Math question

[Zifadel]

What are my chances of making my hand here on the turn OR the river? Making my hand = 9 spades, 8 for OESD, 3 for the A = 20 outs. What percent of the time will I make my hand after all the cards are out?

Please show the math.

Full Tilt Poker - No Limit Hold'em Cash Game - $0.05/$0.10 Blinds - 8 Players - (LegoPoker Hand History Converter)

SB: $19.60
BB: $4.00
UTG: $10.00
UTG+1: $8.00
MP1: $6.20
MP2: $10.00
Hero (CO): $8.75
BTN: $7.10

UTG posts $0.10
MP2 posts $0.10
Preflop: Hero is dealt 9[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/spade.gif[/img] (8 Players)
UTG checks, 2 folds, MP2 checks, <font color="red">Hero raises to $0.30</font>, BTN folds, SB calls $0.25, BB calls $0.20, UTG calls $0.20, MP2 folds

Flop: ($1.30) 7[img]/images/graemlins/spade.gif[/img] 6[img]/images/graemlins/club.gif[/img] 8[img]/images/graemlins/spade.gif[/img] (4 Players)

[jack492505]

you counted some outs too many times. 9 spades, 6 for OESD(because two of those were already counted as spades) and 3 aces. 18 outs. 52 cards in the deck minus the 5 you know. So you have an 18/47 chance on the turn plus an 18/46 chance on the river. .383+.391= .774. So assuming i did that right, 77.4%

[Pauwl]

18 outs as stated above.


Hitting the turn + MIssing the turn and hitting the river
18/47 + (29/47)x(18/46) = 0.6244 or 62.44%

To do it the quick way, just multiply your total outs by 4, then subtract 1 for each out above 8 outs.

(4 x 18) - 10 = 62%

Or just consider outs up to 8 to be worth 4% while outs above 8 are worth only 3%. (This is the same as above)

(4 x 8) + (3 x 10) = 32 + 30 = 62.

[Zifadel]

Could I get some clarification? You both used different ways of deriving a different answer.

[AaronBrown]

5[img]/images/graemlins/spade.gif[/img] and T[img]/images/graemlins/spade.gif[/img] make both the straight and the flush, you counted them each twice to get 20 outs.

18 outs with 47 unseen cards means 29 cards that don't make your hand. You have to figure the chance of not making by the river, then subtract from 1 to get the chance of making it. 29/47 x 28/46 = 0.376. So there's a 0.624 or 62.4% chance of making at straight, flush or pair of Aces.

This is the same as Pauwl's calculation. Jack492505 computed the outs correctly, but just added the odds of turn and river. That double counts the cases where you get an out on both the turn and river.

[uminchu]

get an equity calculator like pokerstove here is the calculations there

246,088,559 games 12.843 secs 19,161,298 games/sec

Board: 7s 6c 8s
Dead:

equity win tie pots won pots tied
Hand 0: 58.381% 56.54% 01.90% 139138260 4677423.33 { As9s }
Hand 1: 06.279% 05.99% 00.30% 14740786 725994.08 { 22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, ATo+, KTo+, QTo+, JTo }
Hand 2: 17.817% 16.39% 01.44% 40341480 3551006.92 { 22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, ATo+, KTo+, QTo+, JTo }
Hand 3: 17.523% 16.13% 01.41% 39691305 3476110.92 { 22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, ATo+, KTo+, QTo+, JTo }

[mce86]

You have 9 spades. Plus 3 non spade tens and 3 non spade 5's. Add your 3 aces and you have 18 outs.
There are 52 cards in the deck, minus the 3 on the flop gives you 49. Minus the 2 in your hand gives you 47. Take away the 18 outs you have (vs. 1 pair) and you have 29. That means 29 cards come and your opponent wins to your 18 cards that beat you. Odds are approximately 29-18 or (divide both of those by 9) 3 to 2. 1.5 to 1, or a slight fav. to the river vs. 1 pair.

[jack492505]

yea that was stupid dunno why i did that wrong.

[mamoose]

That 62% represents the chance that he will improve, but has no indication to hand strength right?

[jstill]

[ QUOTE ]
That 62% represents the chance that he will improve, but has no indication to hand strength right?

[/ QUOTE ]

% to win is hand strength... u shouldnt discern between made hands and unmade hands thats a total noob flaw in thinking (no offense).. its all about equity baby...

I think u guys are giving too much equity though to ur calculations... yes typically in limit when u have two overcards when they are good thats six outs, but we estimate 3 for the times those outs arent good BUT here if the guy wants to get it all in on the flop u probably will actually have less than 18 outs worth of equity against his range (since he ll often have 2 pair sets or straights so ur pair outs arent good and if he boats up that cuts into our chances of winning).

I think from a logical standpoint the best way to do this problem is to see if u want to get it all in or have a profitable call of a shove (or a shove urself even with no fold equity) with just ur truly clean outs. So with 15 outs thats going to be true plus u ll have fold equity (vs the range of hands hes played this way so far) and perhaps an extra out or two worth of equity against his range that will put all the chips in.

There are other factors that come into play though just becuz shoving the flop is +EV doesnt always mean its the most +EV line (perhaps calling to get it all in when u hit would be better vs certain total donks)... usually thats not true becuz after his flop bet or flop raise wed like to exercise our fold equity and are happy to get it all in as a slight favorite with 2 cards to come and we assume most decent villains wont stack off when we make the 4 card straight or they ll recognize when the flush hits on the turn so our implied odds just calling arent thta great...

just things to think about... logically u always want to err on the side of conservatism against whatever action ur arguing for (here that u would want to get it all in) if u can say we want to get it all in vs a very tight range of sets or straights than obviously u dont mind getting it all in vs an even wider range (kind of a transitive property if a&gt;b and b&gt;c than a&gt;c)...

and remember from a logical/ scientific perspective failing to reject the null hypothesis doesnt prove it... thtas why we set up the problem so we are stacking the parameters AGAINST what we hope to deduce (or whatever our hypothesis is of what the correct action would be).