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Old 09-11-2020, 09:47 PM   #26
robert_utk
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Re: Can this new NL Hold'em casino game be beaten?

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Originally Posted by tombos21 View Post
i'll take a crack at this basketball one.

I think you can treat this like an even money bet for 15.75 points since the computer's losses are our gain and vice versa. We want to call with hands that have greater than -1 points EV.

(PWin - Plose)*15.75 > -1
Minimum equity > 0.468

So any hand that has at least 46.8% equity can call in a vacuum. That gives us the following range:

[22+, A2s+, K2s+, Q2s+, J2s+, T5s+, 96s+, 87s, A2o+, K2o+, Q2o+, J5o+, T7o+, 98o]

call (combos) 798/1326
win% 54.76%
lose% 42.03%


EV human = -0.635 points
EV Machine = -1.44 points


Realistically this is a race to the bottom. Yes we will lose points, but the machine will lose points faster, giving us the edge.

I don't know if is the optimal solution, but it seems to be a winning strategy anyway. It doesn't use the Kelly Criterion so I'm assuming that I've missed something here.

Very clever tombos21! Thank you for your winning solution and beating the Tourney Ballers machine.


If you don't mind, let me make an adjustment to the machine...


Now it's called Tourney Ballers Overtime!

There is now a 10 second shot clock for the human to decide whether to shoot or pass (not deciding after ten seconds results in automatic pass).

Also, there is now a 5 minute game clock.

The human deposits 100 dollars for 100 points on the board.

The machine also starts with 100 points.

The game runs until one player goes to zero points, 200 points, or 5 minutes elapses.

If the computer gets to 200 points the game ends with no payout.

If the computer goes to zero, the machine pays out the human based on points. 1 point = 1 dollar.

If the human gets to 200, the human is paid out 200 bucks.

If the game clock expires, the human is paid out on points, 1 point = $1.


EDIT: The Kelly Criterion is of course very useful in the sportsbook, but is not a part of the solution. Mr. Kelly "aka Half Kelly" just alerts the gamblers when there is a broken machine in the wild.

Last edited by robert_utk; 09-11-2020 at 09:53 PM.
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Old 09-11-2020, 10:39 PM   #27
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Re: Can this new NL Hold'em casino game be beaten?

I haven’t read the modified version so I’ll only talk about the first right now.

Tombos’ solution can not be the full one, since it’s easy to come up with trivial examples where that’s not the optimal range.

For example, if the human has one point or less. He should clearly always call because folding is a guaranteed loss.

My approach would be to solve the game by computer, but I’m not motivated to do so. It shouldn’t be too complicated to solve for each possible game state though.
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Old 09-11-2020, 10:48 PM   #28
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Re: Can this new NL Hold'em casino game be beaten?

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Originally Posted by browni3141 View Post
I haven’t read the modified version so I’ll only talk about the first right now.

Tombos’ solution can not be the full one, since it’s easy to come up with trivial examples where that’s not the optimal range.

For example, if the human has one point or less. He should clearly always call because folding is a guaranteed loss.

My approach would be to solve the game by computer, but I’m not motivated to do so. It shouldn’t be too complicated to solve for each possible game state though.
Correct, the machine does not understand the concept of way ahead, way behind, or nearly to zero or nearly to 200. The Tourney Ballers Overtime machine does have more advanced features that will be unlocked eventually.

But for now, you are overthinking it. Just find a +ev call.

Last edited by robert_utk; 09-11-2020 at 10:50 PM. Reason: spelling
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Old 09-12-2020, 01:57 AM   #29
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Re: Can this new NL Hold'em casino game be beaten?

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Originally Posted by browni3141 View Post
Tombos’ solution can not be the full one, since it’s easy to come up with trivial examples where that’s not the optimal range.

For example, if the human has one point or less. He should clearly always call because folding is a guaranteed loss.
My assertion was that we should call with hands that have greater than -1 EV, not +1EV. Do you have an example of a better range?

---

@robert_utk there are two things that should be clarified:

1) When we fold, the computer gains a point. Does that come out of our stack? I assumed no.

2) In the "Ballers Overtime" game, if time expires, do we need a higher score than the computer to get our points paid out? I'm assuming no otherwise the game is likely unbeatable.

Last edited by tombos21; 09-12-2020 at 02:14 AM.
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Old 09-12-2020, 03:42 AM   #30
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Re: Can this new NL Hold'em casino game be beaten?

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Originally Posted by robert_utk View Post
Correct, the machine does not understand the concept of way ahead, way behind, or nearly to zero or nearly to 200. The Tourney Ballers Overtime machine does have more advanced features that will be unlocked eventually.

But for now, you are overthinking it. Just find a +ev call.
The +EV range is different for different "stack" sizes. I don't think I'm overthinking it. The only solution I see for this is by brute force.

Quote:
Originally Posted by tombos21 View Post
My assertion was that we should call with hands that have greater than -1 EV, not +1EV. Do you have an example of a better range?
I misread the rules but it doesn't really matter because the situations still exist. If the computer has 199 points the human should shoot with any two cards because passing gives the computer a point so the human would lose immediately. On the other hand if both the human and computer have very few points the human may want to pass very liberally. For example computer 3, human 5. A win or a loss for either side here wins/loses the game. The human can pass 7 times and this remains the case. It might be favorable to fold fairly strong hands trying to look for a better one.
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Old 09-12-2020, 05:18 AM   #31
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Re: Can this new NL Hold'em casino game be beaten?

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If the computer has 199 points the human should shoot with any two cards because passing gives the computer a point so the human would lose immediately. On the other hand if both the human and computer have very few points the human may want to pass very liberally. For example computer 3, human 5. A win or a loss for either side here wins/loses the game. The human can pass 7 times and this remains the case. It might be favorable to fold fairly strong hands trying to look for a better one.
Fair point, it reminds me a bit of an ICM problem.

However, you don't have to find an optimal strategy to know if a game is beatable, you just need to find a winning strategy.

The "ballers overtime" game is different from the last game in that we're trying to maximize our own points, rather than try to bust the computer. Let's start by calling with any +EV hand:

0 > (pWin%*5.25 - pLose%*10)
minimum equity required = 63.49%
range: 77+,ATs+,AJo+ (100 combos)

EV Human = 0.0815
EV Machine = 0.5268

So this is a simple +EV strategy, however, the computer will gain points a lot faster than us. This is fine as long as they don't hit 200, (we get paid out even if the bot is ahead). Realistically you'd widen or tighten your range near the extremities, but this braindead strategy still works.

If we go as slow as possible, to minimize risk of ruin, we have to play at most (5min/10sec) 30 hands so we are virtually never busting. Our EV in this case is about $2.4 per 5-minute round.
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Old 09-12-2020, 06:19 AM   #32
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Re: Can this new NL Hold'em casino game be beaten?

Update: I built a simulator

Tourney Ballers Overtime Simulator

Inputs:
pWin & pLose (equity of your range not including ties)
hands_per_round (number of hands played per 5 minute match)
num_rounds (iterations, for accuracy)

---
It looks like the highest EV strategy is to aim for around 90-110 hands per match, or roughly one hand every 3 seconds. This strategy busts more than going slow, but it maximizes return. The EV is about $7.7/match. Any faster and you start losing EV due to increased risk of ruin.

This strategy could be improved by adjusting your ranges when one player is close to winning/losing, and also by slowing down your play a lot when the computer is near 200 points. But it's +EV even without these obvious adjustments.

Last edited by tombos21; 09-12-2020 at 06:27 AM.
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Old 09-12-2020, 11:34 PM   #33
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Re: Can this new NL Hold'em casino game be beaten?

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Originally Posted by tombos21 View Post
Update: I built a simulator

Tourney Ballers Overtime Simulator

Inputs:
pWin & pLose (equity of your range not including ties)
hands_per_round (number of hands played per 5 minute match)
num_rounds (iterations, for accuracy)

---
It looks like the highest EV strategy is to aim for around 90-110 hands per match, or roughly one hand every 3 seconds. This strategy busts more than going slow, but it maximizes return. The EV is about $7.7/match. Any faster and you start losing EV due to increased risk of ruin.

This strategy could be improved by adjusting your ranges when one player is close to winning/losing, and also by slowing down your play a lot when the computer is near 200 points. But it's +EV even without these obvious adjustments.
tombos21,

I’m going to drop the kayfabe for this one paragraph and give you the straight shoot. I did not think through the mechanics of the scoring system very thoroughly, my mistake. But your simulator will definitely come in handy and will be very interesting to see how it plays out with the final version of Tourney Ballers Overtime. Also, I am going to unlock the advanced features of the machine ahead of time. These were supposed to wait until someone finds a +ev call (a winning call on average). So, the mechanics of the scoreboard below might seem draconian, but they are just required to get you to think about adding the most to your stack while removing the most from your opponent's stack (On average each time the cards are dealt). Also, every version of all machines should be beatable by the human, and fun, and educational. This one is pretty hard to beat. I could not think of an easier version earlier. But I have thought of it, so if you get stuck on Tourney Ballers Overtime, then stay tuned for ‘Fortune Teller’ that one will be fun too.



So, having said all that...



What? Losing in order to win? Never!



If the human gets to 200, the human wins 200 bucks.

If the computer gets to 200 the human gets no payout.

If the human gets to zero there is no payout.

If the computer gets to zero the human gets paid his score in dollars.

If the 5-minute game clock expires and the human is behind in points, the human gets no payout.

If the game clock expires and the human is ahead or tied in points, the human gets paid his score in dollars.

The human must choose to call or fold within ten seconds, but it takes 5 seconds for the machine to deal the cards. This means the game has a maximum number of 60 turns.



Tourney Ballers Overtime has new advanced features! Let's get to know your opponent....



You are playing versus a giant. His name is Jack O’neal, but his nickname is Big Jack. Since he is so aggressive all he ever wants to do to dunk the ball in your face (bet all-in with any two cards). His opponents simply refer to him as THE BIG JACK. You are going to have to find some way to defend the goal (by calling).



However, in addition to superhuman basketball abilities Big Jack is also a superhuman poker player!

The Machine has these specifications: (In Theory)

Preflop subgame perfection, with CFR+ to examine a billion hands of poker per second.

The Machine assumes the human also has all these abilities.

Hand history memory with facial recognition. It knows who you are and how you play.

If the machine starts to doubt you are superhuman, it will make adjustments to exploit you. It will pick a range of hands to fold, and give you the free point. (Yes there is a free point up for grabs).

It knows the score, it knows what almost to zero means, almost to 200 means, and WAWB.





Human deposits 100 dollars for 100 points on the scoreboard.

Machine starts with the same score, 100 points.

Machine shoves all in every hand with any two cards.

Human can call or fold.

If the human folds, the computer score is increased by 1 point.

If the computer ever open folds the human score is increased by 1 point.

If the human calls and wins the human score is increased by 5.75 points, while the computer score is decreased by 10 points.

If the human calls and loses, vice versa, human loses 10 while computer gains 5.75 points.



The human is risking 10 points to win 5.75 points, but every fold gives the machine 1 point (or the human gets the point if the machine ever folds.)

Last edited by robert_utk; 09-12-2020 at 11:40 PM. Reason: grammar
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Old 09-13-2020, 12:39 AM   #34
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Re: Can this new NL Hold'em casino game be beaten?

if you just take the last game and add the stipulation that "you need to be ahead of the computers score to get paid out", I don't think it's possible.

You can beat the computers score, at the expense of both of you having negative EV. So even though you'll win matches you'll still be paid out less than you deposited.

Alternatively You can choose to only make +EV calls, at the expense of letting the computer get ahead of you, and ultimately losing the match.

Unless I'm missing something, there's no way to have both +playerEV and +matchEV, using a single range.

Updated simulator
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Old 09-13-2020, 03:54 AM   #35
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Re: Can this new NL Hold'em casino game be beaten?

I might have to rethink that actually. The range seems to (55+,A4s+,K9s+,QTs+,A7o+,KTo+) works on paper anyway.

call (combos) 244
win% 63.63%
lose% 34.32%

EV human 0.0417
EV Machine 0.0082
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Old 09-13-2020, 07:52 PM   #36
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Re: Can this new NL Hold'em casino game be beaten?

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Originally Posted by tombos21 View Post
I might have to rethink that actually. The range seems to (55+,A4s+,K9s+,QTs+,A7o+,KTo+) works on paper anyway.

call (combos) 244
win% 63.63%
lose% 34.32%

EV human 0.0417
EV Machine 0.0082


VERY Nice work, tombos21! You found a +ev call. Is there such thing as a paper simulator?

You're gonna have to do better than that however, or Big Jack is going to send you back to the bench (without the 200 bucks on average).
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Old 09-13-2020, 11:48 PM   #37
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Re: Can this new NL Hold'em casino game be beaten?

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Originally Posted by tombos21 View Post
Fair point, it reminds me a bit of an ICM problem.

However, you don't have to find an optimal strategy to know if a game is beatable, you just need to find a winning strategy.

tombos21,

The Tourney Ballers Overtime machine is obviously a solver. It uses brute force to derive a solution. But it does not understand anything.

Understanding is what we humans do. A range of hands is not a strategy, winning or otherwise. A strategy is what produces a range of hands. A correct strategy produces ranges that win the most (or lose the least).


If you understand the underlying game theory, then you can:

Know what ranges to enter into a solver that requires the input of ranges.

Evaluate the output of solvers for error.

Evaluate the advice from books and videos about poker.

Understand the correct output from verified correct solvers.

Discuss poker in a more fundamental theoretical manner.



Now, I have been in your shoes before. Trust me, you are doing great. Hang in there. I am rooting for you. I promise that all of the machines are beatable by humans, and fun, and educational.

But quoting ranges from solvers won't help you or anyone else learn.

For instance, the method that used risk vs reward and then chose a set of hands that have individual pot equity to call did not work.

Do you think that it failed because this is an ICM simulation, or that the "free point up for grabs" somehow throws it off? I assure you that is not the case.


Alright, you have the ball now. You are playing real poker with a full deck of cards versus an artificial intelligence with superhuman abilities. YOU CAN WIN.

So, you can continue to quote ranges from solvers (not recommended). Doing this unlocks the CHALLENGE MODE of the machine which is totally boring.

Or, you can start using words and concepts that are based on fundamental proven theorems of mathematics. These include MiniMax Theorem and Nash's Theorem.
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Old 09-14-2020, 04:02 PM   #38
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Re: Can this new NL Hold'em casino game be beaten?

It's a difficult problem because pointEV ≠ $EV.

Alright, let me try an analytical approach. I'll start with a spreadsheet of equities, and simply graph the expected values (in points EV) of each player by calling frequency. Here's my work.



It doesn't look promising, but if we zoom in we can see an area of the chart where we have positive playerEV, and we are ahead of the computer's EV. I will call this area the "Goldilocks Zone"



The goldilocks zone is between 233-311 combos. If we call any tighter than this, the computer will have a higher EV than us. If we call any wider than this, we will have negative expected value.

Let's define another variable called "match EV", which is simply playerEV-computerEV. The higher our "match EV", the better chance we have of actually winning the match.



----Maximum “player EV” is achieved at 104 combos. This gives the computer a huge edge though.
----Maximum “match EV” (playerEV - computerEV) is achieved at 798 combos. This gives us the highest chance of winning the match, but it’s also hugely -EV.

Zooming in to the intersection points:



At 247 combos, matchEV = playerEV, which I believe represents the optimal range in a vacuum.


Unfortunately this is not the whole story. In this game, losing a match is punished more severely than winning a match. Often this means that we will want to take -(point)EV spots in order maximize our chances of winning the match. In other words, the current scores can drastically influence the optimal strategy. This explains why I couldn't find a profitable call using a fixed range in my updated simulator.

So we need to translate the “matchEV” (player points EV - computer points EV), into something that represents our probability of winning the match, based on the current scores of both players and the number of hands yet to play.

I’m still working on this last part. I’m not sure this can be solved analytically, as we have to adjust our strategy every time the score changes.

Last edited by tombos21; 09-14-2020 at 04:32 PM.
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Old 09-14-2020, 08:58 PM   #39
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Re: Can this new NL Hold'em casino game be beaten?

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[redacted]


What!?! Q&A Mode already?



Let me check the manual...



"Human player must unlock the hidden Neato Easteregg before Q&A mode."



Wow! Rules are rules, tombos21. Your first move is wrong, so how are you gonna beat the Tourney Ballers Overtime with all this graphs and spreadsheets?



How about you save all that hard work for the near future (or never) when you unlock the hidden ‘Neato Easteregg’, whatever that is.



While you think about the three magic (or is it mathematic) words that describe whatever it is you are looking for, I'm going to tell you a story....



Once upon a time there was this mathematician. Not just any math nerd, this guy was one of the greatest living mathematicians! The only problem was he was a losing poker player. Total master of probability theory, total master of decision theory, but a total loser at poker. This was like a hundred years ago!



Now, it turned out there was a way to figure out poker, and all sorts of games that can be used to model risk and competition and all sorts of neato stuff! It was a new way that had never been done before. These things take time, since mathematicians are all about proofs. So about 15 years later, everything was provable and very useful and he published his book.



This book was all the rage! And it had lots of graphs just like yours. However, back in the days before surplusplus they had to draw them with plots and connect the dots.



This was a lot of hard work, but its a living. What are ya gonna do?



But then came along this graduate student. This guy was odd, downright weird. But he could draw all the graphs and crunch all the numbers better than the other students by a country mile!



Then he noticed something. Every time he solved a model with two non-cooperative players (and other considerations) there was a pattern. Now let me tell ya, mathematicians love patterns. This guy was obsessed with it and bet his entire doctoral thesis that he was right. And he was!



The advantage of this new breakthrough was that it quickly bypassed a lot of the graphs and spreadsheets that he was tired of plotting. You could just check for this, see if it was a usable strategy, and boom!



These days, the only mathematicians that really care anymore about poker are computer scientist types. Gone are the days when toy poker games were in textbooks. You have to find an old edition just to read about it. Old timey talk about seeing, and raising. Did you know that mathematically a poker raise is first a ‘see’ and then a ‘raise’? Don’t use that language in Vegas, or the dealer will not be happy.



Ok tombos21, story time is over. The Tourney Ballers Machine is locked, and only three mathmagical words can unlock it.



Aiso, did I not make it clear that your solver answer was wrong? I thought I had, but sometimes communication with stubborn people such as myself can be difficult.
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Old 09-15-2020, 01:44 AM   #40
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Re: Can this new NL Hold'em casino game be beaten?

The GTO solution should maximize $EV.

$EV = MatchWin%*(PlayerPointsEV - $100) - MatchLose% * $100

where:

PlayerPointsEV is the amount of points you expect to have at the end of the match.
MatchWin% = The probability of getting paid out.

Finding your probability of winning the match is complicated, because every possible combination of scores needs to be mapped out. I guess you could start with strictly dominant strategies and work backwards from there.

For example, if we both have 199 points, then we must call any two. Our EV in this spot is zero. (50%*$100 - 50%*100)

Now lets say that we have 199 to jack's 198. We know the EV of folding is equivalent to the above situation, so we call with any hand that has greater than $0EV. So roughly minimum equity is 50% to call. That gives us the following EV
(49.32% callfreq%) * (56.64% win%*$100-40.38 lose% *$100) + (50.68% foldfreq% * $0) = $8.007

Now lets say we have 199 to 197. We know the EV of folding is $8, so you call with hands that make more than $8. etc etc

Last edited by tombos21; 09-15-2020 at 02:03 AM.
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Old 09-15-2020, 01:57 AM   #41
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Re: Can this new NL Hold'em casino game be beaten?

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Originally Posted by tombos21 View Post
The GTO solution should maximize $EV.

$EV = MatchWin%*(PlayerPointsEV - $100) - MatchLose% * $100

where:

PlayerPointsEV is the amount of points you expect to have at the end of the match.
MatchWin% = The probability of getting paid out.

Finding your probability of winning the match is complicated, because every possible combination of scores needs to be mapped out. I guess you could start with strictly dominant strategies and work backwards from there.

For example, if we both have 199 points, then we must call any two. Our EV in this spot is zero. (50%*$100 - 50%*100)

Now lets say that we have 199 to jack's 198. We know the EV of folding is equivalent to the above situation, so we call with any hand that has greater than $0EV. So minimum equity is 50% to call. That gives us the following EV
(call freq%) * (56.64% win%*$100-40.38 lose% *$100) + (fold freq% * $0) = $8.007

Now lets say we have 199 to 197. We know the EV of folding is $8, so you call with a range of hands that makes more than $8. etc etc, repeat until all possible combinations of scores are solved.

Do I sound like the kind of guy that lurks about in shady alt usernames?

I assure you that is not the case.

What other people are trying to remind you is that this is a model. It is a model of ICM. You are so deep in programmer mode that you don't realize that you are working really hard to use ICM WHILE INSIDE AN ICM SIMULATOR.

The model helps you make hard decisions in the real world. Are you going to lose EV at a final table of a tournament because you know how to ICM ICM?

Now, if you want to keep it up with your charts and graphs, while the answer is right there in the graph, go right ahead. Have at it. whatever answer you come up with will get crushed into an oila puddle with exponential speed vs the right answer.

I know you know the words. I don't know why you won't say them.
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Old 09-15-2020, 05:11 AM   #42
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Re: Can this new NL Hold'em casino game be beaten?

Remember when I said this:
Quote:
Fair point, it reminds me a bit of an ICM problem.
And isn't this essentially the underlying math behind an ICM model?
Quote:
$EV = MatchWin%*(PlayerPointsEV - $100) - MatchLose% * $100

The thing is, I'm not convinced "traditional" ICM actually works here.

-ICM assumes fixed payouts, but this game doesn't have fixed payouts.
-ICM ignores future EV.
-ICM assumes that (our points)/(total points) is our probability of winning (HU), but that clearly doesn't work here.
-ICM is based on zero-sum games. Why would I assume it extends to funky general-sum games with ceilings and floors, and non-linear EV functions, and bots that usually shove all in with any two but might at any moment change their mind and start playing perfectly.
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Old 09-15-2020, 08:54 AM   #43
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Re: Can this new NL Hold'em casino game be beaten?

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Remember when I said this:

And isn't this essentially the underlying math behind an ICM model?



The thing is, I'm not convinced "traditional" ICM actually works here.

-ICM assumes fixed payouts, but this game doesn't have fixed payouts.
-ICM ignores future EV.
-ICM assumes that (our points)/(total points) is our probability of winning (HU), but that clearly doesn't work here.
-ICM is based on zero-sum games. Why would I assume it extends to funky general-sum games with ceilings and floors, and non-linear EV functions, and bots that usually shove all in with any two but might at any moment change their mind and start playing perfectly.
Where did browni go?!?


He is a bit snarky but I like it. Someone gets to win this prize.
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Old 09-15-2020, 12:34 PM   #44
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Re: Can this new NL Hold'em casino game be beaten?

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Originally Posted by tombos21 View Post
Remember when I said this:

And isn't this essentially the underlying math behind an ICM model?



The thing is, I'm not convinced "traditional" ICM actually works here.

-ICM assumes fixed payouts, but this game doesn't have fixed payouts.
-ICM ignores future EV.
-ICM assumes that (our points)/(total points) is our probability of winning (HU), but that clearly doesn't work here.
-ICM is based on zero-sum games. Why would I assume it extends to funky general-sum games with ceilings and floors, and non-linear EV functions, and bots that usually shove all in with any two but might at any moment change their mind and start playing perfectly.
Zero-sum games?

HU?

Wow. You don’t even know how many participants are in this machine, I mean model.

Plus, you can’t even protect Goldilocks from the Three Bears.

Finally, I already told you that a strategy produces a range. Not the other way around.

The rest of your post sounds like a sales pitch. Are you one of those soapy software sellers?
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Old 09-15-2020, 04:25 PM   #45
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Re: Can this new NL Hold'em casino game be beaten?

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Zero-sum games?

HU?

Wow. You don’t even know how many participants are in this machine, I mean model.

Plus, you can’t even protect Goldilocks from the Three Bears.

Finally, I already told you that a strategy produces a range. Not the other way around.

The rest of your post sounds like a sales pitch. Are you one of those soapy software sellers?
I retract my rude comment above regarding software.

tombos21, you are a nice guy after all. Probably nicer than I am. Let’s just skip over all this nonsense. You have the solution in your graph, but refuse to spike the football for some reason.

I did say that your simulator would be fun, and it will.

But if you don’t want to even get the first trial correct, with both players symmetrically identical then you are just toying with me. That would not be very nice.

The winning strategy pays off in ways that will be fun in your simulator in my opinion.

Last edited by robert_utk; 09-15-2020 at 04:30 PM. Reason: Spelling
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Old 09-16-2020, 06:08 PM   #46
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Re: Can this new NL Hold'em casino game be beaten?

Isn’t there a super smart, super friendly, well respected Statistical Man around these parts? Come on buddy, I KNOW you got what it takes. First and goal on the one yard line.
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Old 09-18-2020, 12:58 AM   #47
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Re: Can this new NL Hold'em casino game be beaten?

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The GTO solution should maximize $EV.

$EV = MatchWin%*(PlayerPointsEV - $100) - MatchLose% * $100

The solution simultaneously increases MatchWin% and [PlayerPointsEV-ComputerPointsEV] (VS your latest answer of 247 combos)

This gives you the best result after first trial. Then you can have fun adjusting for asymmetries. I never said you were stuck with a single range, you assumed that (although the machine is crushable with a single range obviously).

Last edited by robert_utk; 09-18-2020 at 01:00 AM. Reason: added (VS your latest answer of 247 combos)
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Old 09-18-2020, 04:54 AM   #48
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Re: Can this new NL Hold'em casino game be beaten?

With no payout if the human is behind in score after the time expires, I don't think it's all that obvious that there exists a single range that crushes the machine. Maybe posting a clean game definition without the whole storytelling distraction would get more replies, idk.

Fwiw, people post here in their spare time to have fun. If they aren't having fun then they'll stop interacting. No idea what your goal is when you intentionally piss off the regular posters for no obvious reason, but you are pretty much seeing the endgame of that behavior playing out.
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Old 09-19-2020, 10:01 PM   #49
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Re: Can this new NL Hold'em casino game be beaten?

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With no payout if the human is behind in score after the time expires, I don't think it's all that obvious that there exists a single range that crushes the machine. Maybe posting a clean game definition without the whole storytelling distraction would get more replies, idk.

Fwiw, people post here in their spare time to have fun. If they aren't having fun then they'll stop interacting. No idea what your goal is when you intentionally piss off the regular posters for no obvious reason, but you are pretty much seeing the endgame of that behavior playing out.
All true. All correct.



I apologize.



I have been away for a while and forgotten my manners.



There is no reason for me to get all negative and jump on someone who is just trying to have fun, solve a puzzle, and has the best answer of anyone else in the thread. After all, who needs any of that in 2020?



So, I will do my best to explain the scoring system, which I broke because the players were spiraling their stacks into the felt. Then I will hang out for a couple days for any further input on this thread (if any) before taking a further 30 days to think about my manners. Then after that I got a puzzle specially made for someone who is gonna love it!



Here, as best as I can, is what is going on inside the machine.



When the human deposits 100 dollars, the machine matches the deposit with 100 dollars.

The total 200 dollars is wired to the “House” which owns the joint, but not the machine.

If the human gets to 200, the House pays all the 200 out to the Human.

If the human is ahead, but below 200 when the game ends, the House pays the human his score in points, and keeps the rest of the 200 as a “House Fee”.

If the computer gets to 200 points the House pays the operator of the machine the 200 bucks.

If the computer is ahead but below 200 when the game ends, the operator of the machine gets paid the score in points and the House keeps the rest as a fee.



The players are the Human and the machine, no other cards are dealt.

When cards are dealt, the machine says “All 10” and bets 10 points with ATC in order to win the 1 extra free point. Free point is free, comes from nowhere, really free.

Human can call or fold.



In addition to the player and the machine, there are the following participants...



The Dealer. The dealer deals the cards, and then waits to see if a community pot happens. When there is a community pot, the dealer charges a high risk of 25 percent and reduces the reward given to the winner of the hand.



The TD. The Tournament director is watching carefully just in case a tie happens. When a tie does happen, he says “No Risk” and the turn happened but the scores for each player are increased by 0.5 points.



The scorekeeper. Scorekeeper posts the score on the board and watches to see if one player is ahead, behind, nearly to 200, nearly to zero. The first hand the scorekeeper is just waiting for a result, because the score is tied 100-100.



The Cashier. The cashier watches the scoreboard to get ready to pay out the winner either based on points or the full 200.



In order to best account for a real shuffled deck of cards, proper runs of Monte Carlo will provide the precise answer because most of the tools available only have 4 digits of precision.





Is there a simple (doable by Human in real time) initial calling strategy by which the caller can call in a manner that produces...



Risk = Reward?

Last edited by robert_utk; 09-19-2020 at 10:23 PM. Reason: fixed ties
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Old Yesterday, 02:55 AM   #50
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Re: Can this new NL Hold'em casino game be beaten?

Just as clarification, the time limit is still in place as described earlier?

Iirc: 300 seconds overall time limit. The human can control the pace of the game within the limits of 5 to 15 seconds per hand, that time includes shuffling/dealing etc.

And when a player reaches zero points, the other is paid out 200$?

Last edited by plexiq; Yesterday at 03:01 AM.
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