Win rate with optimal strategy against limit raise bot

[Ludanto]

mykey1961 wrote:

[ QUOTE ]
This shows that even though this hand has 50%+ equity, it's still better to call on the flop than to cap.
If you had capped 98o preflop, then capping would have been the better option on the flop, but that option still wouldn't be as good as calling preflop, and calling on the flop.
The 4, and 8 represent the pot size on the flop.
-2.00000000 4-Fold 8h9s JcTd2s
3.15568077 4-Call 8h9s JcTd2s
3.13601884 4-Cap4 8h9s JcTd2s
---------------------------------------------
-4.00000000 8-Fold 8h9s JcTd2s
3.13266056 8-Call 8h9s JcTd2s
3.15201973 8-Cap4 8h9s JcTd2s

[/ QUOTE ]

The EV I get on a JT23r board (with capped flop) is significantly higher than the EV you have calculated. Here is my way of doing this:

I assume that the turn card is a 3 with a suit that wasn't on the flop. It is the worst turn card that can come in terms of EV so if you calculate EV for all river cards it should be even higher than what I will show below.

Holecards: 8h9s Board: JcTd2s3h # of unseen cards: 46 of which
On River the raise-bot bets out -> pot = 18 sb, call = 2 sb -> 10% EV is break even -> EV < 10% = fold, EV > 10% but < 50% = call, EV > 50% = cap

If I call I win/lose 10 sb. If I cap I win/lose 16 sb.


4 x A (EV = 18.232%) -> CALL -> EV = 4 x 10 sb x .18232 = 7.293 sb
4 x K (EV = 19,848%) -> CALL -> EV = 4 x 10 sb x .19848 = 7.939 sb
4 x Q (EV = 96.717%) -> CAP -> EV = 4 x 16 sb x .96717 = 61.899 sb
3 x J (EV = 19.848%) -> CALL -> EV = 3 x 10 sb x .19848 = 5.954 sb
3 x T (EV = 19.848%) -> CALL -> EV = 3 x 10 sb x .19848 = 5.954 sb
3 x 9 (EV = 63.434%) -> CAP -> EV = 3 x 16 sb x .63434 = 30.448 sb
3 x 8 (EV = 64.747%) -> CAP -> EV = 3 x 16 sb x .64747 = 31.079 sb
4 x 7 (EV = 99.545%) -> CAP -> EV = 4 x 16 sb x .99545 = 63.709 sb
4 x 6 (EV = 10.960%) -> CALL -> EV = 4 x 10 sb x .10960 = 4.384 sb
4 x 5 (EV = 10.960%) -> CALL -> EV = 4 x 10 sb x .10960 = 4.384 sb
4 x 4 (EV = 10.960%) -> CALL -> EV = 4 x 10 sb x .10960 = 4.384 sb
3 x 3 (EV = 17.424%) -> CALL -> EV = 3 x 10 sb x .17424 = 5.227 sb
3 x 2 (EV = 17.424%) -> CALL -> EV = 3 x 10 sb x .17424 = 5.227 sb

237.871 sb / 46 hands = 5.171 sb / hand

My calculation suggests that by capping the flop our EV is higher than 5.171 sb/hand (because any card is better on turn than the 2). Where is my mistake?

[pzhon]

[ QUOTE ]
My calculation suggests that by capping the flop our EV is higher than 5.171 sb/hand (because any card is better on turn than the 2). Where is my mistake?


[/ QUOTE ]
You computed the expected amount won. You didn't subtract the money you put into the pot. Your 0 means you lost the pot. Mykey1961's calculations are the net amounts, so losing 10 sb on the hand is -10, not 0.

[mykey1961]

Lets assume an sb = $1.00.

You are dealt 9s8h, you call $0.50, the bot raises to $2.00, and you call.

At that point the pot is $4, and you've put in $2.00 of it.

The flop comes JcTd2s.

You decide to cap, so the pot is now $12.00, and $6 of that comes from you.

The turn is 3h, you call $2.00 making the pot $16.00, $8.00 is your investment.

The river comes any kind of 6, the bot makes it $2 to go in an $18 pot.

Folding's EV = $18.00 * 0.00000 - $8.00 = -$8.00
Calling's EV = $20.00 * 0.10960 - $10.00 = -$7.808

Compare that to not capping on the flop.

You are dealt 9s8h, you call $0.50, the bot raises to $2.00, and you call.

At that point the pot is $4, and you've put in $2.00 of it.

The flop comes JcTd2s.

You decide to call, so the pot is now $6.00, and $3 of that comes from you.

The turn is 3h, you call $2.00 making the pot $10.00, $5.00 is your investment.

The river comes any kind of 6, the bot makes it $2 to go in a $12 pot.

Folding's EV = $12.00 * 0.00000 - $5.00 = -$5.00
Calling's EV = $14.00 * 0.10960 - $7.00 = -$5.4656