Sage said:
Matt21
Does your math also prove that the win rate per hand would stay the same even if the table was full? Would you run another test with 5 or 6 players at the table? When the AP get 194 hands [regardless of the number of rounds] will the win still be $141?
I checked this. Yes the win rate would stay the same even if you had 5 other players sharing the table with you. However, the crucial point is that you will need a much higher number of shoes to complete the required number of hands. Running with the 194 hands I computed very similar win rates (a little different from yesterday's rate because I couldn't recall the exact parameters)
Heads-up, 4 shoes, 194 hands, win rate $134
With 1 other, 5.8 shoes, 195 hands, win rate $135
With 3 others, 9.3 shoes, 194 hands, win rate $134
With 5 others, 12.8 shoes, 194 hands, win rate $134
(by the way the ramp used here is 1x25-2x350 - this was on a starting roll of $50k)
Notice how the number of shoes required to hit your 194 hands really increases as the table becomes more populated. In my counting I found that the number of shoes completed per hour didnt really change significantly as players increased - this implies that you are really lowering your EV rate by playing at a full table.
Another way of looking at it is to keep the number of shoes/hour the same, and see what happens to the AP's hands/hour and thus the win rate.
Heads-up, 4 shoes, 194 hands, win rate $134
With 1 other, 4 shoes, 134 hands, win rate $93
With 3 others, 4 shoes, 83 hands, win rate $58
With 5 others, 4 shoes, 60 hands, win rate $42
the numbers are from my own spreadsheets, but they correlate fairly well with outputs from CVD.
Sage said:
I have always thought the more players, the less chance I would have of getting the good cards. So I have been staying away from full tables, thus I will go to the small local casino and if it was crowded I would not play. Since you have proven the win rate per hand [not per hour] is the same regardless of the number of players, I will begin to play more. Thanks!
This is the same thinking that I had always adopted and have argued about furiously with some fellow counters in the past. But running through some of my models yesterday made me realise that this thinking is not correct.
As Southpaw already pointed, the EV can be increased by wonging on full tables - so there are ways you can increase the EV on populated tables. But all in all I am sometimes amazed at why counters are happy to play at full tables!!
An alternative approach is to think of your EV per shoe - the EV/shoe for a full table is lower than for EV/shoe for heads-up table.