# Money management in oasis poker

My advice is to use Kelly criterion to select you bet size:

Bet = Bankroll * Expectation / Variance

Then you can estimate you win rate:

Win_Rate = Game_Speed * Bet * Expectaion

Bankroll is the money you willing to risk (not necessary in the pocket today)

Always use current bankroll, not initial one. If you got unlucky and lose significant part of you initial bankroll, you should decrease you bet accordingly.

### Example 1

One box oasis-poker. Expectaion = 2% (ante). Variance = 7.7. Game speed is 40 hand per hour. Bankroll = 10000\$

What is optimal bet and winrate?

Bet = 10000 * 0.02 / 7.7 = 25.97 \$

Really we will bet 25\$

Win_Rate = 40 * 25 * 0.02 = 20 \$ / hour

## What is the Variance and Risks

Variance (dispersion) is the measure of how the real results may differ from expectaion.

Physical meaning of Variance is better to describe with Standard Deviation, wich is usualy signed as σ (sigma) and has the same units of measure as Expectation.

σ = √Variance (square root from Variance)

If random variate comply to normal distribution, then:

• Value of random variate deviates from expectaion not more than σ with 67% probability.
• Value of random variate deviates from expectaion not more than 2*σ with 95% probability (2 sigma rule).
• Value of random variate deviates from expectaion not more than 3*σ with 99.74% probability (3 sigma rule).

Let's consider N hands session in oasis-poker with expectaion Ex (ante) and standard deviation σ.

If N is big enough, the result of session is random variate with normal distribution.

Expectaion and standard deviaion for the result of the session of N hands:

Ex_N = Ex * N

σ_N = σ * √N

Session result would be:

• In range of Ex_N ± σ_N with 67% probability
• In range of Ex_N ± 2*σ_N with 95% probability
• In range of Ex_N ± 3*σ_N with 99.74% probability

### Example 2

One box oasis-poker. Expectaion = 2% (ante). Variance = 7.7. Game speed is 40 hand per hour. Bankroll = 10000\$

We use kelly bet of 25\$. What is the probable worse result of 1000 hand session (25 hours)?

Expectaion and standard deviaion for the result of the session of 1000 hands:

Ex_N = Ex * N = 0.02 * 1000 = 20 ante (500 \$)

σ_N = σ * √N = √7.7 * √1000 = 87.75 ante (2194 \$)

 Probability Min, \$ Expected, \$ Max, \$ 67% -1694 500 2694 95% -3887 500 4887 99.74% -6081 500 7081

This shows how dangerous is the game. You expect to win 500\$ in 25 hours. But you may easily lose 1700\$ (or win 2700). And the loss of 4000 is not something unreal.

All computations is in money_management_e.xlsx

You can use this file to examine you own game situation.

### Example 3

Russian poker in it's best version (this one). We play one box ans see cards from other two boxes. Theretical Ev = 6.1%, Dispersion = 11.82. Taking into account our moderate skill, estimated Ev = 4.5%.
Bankroll 10000\$. Game speed 40 hands/hour.

How much should we bet and what is eхpected hour rate?

Bet = Bankroll * Ev / Dispersion = 10000 * 0.045 / 11.82 = 38.07
Real bet would be 40.
Win_Rate = Bet * Ev * Game_Speed = 40 * 0.045 * 40 = 72 \$/hour

### Example 3A

The same game. But now we play all three boxes at the table in a team of three players. We have commpn bankroll of 30000\$.
Ev = 4.5, as in previous example. Disperdion = 13.76, higher, since we play three boxes at one table

How much should we bet and what is eхpected hour rate?

Bet = Bankroll * Ev / Dispersion = 30000 * 0.045 / 13.76 = 98.11
Real bet would be 100.
Win_Rate (for each box) = Bet * Ev * Game_Speed = 100 * 0.045 * 40 = 180 \$/час