3/6: Str8 draw with multiway action.

[kendal14]

[ QUOTE ]
Now assume a hand you'll win by the river for sure 1/3rd of the time. The other 2/3rd you loose. If the pot is $90 now, and nothing else happens, you win an expected $30 per hand.

On the flop there's you and 5 people. Suppose you bet $10 and they all call. Now the pot is $90 + 6x $10 = $150. Now you expect to win 1/3rd of this as before giving you $50 instead of $30. But wait, it did cost you $10 to bet, so you have to subtract that. Your expected profit is now $40. an improvement.

Another way to see this is saying you own 1/3rd of every extra bet. With you and 5 people, for your 1 bet, 5 others will go in. So that's 6 extra bets if you bet. But your return on this extra money is 1/3 x 6bets = 2bets. It costs you 1, so your net expected gain is 1 bet. Exactly that extra $10.

So when you "own" 1/3 of a pot (have 33% equity), you need you and 2 other callers to break even. Three bets are going in, you get a return of 3*1/3=1, but you also pay 1. More than 3 people results in a gain. Less is a loss. Now suppose you have 20% equity, that's 1/5, you need 5 people in total, so you and 4 others, to break even.

[/ QUOTE ]

Thank you very much for breaking down your math. I am totally following you in your previous post now all the way up to the 8 outs is 1:2.2 and 9 is 1:1.9.

And I get the quoted post regarding your equity edge and owning a certain percentage of the pot.

So in terms of making value bet/raise/call decision, would the steps and reasoning look like this?

1. Determine the probability of hitting your draw with 2 (in this case) cards to go (1 - chance of not hitting)
2. Won't this number in and of itself (assuming that you will win 100% of the time) equal your pot equity? In other words, for every bet you place in the above example (8 outs) you own 31% of it. And as long as you expect to put in one bet for at least every other 2+ players... you are at least breaking even.
3. If you think there will be more than 2 players (besides yourself), you can justifiably raise because you have the pot equity.

Thank you very much for your patient explanation of the numbers.

kendal14