You are drawing dead anytime a made flush calls, we will need to assign a number for this eventuality to get a feel for the rest of the play. Let’s try 50% to start. So in a 100 hand sampling you lose $168 x 50 = $8400.
We need to assign a number to the amount of times your AI wins the pot, let’s say 5%
5x $129 = $645. We now have 45 hands where we are called by one or both players.
Our worst case here is facing any AQ. On those hands where we even have a draw we will tie the pot 3.5% of the time. The probability of being dealt any AQ is 82:1 against. Since we are dealing with 100 hand sample we should add another $162.12 loss to our loss total ($168 x .965 to account for our tie possibility) and raise our loss total to $8562.12. That leaves us with 44 hands. Let’s say we get one caller 60% of the time and two callers the rest. That means 26 times we have a single caller. I think we should deal only with flush draws and boat draws here. The only boat draw with a flush draw possible is 77. I think it’s unlikely. I ran simulations on Poker Stove for the Q9 vs. AhKc and the straight wins 75%. So if we think we’ll see a FD 75% of the times we have 1 caller we get 20 hands (rounded from 19.5). 15 times we win $440 changing our win total to $7245 and 5 times we lose $168 raising our losses to $9402.12.
Six times we will face a set. We win 77% of the times we face a set HU (except for a 77 with a flush draw, the most favorable case which wins 43% of the times it plays.). We win 4.62 of 6 hands at $440 per hand raising our win total to $9277.80. We lose 1.38 of 6 hands at $168 per hand raising our total losses to $9632.96.
Eighteen times we will face two callers. The worst case for us that hasn’t been covered is when we face one flush draw and one set other than 7h7. That is when the two callers don’t compete for outs and neither is drawing dead. I will use that scenario for the rest of the hands.
Even here we are 55%-45%. We win 9.9 hands at $583 each making our win total $15049.50. We lose 8.1 hands at $168 each making our total loss figure $10993.76. Our
total win is $4055.74 making our AI play +$40.56
Maybe you don’t think my estimates are anywhere close to accurate, ok. Still I think there is a case here for considering a push into this board unless you think you are drawing dead more than 50% of the time when you push.Statistics: Posted by Calaziar — Sun Oct 15, 2006 2:02 pm
]]>