Quote Originally Posted by DSchles View Post
The validity of the results from a SIM of 5,000 hands is meaningless. But that has nothing to do with what Dog Hand calculated. His work had nothing to do with a sim, and the results are accurate, no matter what the number of hands.

Don
Just to elaborate on Don's comment concerning 5000-hand sims:

I have an Excel file containing 300,000 hands of BJ played by a heads-up B.S. player flat-betting $5/round for a 6D, H17, DAS game with 75% penetration. For this game, billion-round simulation results give the player's IBA as -0.5580% and his SD as 1.16.

I used Excel to look at every 5000-hand set in these data: thus hands 1-5000, 2-5001, 3-5002, etc. The best set had the player winning $1,285 on total initial bets of $24,425 (4,885 rounds, EV = -$136.29), for an edge of a whopping +5.2610% and a z-score of 3.5061. The worst set had the poor guy losing $1,557.50 on total initial bets of $24,375 (4,875 rounds, EV = -$136.01), for an edge of -6.3897% and a z-score of -3.5102.

The wide range of results for 5000-hand sims indicates clearly why such small sample sizes are not useful when the edge is so close to zero.

In fact, for these 300,000 hands the player was "lucky": instead of losing the expected $8,133.35, he lost "only" $7,070.00, for a z-score of 0.3396. Thus, even 300,000-hand sim are not sufficient to generate useful results.

Hope this helps!

Dog Hand