Originally Posted by

**FishBear**
Thanks Don.

I'm asking for a recreational player who is not card counting. I understand this is theoretically a losing game. The question is how do I calculate the ROR given a 320 hand constraint. I'm assuming near perfect basic strategy and the house edge to be around -0.67%. If I had to guess, the game is probably a standard shoe game, so: h17, das, da2, rsa, no surr.

He is using a betting system where I gauged $75 to be a rough estimate as the average bet. Based on your tone, it seems like I cannot just use 1.14 unit as stdev.

The betting system to be precise is to start with 2 units and increase the bet for every previous win. The maximum to be risked is 5 units. If he loses a bet then he'll return to 2 units. 1 unit is $25.

I ran a very quick simplified sim of 10M hands with "rand() < 0.5" as the factor to increasing a unit or going back to 2 units, and I arrived at 2.875 or so units ($71.88) as the average bet.

50: 4,999,300

75: 2,498,470

100: 1,250,711

125: 1,251,519

(yes I see what they converge to)

I get in the actual world, there are splits and doubling in BJ and the game is not 50-50 but something along the lines of 42-48-10. I assume all this overcomplicates the equation when all I want is a rough estimate (within 5% is fine) on one's ROR after 320 hands.

So my question is approx what are the odds of tapping out (within 5% accuracy) if he brought

a) $1500

b) $2000

c) $2500

My assumption is there exists a ROR formula where I can just plug in

- sample size

- expected value,

- average bet,

- stdev, and

- session bankrol

to arrive at an approx answer.

My gut tells me $1500 and even $2500 is not enough (impractical) as a session bankroll, because he is likely to go bust a high frequency of the time, but I am unable to convince him that without the actual math. He seems fixated on the idea that the tail end of 1stdev is a good estimate as to what a session bankroll should be.

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