NL Simulations: a simple effort to simulate variance in NL

I was fooling around with some simulations and was curious if anyone had some useful comments if my assumptions might be way off...

There is no way that I know of to do this really well so I have simplified it down to just the all-in plays in NL... (assume for this that all other plays offset each other -- bluffs/semi-bluffs that work are offset by those that don't + all the times you flop nothing/give-up/get-bluffed --- this is purely about the lumpiness/variance of the big all-in plays)

1. I assume you get all-in 2x every 100 hands played (2%)

2. When all-in, on average you have 60% pot equity (comments?)

3. All all-ins are heads-up pots

4. This is 6-Max so you pay 1 BB & 1 SB ~17% of the time...

5. You buy-in for 100 BB's

(To keep this simple, I had to assume that you have exactly 100 BB's each time you are all-in... when you already have doubled-up, it is assumed your opponent only has 100 BB's in his stack so you don't win 200 BB's on second double up, you win 100 -- likewise when you lose after doubling-up)...

The goal is to run scenarios and see what are typical swings given these assumptions...

Goal of this post is just to get some reaction to the assumptions...

FYI, my results for simulation 1 were:

(Each 'session' equals 10,000 hands)
Session 1: -5 Buy-ins (-500 BB's)
Session 2: +19 Buy-ins
Session 3: +12
Session 4: +5
Session 5: +30
Session 6: +19
Session 7: -14
Session 8: +3
Session 9: +7
Session 10: +17

Total: +93 buy-ins for 100,000 hands
9300 BB's @ 65 hands per hour = ~6 BB's per hour

any comments/questions?

(if there are any great simulations out there, please let me know)

[Yeti]

People are probably gonna poke holes in your assumptions.

Anyway, I like how there were around 30k+ hands of breakeven.

Nice work.

People are probably gonna poke holes in your assumptions.

That is what I was hoping for....

I was inspired by the other thread about what is the most buy-ins you have won during a session... the numbers people were giving sounded low to me...

I wanted to develop a model that would break this down into sub-sessions and have it run random numbers based on the constraint that it had to equal 60% pot equity over time...

When I run it over and over again, if you assume you sit at one table and play exactly 500 hands, you should easily be having some sessions where you win 6+ buy-ins... 7 or 8 buy-ins happen now and then although it is quite reasonable to go long stretches without +7 buy-in session, using these assumptions... but maybe very few people actually play 500 hands at one table very much... don't know the answer to that.

EDIT: btw, a nice 10+ buy-in session seems to come up around once every 150,000 hands or so (150k hands played 500 hands at a time)

[edge]

500 hands at a table is somewhere around 7 hours 5- or 6-handed. It would have to be something like 9 hours for a full table. My sessions are very rarely more than 3 hours, and that's a long one for me.

500 hands at a table is somewhere around 7 hours 5- or 6-handed.

yah, if people play sub-4hr sessions on average.. that would explain it...

the offsetting factor is that I thought my original assumptions were a bit conservative in that your all-ins will sometimes win more than 100 BB's if other is big stack (ie, 200 BB's) and/or the pot gets multiway (200+ BB;s) all-ins... This would exacerbate the swings both ways I guess...

I guess using 250 hand sessions makes more sense...

good point

[XChamp]

[ QUOTE ]

I guess using 250 hand sessions makes more sense...


[/ QUOTE ]

This is very interesting. I'm looking forward to the 250 hand sessions.

1 1 - 250 -0.6
2 251 - 500 +2.4
3 501 - 750 -1.6
4 751 - 1000 +2.4
5 1001 - 1250 -0.7
6 1251 - 1500 -0.6
7 1501 - 1750 +3.4
8 1751 - 2000 +1.3
9 2001 - 2250 +1.3
10 2251 - 2500 +0.3
11 2501 - 2750 +2.3
12 2751 - 3000 +1.2
13 3001 - 3250 +0.4
14 3251 - 3500 +0.4
15 3501 - 3750 -0.6
16 3751 - 4000 +1.4
17 4001 - 4250 +2.3
18 4251 - 4500 -1.7
19 4501 - 4750 -2.7
20 4751 - 5000 -3.7
21 5001 - 5250 -3.7
22 5251 - 5500 -0.4
23 5501 - 5750 +1.5
24 5751 - 6000 -0.5
25 6001 - 6250 -1.8
26 6251 - 6500 +2.5
27 6501 - 6750 +0.3
28 6751 - 7000 +3.4
29 7001 - 7250 -1.6
30 7251 - 7500 +2.3
31 7501 - 7750 +0.3
32 7751 - 8000 +0.5
33 8001 - 8250 -1.6
34 8251 - 8500 -2.7
35 8501 - 8750 -0.5
36 8751 - 9000 +0.4
37 9001 - 9250 +2.2
38 9251 - 9500 -1.6
39 9501 - 9750 +3.4
40 9751 - 10000 +1.4

Total +11.4
Max +3.4
Min -3.7

1 1 - 250 -3.7
2 251 - 500 +0.3
3 501 - 750 +0.3
4 751 - 1000 +0.4
5 1001 - 1250 +1.5
6 1251 - 1500 +0.5
7 1501 - 1750 +0.5
8 1751 - 2000 +1.3
9 2001 - 2250 -2.7
10 2251 - 2500 +2.4
11 2501 - 2750 +2.3
12 2751 - 3000 +0.5
13 3001 - 3250 +1.4
14 3251 - 3500 +1.4
15 3501 - 3750 +0.3
16 3751 - 4000 +0.3
17 4001 - 4250 -4.6
18 4251 - 4500 -0.7
19 4501 - 4750 +5.3
20 4751 - 5000 +3.4
21 5001 - 5250 +1.4
22 5251 - 5500 -1.7
23 5501 - 5750 -2.7
24 5751 - 6000 +2.4
25 6001 - 6250 -2.6
26 6251 - 6500 +3.4
27 6501 - 6750 +2.5
28 6751 - 7000 -1.5
29 7001 - 7250 +0.3
30 7251 - 7500 -0.8
31 7501 - 7750 +4.4
32 7751 - 8000 +0.4
33 8001 - 8250 -1.7
34 8251 - 8500 +1.3
35 8501 - 8750 +1.3
36 8751 - 9000 -1.5
37 9001 - 9250 -4.6
38 9251 - 9500 +2.4
39 9501 - 9750 -1.5
40 9751 - 10000 +2.4

Total +17.6
Max +5.3
Min -4.6

1 1 - 250 +0.4
2 251 - 500 +2.4
3 501 - 750 -1.5
4 751 - 1000 -1.8
5 1001 - 1250 +3.5
6 1251 - 1500 +0.4
7 1501 - 1750 +2.4
8 1751 - 2000 -1.6
9 2001 - 2250 -0.7
10 2251 - 2500 -1.6
11 2501 - 2750 +0.4
12 2751 - 3000 +0.4
13 3001 - 3250 +2.5
14 3251 - 3500 +2.5
15 3501 - 3750 +2.4
16 3751 - 4000 -0.6
17 4001 - 4250 +2.5
18 4251 - 4500 +3.3
19 4501 - 4750 -1.6
20 4751 - 5000 -0.7
21 5001 - 5250 -2.5
22 5251 - 5500 -0.7
23 5501 - 5750 +1.4
24 5751 - 6000 +0.3
25 6001 - 6250 -0.6
26 6251 - 6500 +0.3
27 6501 - 6750 -2.6
28 6751 - 7000 +1.3
29 7001 - 7250 +2.3
30 7251 - 7500 +0.4
31 7501 - 7750 -2.6
32 7751 - 8000 +4.2
33 8001 - 8250 +0.4
34 8251 - 8500 -2.7
35 8501 - 8750 -0.6
36 8751 - 9000 +1.4
37 9001 - 9250 +2.5
38 9251 - 9500 +0.2
39 9501 - 9750 -0.7
40 9751 - 10000 -2.6

Total +11.2
Max +4.2
Min -2.7

1 1 - 250 +1.4
2 251 - 500 +1.3
3 501 - 750 +4.4
4 751 - 1000 -0.6
5 1001 - 1250 +0.5
6 1251 - 1500 +0.4
7 1501 - 1750 +4.3
8 1751 - 2000 +0.4
9 2001 - 2250 -2.7
10 2251 - 2500 -1.7
11 2501 - 2750 +0.5
12 2751 - 3000 +0.4
13 3001 - 3250 +3.5
14 3251 - 3500 +3.5
15 3501 - 3750 -0.7
16 3751 - 4000 +2.4
17 4001 - 4250 +0.2
18 4251 - 4500 -2.6
19 4501 - 4750 +0.5
20 4751 - 5000 +2.2
21 5001 - 5250 +1.3
22 5251 - 5500 +0.3
23 5501 - 5750 +1.4
24 5751 - 6000 +0.4
25 6001 - 6250 +4.4
26 6251 - 6500 +1.2
27 6501 - 6750 +3.3
28 6751 - 7000 +1.4
29 7001 - 7250 -0.7
30 7251 - 7500 -2.5
31 7501 - 7750 +3.4
32 7751 - 8000 +2.3
33 8001 - 8250 +4.3
34 8251 - 8500 +0.4
35 8501 - 8750 -5.8
36 8751 - 9000 +2.5
37 9001 - 9250 +4.4
38 9251 - 9500 -0.6
39 9501 - 9750 +6.4
40 9751 - 10000 -0.7

Total +43.5
Max +6.4
Min -5.8

1 1 - 250 -2.6
2 251 - 500 -1.7
3 501 - 750 -3.6
4 751 - 1000 +4.5
5 1001 - 1250 -0.5
6 1251 - 1500 -0.7
7 1501 - 1750 -0.7
8 1751 - 2000 +1.4
9 2001 - 2250 -0.6
10 2251 - 2500 -3.6
11 2501 - 2750 +3.3
12 2751 - 3000 +0.3
13 3001 - 3250 -1.8
14 3251 - 3500 -1.8
15 3501 - 3750 +5.3
16 3751 - 4000 +1.3
17 4001 - 4250 -3.4
18 4251 - 4500 -1.7
19 4501 - 4750 -0.6
20 4751 - 5000 -0.7
21 5001 - 5250 +1.4
22 5251 - 5500 -0.7
23 5501 - 5750 -2.7
24 5751 - 6000 +5.4
25 6001 - 6250 +0.4
26 6251 - 6500 +3.3
27 6501 - 6750 -0.6
28 6751 - 7000 +1.4
29 7001 - 7250 +1.4
30 7251 - 7500 +0.3
31 7501 - 7750 -1.6
32 7751 - 8000 +6.4
33 8001 - 8250 -2.6
34 8251 - 8500 -1.5
35 8501 - 8750 -1.6
36 8751 - 9000 -2.7
37 9001 - 9250 -2.7
38 9251 - 9500 +1.4
39 9501 - 9750 +2.3
40 9751 - 10000 +3.3

Total +5.0
Max +6.4
Min -3.6

If I just summarize it for 200,000 hands, I get:

Total Max Min
1 +30.4 +5.4 -2.8
2 -13.6 +3.4 -4.7
3 +24.7 +6.4 -3.7
4 +19.1 +4.4 -4.6
5 +5.9 +6.4 -3.7
6 +30.7 +3.5 -2.8
7 +36.6 +5.4 -3.7
8 +8.7 +4.4 -4.5
9 +26.7 +6.3 -3.8
10 +25.0 +8.2 -5.7
11 +49.5 +7.4 -2.6
12 +5.9 +4.4 -3.6
13 +25.0 +5.4 -3.6
14 +1.7 +5.4 -6.6
15 +22.7 +6.4 -4.7
16 +12.5 +4.4 -4.7
17 -2.5 +4.4 -2.7
18 +10.0 +4.5 -3.6
19 +21.5 +5.3 -3.8
20 +13.3 +6.5 -5.7

Best +8.2
Worst -6.6

----------------

+8.2 buy-ins was best result over this 200,000 hand sample (read as: "the most buy-ins I won in one-sitting, playing 250 hands at a time -- over this 200,000 hand period -- was 8.2")...

-6.6 buy-ins was worst result over this sample

[rwperu34]

I'll go ahead and poke a few holes in your assumptions. I play mostly full ring at $2/$4, so take that as a caveat.

1. It's unlikely that you get all in 2% of the hands.

2. 60% is a lot of pot equity when all in.

5. You buy in for 100 BB's, but rarely are you all in for that many. Most of the time you get all in, it will be against a short stack. And certianly any time you get all in for 100 BB's, you are not a 60% favorite on average. The bigger the buy in, the smaller your all in advantage.

I'd like to see what your numbers come out at with different variables.

Have the all in % be 0.5%, 1%, and 2%.

See how it works with pot equity at 60%, 55%, 52.5%, and 50.5%.

Make the buy in 50 BB's.

Do this for six max and full ring.

I've got some good stats and can probably give you my exact pot equity number and average buy in, as well as an estimate of all in/big pot %. It will take me some time to put it together.

I think this is a good exercise, especially for newer players that haven't experienced the VIOLENT swings of no limit. Note the 30,000 hand (session 7,8,9) run that ended in the red. My personal worst was about 42,000 hands of break even.

[ QUOTE ]
I'll go ahead and poke a few holes in your assumptions. I play mostly full ring at $2/$4, so take that as a caveat.

1. It's unlikely that you get all in 2% of the hands.

2. 60% is a lot of pot equity when all in.

5. You buy in for 100 BB's, but rarely are you all in for that many. Most of the time you get all in, it will be against a short stack. And certianly any time you get all in for 100 BB's, you are not a 60% favorite on average. The bigger the buy in, the smaller your all in advantage.

I'd like to see what your numbers come out at with different variables.

Have the all in % be 0.5%, 1%, and 2%.

See how it works with pot equity at 60%, 55%, 52.5%, and 50.5%.

Make the buy in 50 BB's.

Do this for six max and full ring.

I've got some good stats and can probably give you my exact pot equity number and average buy in, as well as an estimate of all in/big pot %. It will take me some time to put it together.

I think this is a good exercise, especially for newer players that haven't experienced the VIOLENT swings of no limit. Note the 30,000 hand (session 7,8,9) run that ended in the red. My personal worst was about 42,000 hands of break even.

[/ QUOTE ]

I looked at 6 common all-in situations and their pot equities...

Set vs Overpair 90% / 10%
2-Pair vs Overpair 75% / 25%
Set vs Flush + Gutshot draw 67% / 33%
Pair + Flush Draw vs Big Pocket Pair / Top Pair 51% / 49%
Big Pair vs Nut Flush + 1 Live Over 55% / 45%
Big Pair vs OESD + 1 Live Over 57% / 41%

The average of these is 66% pot equity if you are on the good side of these situations. Assuming you can actually execute and get on the good side 2/3 of the time, your average equity is ~55% (.66 x .667)...

Maybe 55% equity is a better estimate... That said, you pick up dead money and so you are getting paid a bonus to put your money in (you make more than you can lose)... you also get multiway situations where you triple up but can only lose 1x...

This gets complex in a hurry...

I am not sure how to better estimate how often you get all-in... I should start keeping track... Most 6Max players are around 35% VP$IP and aren't bashful about getting the money in... The number is closer to 2/100 than 1/100...

Why only 50 BB's?

[Alex/Mugaaz]

People who play NLHE and complain about variance need to learn to visit the other forums, even if they don't play those games.

[rwperu34]

I'd actually like to see how things come out in all situations.

I go with the 50 BB nimber because you are much more likely to get all of the money in against them. There will also be many times you get all in against a 25 BB stack. I think, even if you have 100 BBs in front of you at all times, you will average no more than 50 BB's in all in situations. Plus, my stats are not only for all in situations, they are for all big pots. Meaning if I have 100 BB in front, and I get half of it in, but don't take the guys stack, it's still a 100 BB big pot.

With regards to the big pot win %, I've kept track of every pot I've played that's 50 BB's or more (25 each). The thing is, that's a lot of pots, so it will take me some time to compile the numbers. Off the top of my head, I'd say it's going to be a number right around 55%.

6 max the money does get in more often, and I haven't played a whole lot of 6 max. That's why I'd like to see some for full ring also.

With regards to dead money, I've found that most of my profits come from the big pots. I actually probably lose money overall in pots that don't reach 50 BBs. It's because this is where I pay for my blinds, pay to see flops that miss, and get pushed out on my continuation bets. I probably drop 0.5 BB to 1 BB per table hour in "small" pots.