Part II. Short-term perspective

You probably know or have read about people who have won at the GGNetwork AoF. This may seem to contradict the previous findings. It really doesn't. As in any probabilistic process there is variance, which is largely what determines the behavior of the system in the short term. When the variance is on your side, you will be at an advantage for a while. It is during this period of time that players like to talk about their victories, but in reality - the player was just lucky.

Luck is an abstract and subjective thing. Let's try to be more specific. Two situations come to mind. The first one - I doubled, tripled, etc. my bankroll, the second one - I played a hundred, thousand or ten thousand hands and won.

In order to evaluate how short-term AoF play is financially beneficial, we will compare it to playing French roulette. It is known about roulette that it is also unprofitable in the long term, and the main thing is that it does not require any knowledge and skills at all and depends only on luck.

Let's check the first statement about bankroll multiplication. Bankroll size in AoFGGNetwork is a meaningless concept. No matter how big your bankroll is, you will lose it sooner or later. For the sake of certainty, let's take three different bankroll sizes: one buy-in, thirty buy-ins and one hundred buy-ins. Our choices are based on the different strategies a player can employ. The strategy of a player with a bankroll of one buy-in is to double up quickly and walk away from the table. In order to reduce the risk of ruin, it is considered that the minimum bankroll for Texas Hold'em should be at least thirty buy-ins, and for the strategy of short stacks at least one hundred buy-ins. One, thirty, one hundred buy-ins are 8BB, 240BB and 800BB respectively.

Let's build the following model. A player has a bankroll of 8BB, 240BB or 800BB. He will play until he either multiplies his bankroll or goes broke. We will play ten thousand such sessions to calculate how many times the player wins and how many times he loses. Dividing these numbers by the number of sessions, we get the probabilities of increasing the bankroll or ruin. The simulation results, for different bankroll values, are shown in Table 2, Table3 and Table4 . They show the probabilities of increasing the bankroll and compare them with the probabilities of doing the same on roulette.

Probability of bankroll multiplication (8 BB)

Multiplier	Probability Hero EV %	Probability Hero GTO %	Probability Hero ABC %	Probability Hero Fish %	Probability Roulette %
x2	42.87	43.04	36.34	41.41	48.65
x3	29.18	29.43	23.14	26.29	32.43
x6	15.05	15.02	9.36	10.75	16.22
x9	9.97	9.14	4.81	5.50	10.81
x12	6.53	6.07	2.09	2.99	8.11
x18	3.89	3.79	0.95	0.93	5.41

Probability of bankroll multiplication (240 BB)

Multiplier	Probability Hero EV %	Probability Hero GTO %	Probability Hero ABC %	Probability Hero Fish %	Probability Roulette %
x2	23.40	26.07	10.50	4.30	48.65
x3	14.41	17.39	9.01	3.10	32.43
x6	3.00	5.07	0.74	0.05	16.22
x9	0.70	2.00	0.08	0.00*	10.81
x12	0.20	0.60	0.02	0.00*	8.11
x18	0.03	0.08	0.00*	0.00*	5.41

Probability of bankroll multiplication (800 BB)

Multiplier	Probability Hero EV %	Probability Hero GTO %	Probability Hero ABC %	Probability Hero Fish %	Probability Roulette %
x2	12.02	19.7	3.81	0.5	48.65
x3	2.31	6.86	0.37	0.01	32.43
x6	0.10	0.25	0.00*	0.00*	16.22
x9	0.00*	0.01	0.00*	0.00*	10.81
x12	0.00*	0.00*	0.00*	0.00*	8.11
x18	0.00*	0.00*	0.00*	0.00*	5.41

*- probability zero means probability less than 0.01%

Based on the modeling data, we can draw several conclusions:

• The probability of increasing the bankroll for all strategies is less than 50%. This means that you will be losing more often than winning;
• The size of the bankroll is important in the sense that the larger the bankroll, the less likely to increase it;
• Game strategy affects the probability of capital gains;
• surprising but true - playing ABC-poker strategy from the point of view of doubling the bankroll in the amount of one buy-in is less profitable than the strategy of 100% all-in (Fish). That is, waiting for a strong hand to come in is pointless. Call in the first hand or choose the EV or GTO strategy. These strategies are a couple percent more profitable than Fish.

And the main conclusion: more profitable to play roulette to multiply your bankroll.

For the second variant the model will be as follows. We play a session of ten thousand hands. During the session, after a certain number of hands, we record whether the player is in profit or loss. We will spend ten thousand such sessions and then calculate how many times the player won or lost. By dividing these numbers by the number of sessions, we find out the probability of staying in profit or loss after a given number of hands. The results of modeling are shown in Table 5 and Fig. 3.

Hands	Probability win Hero EV %	Probability win Hero GTO %	Probability win Hero ABC %	Probability win Hero Fish %	Probability win Roulette %
250	42.7	41.2	23	12.7	34.6
500	38.4	38.5	14.6	8.1	27.9
1000	35.2	34.2	13.7	5.1	20.2
2500	29.3	32.1	12.9	0.6	10.2
5000	26.1	31.9	8.3	0.1	3.7
10000	21.5	27.4	3.1	0*	0.4

*- probability zero means probability less than 0.01%

According to the results of modeling we formulate several statements:

• After ten thousand hands, if the game is played correctly (Hero EV, Hero GTO), there is a chance to stay in profit, in the sense that approximately every fourth player will not be at a loss. However, the truth is that three out of four players will lose;
• - with the wrong strategy (Hero ABC, Hero Fish), there is virtually no chance of remaining profitable;
• If you want to prolong the "pleasure" of losing slowly, playing AoF is better than roulette. You will lose longer.

Conclusions

With a small number of hands there is a chance to be in profit, but it is always less than 50% and you will more often find yourself losing than winning. As for the possibility to multiply your bankroll, the chances in AoF are less than in French roulette.

In the third part we will consider some special techniques for the game All-in or Fold.