE even for an omaha newbie like me, just playing pure value poker .. Anyways it is a lot of fun and a bit of gamble Maybe the fish and recreational gamblers are moving to the PLO tables where they have a better chance of sucking out ?

A little bit of surprising thing is for a non-omaha player, that the nuts on the flop can be actually be in very very bad shape, which is interesting from the math point of view. I created a situation, when a player holding the nuts on the flop heads up is actually only about 25% to win the hand .. Can you figure out something even worse for the nuts ?

Here is a hand I created :

Player 1 : Q♥ J♥ 10:diamond: 10:spade:
Player 2 : 2 3♥ 7♠ 8♣

FLOP: 9♥ 10:heart: 6♠

Player 1 has top set with an OESFD has 74,268% to win,
Player 2 has the nuts and amazing 25,732% to win the hand.

BTW. for iPhone users, I did the calculation with a great and free application called SidePod

very cool blog!

Originally posted by AugustusCaesar
Hi there,

These day I have kind of a lot work to do, so I do not have much time to concentrate and play poker and I got pretty bored by grinding NL SH, so I was thinking about trying something else. After watching some bahmrock's videos I decided to give PLO a try, of course on PLO10, as I am a total newbie to the game. I find it very interesting, funny, and sort of "mind challenging", as combining 4 cards with a 3 card flop is much funnier than combining 2 with 3. Surprising thing - I found PLO10 very profitable in comparison with NLHE even for an omaha newbie like me, just playing pure value poker .. Anyways it is a lot of fun and a bit of gamble Maybe the fish and recreational gamblers are moving to the PLO tables where they have a better chance of sucking out ?

A little bit of surprising thing is for a non-omaha player, that the nuts on the flop can be actually be in very very bad shape, which is interesting from the math point of view. I created a situation, when a player holding the nuts on the flop heads up is actually only about 25% to win the hand .. Can you figure out something even worse for the nuts ?

Here is a hand I created :

Player 1 : Q♥ J♥ 10:diamond: 10:spade:
Player 2 : 2 3♥ 7♠ 8♣

FLOP: 9♥ 10:heart: 6♠

Player 1 has top set with an OESFD has 74,268% to win,
Player 2 has the nuts and amazing 25,732% to win the hand.

BTW. for iPhone users, I did the calculation with a great and free application called SidePod

Yes it is quite funny in what kind of bad shape you can be on the flop. It is possible to be in even worse shape though

I'll just modify your example a bit:

9:h 10:h 6:s

Player 1: 2:d 3:d 7:s 8:c
Player 2: T:d: T:s 7:h 8:h

Now we have 17,93% Pot Equity vs 82,07% with the nuts, winning 0 times, splitting 294 times and losing 526 times

You can get similarly bad situations when combining re-draws to higher straights + flush redraws in which the nuts are getting freerolled and losing 30%+

Another one:

9:h 10:h 6:s

Player 1: 2:d 3:d 7:s 8:c
Player 2: J:s Q:s 7:h 8:h

11.52% vs. 88.48% with 0 wins, 189 ties and 631 losses

Thats why its always good to have a pair or a flushdraw in your wrap hands and why non-FD wrap hands are not that strong (since if you get action with a nutstraight you are most likely going to split - with the worst case you being freerolled if you don't have redraws.

Essentially you want to be the one that gets the money in with the nuts with redraw versus the nuts without redraw so that you can have a freeroll. Omaha is therefore also the only format in which its ok to fold a "weak nuts" on the flop against heavy action by multiple opponents while not having invested anything.

Very nice blog btw

Best regards
SoyCD