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Old 04-16-2018, 06:41 AM   #1
Natalino1978
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Optimal strategy to minimize risk

Hello everyone! I am an Italian university student who is conducting a scientific research on the game of poker; to be precise I'm trying to do a risk analysis on the No Limit Texas Holdem. The goal is to find a strategy that provides rational solutions during the game. The specialty that I would like to focus on is that of Sit&Go 6max or 9max. Any good soul would be willing to pass me a sample of 300000/400000 hands played on this type of game to make a fairly accurate analysis?
I would be very grateful! Have a nice day.
I specify that this research will most likely be my degree thesis; it all depends on whether I will be able to have this amount of data listed above. Also, once I graduate, I am willing to provide all my research.

P.s. Sorry for my bad English

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Old 04-16-2018, 06:45 AM   #2
Natalino1978
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Optimal strategy to minimize risk

Hello everyone! I am an Italian university student who is conducting a scientific research on the game of poker; to be precise I'm trying to do a risk analysis on the No Limit Texas Holdem. The goal is to find a strategy that provides rational solutions during the game. The specialty that I would like to focus on is that of Sit&Go 6max or 9max. Any good soul would be willing to pass me a sample of 300000/400000 hands played on this type of game to make a fairly accurate analysis?
I would be very grateful! Have a nice day.
I specify that this research will most likely be my degree thesis; it all depends on whether I will be able to have this amount of data listed above. Also, once I graduate, I am willing to provide all my research.

P.s. Sorry for my bad English

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Old 04-16-2018, 11:59 AM   #3
nickthegeek
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Re: Optimal strategy to minimize risk

I bet that you won't receive much attention. As expressed, it just seems that you want some free hands. Also, it's totally unclear why you need hands if you are finding the "rational solutions during the game" (whatever that means).

You should also incentivize a cooperation; what's for the guy who cooperates? Why should someone send you any hand at all? Be aware that sharing hands is also forbidden by most poker rooms.

Maybe you might find better luck if you give some details about your study.
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Old 04-17-2018, 12:34 AM   #4
coon74
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Re: Optimal strategy to minimize risk

I am afraid no one will give you 300K hands, as collection of others' hand histories in bulk (datamining) is against PokerStars' terms and conditions, and there is no guarantee that you will not sell the info to our opponents.

Also, the risk does not matter much during a Sit & Go - the bankroll size dictates which buy-in level to play, but after the tournament starts, the strategy that maximises the expected bankroll growth is so close to the one that maximises the monetary equity in the current Sit & Go that regular players strive to maximise the equity (the expected value of winnings) regardless of the bankroll size. No matter if the bankroll is 20, 60 or 200 buy-ins, the correct decision is the same (except a tiny minority of cases when the expected values of two decisions are very close to each other).

This is because there are only 2 or 3 different prizes, and they are all less than 5 buy-ins, therefore, playing in a risky style does not increase the variance much, even though it makes the probability distribution more polarised between first and last places. In a multi-table tournament, a risky style would increase the variance more significantly because the first place prize is large, and at the final table of a tournament with thousands of entrants, some of the pots may be worth a large fraction of the bankroll. However, due to final table deals, such pots are quite rare even in big tournaments.

Let me give you a simplified example showing how little the bankroll size matters for the strategy of playing a single Sit & Go hand.

Let us assume for simplicity that the value function of a bankroll is its natural logarithm like it is commonly assumed in financial mathematics (such as the Kelly criterion for portfolio management or sports betting).

Suppose that the bankroll is €200 (after you bought in) and you're playing a €10 6-max SNG with prizes €35.10 (65% of the €54 prize pool) and €18.90 (35%). Thus, if you finish in first, the bankroll will become €235.10, and its value will increase by ln(235.10) - ln(200) ~ 0.1617. If you finish in second, the bankroll will become €218.90, and its value will increase by ln(218.90/200) ~ 0.0903.

For comparison, the relative increase of the bankroll size (not its logarithm) will be €235.10 / €200 - 1 = 0.1755 (i.e. by 17.55%) or €218.90 / €200 - 1 = 0.0945 (by 9.45%).

Assume that the blinds are negligibly low, you have 2000 chips left on the bubble, the chip leader has 3000 chips and has gone all-in, the third player has 1000 chips. What equity do you need to call the all-in?

According to the ICM (independent chip model), if you fold, your probability of a first place finish will remain 0.3333 (33.33%), and the one of the second place will be 0.4 (40%).

If you call and lose, you'll win no prize, of course. If you call and win, you'll have 4000 chips and both opponents will have 1000, and your probabilities of the 1st and 2nd place will be 0.6667 and 0.2667.

Let us calculate the pot equity that is required so that the expected value of 1) the relative bankroll increase (corresponding to the monetary expected value without bankroll management considerations) or 2) the increase of the value function (the logarithm) of the bankroll is positive if you call the all-in.

Denote the needed pot equity of your hand against the opponent's range as 'x'. For the monetary expected value, the equation is:

(0.6667 * 0.1755 + 0.2667 * 0.0945) * x > (0.3333 * 0.1755 + 0.4 * 0.0945)

0.1422 * x > 0.0963

x > 0.0963 / 0.1422 ~ 0.6772 = 67.72%

As expected, you should have a very tight calling range when you have the middle stack and are facing a leader's all-in because you need to be a 68% favourite to win the pot.

If you wish to maximise the expectation of the logarithm of the bankroll, the equation is:

(0.6667 * 0.1617 + 0.2667 * 0.0903) * x > (0.3333 * 0.1617 + 0.4 * 0.0903)

0.13188 * x > 0.09002

x > 0.09002 / 0.13188 ~ 0.6826 = 68.26%

As we see, even if your bankroll is merely 21 buy-ins, the adjustment to the calculated value of the needed pot equity when the risk of bankroll ruin is taken into account is only 0.54%. This difference is negligible in practical decision-making during a poker hand. The range remains the same whether or not you account for risk. For bankroll sizes that most professional players use (50 or more buy-ins), the difference is even smaller.

For example, with a €500 bankroll in the above scenario, if you wish to maximise the short-term expectation of the winnings, the needed equity is of course the same 67.72% as above, whereas if you wish to maximise the expectation of the logarithm of the bankroll, the equation becomes:

(0.6667 * ln(535.10/500) + 0.2667 * ln(518.90/500)) * x > (0.3333 * ln(535.10/500) + 0.4 * ln(518.90/500))

x > 67.94%

I advise you to choose another topic for your research because the fact that, if a professional plays for adequately low stakes, the bankroll size never affects the strategic decisions during a hand, is so obvious to almost all professional poker players that such a research would be a waste of effort, in my opinion.

Last edited by coon74; 04-17-2018 at 12:59 AM. Reason: added calculation for a €500 bankroll
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Old 04-17-2018, 06:55 AM   #5
Natalino1978
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Re: Optimal strategy to minimize risk

My research is based on using risk dominance strategy on poker. It's a mix between Statistics and Game Theory. Now I can not say more than that, but I will provide all the information about the work I am doing. Once I finish my thesis I will provide all the material to him (if there will be someone) who will give me a sample of those dimensions that I mentioned in the initial message. I am also willing to review the type of game to choose from. I accept any advice. I also guarantee maximum discretion and availability.

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Old 04-17-2018, 09:33 AM   #6
Didace
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Re: Optimal strategy to minimize risk

Quote:
Originally Posted by Natalino1978 View Post
It's a mix between Statistics and Game Theory.
Tell us about game theory that doesn't use statistics.
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Old 04-17-2018, 09:44 AM   #7
Natalino1978
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Re: Optimal strategy to minimize risk

When I talk about statistics I refer to decision trees, to possible simulations with R, ...

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Old 04-17-2018, 06:35 PM   #8
CHUCKyaMUCK
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Re: Optimal strategy to minimize risk

Well I learnt more in that post than I have in a long time; thanks...

BR,
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Old 04-18-2018, 09:43 AM   #9
heehaww
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Re: Optimal strategy to minimize risk

Was coon74's post there the entire time? I read the thread yesterday (up to Didace's post and Natalino's reply) and I feel crazy for thinking the timestamp is way off. It's a pretty hard post to miss, being taller than my monitor and all.
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Old 04-18-2018, 10:13 AM   #10
coon74
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Re: Optimal strategy to minimize risk

Quote:
Originally Posted by heehaww View Post
Was coon74's post there the entire time? I read the thread yesterday (up to Didace's post and Natalino's reply) and I feel crazy for thinking the timestamp is way off. It's a pretty hard post to miss, being taller than my monitor and all.
OP made 2 threads - first in STT Strategy, then in Probability. I and CHUCKyaMUCK responded to the STT thread. Then the threads were merged.

In the hindsight, I should have given a more realistic example, with reasonably large blinds and antes (like 75/150) and accurate Nash equilibrium push/fold ranges; the equity calculation is done the same way there. I'll give such an example if anyone requests it, lol.

Quote:
Originally Posted by Natalino1978 View Post
My research is based on using risk dominance strategy on poker.
Risk dominance is only useful when there's more than one Nash equilibrium. In push-or-fold scenarios, it seems that there's usually 1 equilibrium, to which fictitious play converges quite fast. If we allow calls (limps) or small raises, fictitious play converges slowly, but I'm still not sure if there are ever 2 or more equilibria to select from.

Besides, when you study Nash equilibria, it's useless to consider hands played in real games - most of the real players deviate from Nash equilibria anyway; weak players deviate so much that, actually, it's more worthwhile to assign fixed strategies to all opponents on the basis of population tendencies found in real data (or, for strong regular players, basing on the results given by the commonly used calculators - Holdemresources and ICMizer), and calculate the optimal response to those strategies.

Even if you intend to create a new commercial calculator using risk dominance, it won't sell well in the first year because it will be not more useful for the real games than the current calculators are - most opponents will be playing either irrationally or according to the strategies advised by the current calculators, based on superficial assumptions about bet sizes, not according to the equilibria found by your new calculator. It will take long until most regular players adopt the new calculator, so you have to be patient.

Last edited by coon74; 04-18-2018 at 10:42 AM.
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Old 04-20-2018, 11:24 PM   #11
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Re: Optimal strategy to minimize risk

If you are actually doing this research, you do not need the hands. You can simulate as much data as you want.
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